Russian May Have Solved Poincare Conjecture

nev4 writes "Reuters (via Yahoo News) reports that Grigori Perelman from St. Petersburg, Russia appears to have solved the Poincare Conjecture. The Poincare Conjecture is one of the 7 Millenium Problems (another is P vs NP, also covered on /. recently). Solving a Millenium Problem carries a reward of $1M, but apparently Perelman isn't interested..." nerdb0t provides some background in the form of this MathWorld page from 2003.

Comments

He'd post AC

[SYFer]

True math genius and the desire for money (and fame and babes, etc.) seem to be mutually exclusive traits and I think that's rather inspiring (and damned practical).

Take the case of Paul Erdos who was essentially homeless, but published over 1500 papers and is considered one of the all time greats in the field.

Perelman just casually posted his solution out to the web in much the same way that some of the most brilliant posts on /. come form "anonymous cowards" sitting in their offices at MIT. What a god.

Re:He'd post AC

[Stevyn]

It makes sense. Anyone that brilliant would see how pointless it is to worry about money. When will the rest of us learn? There's more to life than money.

Yeah, it's broadband.

Re:He'd post AC

[SYFer]

Hmmmm. Is your IP 18.72.0.3?

Re:He'd post AC

[k98sven]

Well.. I think it's kind of a general thing for all good Science too.

Einstein's original paper on Special relativity was named "On the electrodymanics of moving bodies".. It was not named "Revolutionary new discovery by me, Albert Einstein which will revolutionize the world of physics".

I guess there are several reasons for this.. one is simply manners. Boasting is unpolite. Scientific papers rarely have exciting titles, even when the results are exciting.

The second is of course, that a good scientist realizes the if a result may be revolutionary. A good scientist also always leaves room for doubt.

So the natural behaviour would of course to be careful and discreet, and not go confidently telling the world of your revolution until it has been verified. Otherwise, you'll end up with a lot of egg on your face.

Conversely, most scientists are highly sceptical of 'revolutionary' results which are announced in the press before being published. In fact, most pseudoscientists are very good at publicizing themselves and their 'revolutions', probably because they are totally convinced of their own theories, and are lacking the 'self-doubt' bit.

Re:He'd post AC

[Matt Moyer]

Someone's been watching too much Good Will Hunting... :-)

Re:He'd post AC

[Anonymous Coward]

This observation of Stevyn and the answer to his question "When will the rest of us learn?" is well explained by Maslow's heirarchy of needs. The was Maslow would havd put it is that this guy and other brillian people are 'self actualized' "A musician must make music, the artist must paint, a poet must write, if he is to be ultimately at peace with himself. What a man can be, he must be. This need we may call self-actualisation. (Motivation and Personality, 1954)". This happens after the various esteem needs, love needs, safety needs, and physiological needs are met. I think the average person gets stuck dealing with the "safety needs" (thus easy 9/11 manipulation). And the average reasonably-successful-slashdotter-guy gets stuck with the "esteem needs" stage aiming for Karma.

Only us self-actualized "Anonymous Coward" guys rise above this with insightful and informative posts such as this one without whoring for karma.

Re:He'd post AC

[Paradise Pete]

Anyone that brilliant would see how pointless it is to worry about money. When will the rest of us learn?

Oh please. What is this? The 60s? Apparently the guy is able to find enough time to work on these problems. That kind of freedom is what money buys. If he didn't have enough money to do that then it would suddenly become much more important.

"Money" is not some stack bills in your wallet. It represents some tangible effort that had value, and that value is now stored in a convenient form, ready to be exchanged for something else of value.

Re:He'd post AC

[Anonymous Coward]

And the average reasonably-successful-slashdotter-guy gets stuck with the "esteem needs" stage aiming for Karma.

But the geeks are all kept equal with hatchet, ax, and 50-point karma cap.

Re:He'd post AC

[halowolf]

What would be nice I think would be if he is not interested in the money at all, then he could still take the money anyway and donate it to a charity.

There are more than enough needy causes that could do with such a boost to their funds.

Re:He'd post AC

[Waffle Iron]

Apparently the guy is able to find enough time to work on these problems. That kind of freedom is what money buys.

It probably would only take $15K in the US to rent a small apartment in a cheap city and buy food for a year, allowing him to work on his problems. I think the point is that this guy may have been able to make a significant contribution to human knowledge and maybe centuries of notoriety with what it cost to live for a few years. Most of the rest of us would have taken the same amount of money and just dumped it into buying an upscale SUV.

Re:He'd post AC

[SYFer]

We don't need to "learn" from this, really. it's perfectly OK in our society to take pride in our achievements and to try to gain from them. Unless you're truly self-actualized (as another poster astutely pointed out), we're all subject to certain realities and desires. After all, monetary reward can enhance your ability to do more good. As Hunter S. Thompson once said, "feed the body or the head will die." There's no shame in that. I find it interesting though, that some artists and scientists seem to exist on another plane altogether.

Re:He'd post AC

[spektr]

There's more to life than money.

Yes, but he could reinvest the money into rubber bands and apples and solve thousands of Poincaré conjectures at once and thus gather even more money to buy apples for the hungry children in the world and rubber bands for their trousers. Well, if this business model isn't patented yet, of course...

Re:He'd post AC

[Stevyn]

I appologize, my comment was mistaken.

I meant to say is that we'd all be happier if we didn't have to worry about money. However, a lot of people are living paycheck to paycheck and the little things in life (broadband, it's a joke) make the effort meaningful.

Your reply was dead on though, and insightful.

Re:He'd post AC

[Stevyn]

You're completely correct; I think my comment was mistaken. Without the reward of money at the end of the tunnel, I probably wouldn't be in school now working towards a goal. There is no shame in working for money because it represents a reward for an invaluable effort.

However, I've seen many intelligent people work hard without stopping because it was the right thing to do, not because of the monetary gain. That is what I'd hope to highlight.

Re:He'd post AC

[NoMoreNicksLeft]

I'm confused, you're clueful enough to realize money (in it's ideal form) is an abstract of work/effort... but you fail to see what it is in it's more corrupt actual form.

In truth, money is a loan from a central bank to a government, that due to interest can never be repaid. Think about it a moment, if you get a $100,000 home loan, you don't walk away with a brief case of bills (and even if you did, they can't be exchanged for gold), the bank assigns some numbers to your account briefly, which gets assigned to someone else's account who then lets you have a house.

All money is, is slavery to a bank, which gives permission for someone to transfer real property to you.

Re:He'd post AC

[tlord]

Actually, the title:

"On the electrodynamics of moving bodies"

is exceedingly boastful.

In computer science, an analogy might be to publish a paper titled:

"On datastructures, in general"

What an oddly broad topic to choose, unless
you are claiming to be saying something
rather profound.

Re:He'd post AC

[G-funk]

Erm, perhaps you missed the joke? GP said "there's more to life than money... it's broadband"

Re:He'd post AC

[St. Arbirix]

My girlfriend was held by Paul Erdos as a baby when he stayed over at her father's house. Does she get an Erdos number?

Neat fact: he made my girlfriend's mother wash his underwear and fold them a specific way. The guy was interesting.

Re:He'd post AC

[mbw314]

I guess there are several reasons for this.. one is simply manners. Boasting is unpolite. Scientific papers rarely have exciting titles, even when the results are exciting. The second is of course, that a good scientist realizes the if a result may be revolutionary. A good scientist also always leaves room for doubt.

Contrast this lack of fanfare with another recent publication, Stephen Wolfram's A New Kind of Science. This 'new' science seems to have been met with mixed reviews at best, and not the paradigm shift that the author seems to have been hoping for. Of course only time will tell who is right... But in the event that Perelman's is incorrect, his humility and lack of hubris regarding his solution definitely earns him my respect, and undoubtedly that of many others in the field.

Re:He'd post AC

[holysin]

While I agree, he recognizes that money is more or less pointless, I am a little surprised he didn't accept the prize and swiftly turn it over to his favorite charity. Or favorite impoverished country.

Shrugs, either way, VERY cool.

Re:He'd post AC

[Chasuk]

some of the most brilliant posts on /. come form "anonymous cowards" sitting in their offices at MIT.

Really? I've read a few interesting posts from AC's, but not a single one that I would consider brilliant. We may be using different units of measure, but I'd certainly be curious to read a few of these brilliant AC posts.

Provide links, please.

Re:He'd post AC

[skraps]

Most of the rest of us would have taken the same amount of money and just dumped it into buying an upscale SUV.

Remarkably, in my experience, some people prefer that - or at least claim to.

I think you end up throwing away a good deal of your personal happiness in order to become specialized enough to create anything significant. A lot of people seem to more-or-less weigh the possibility of being significant against the 6+ billion people on earth, and decide against being a martyr.

Re:He'd post AC

[Lord Kano]

It makes sense. Anyone that brilliant would see how pointless it is to worry about money.

Perhaps all of these years of fertilizing your organic garden with human feces has lead to some sort of spongiform encephalitus.

Money IS important. It may not be the most important thing in the world, but we all need to eat and have a safe place to sleep at night. Those things take money.

LK

Re:He'd post AC

[KjetilK]

That's an interesting comment. I find no motivation in money at all, and I did go to University for close to 9 years...

However, the last couple of years since I finished, I have lived very close to the official poverty limit of my city, and I know that is bad.... So, I need to do something to get a higher influx of cash. I find no motivation in doing it, though, to the contrary, it feels like I have to abandon the pursuit of interesting things to get it.

I just need to be fed, kept clothed when it is cold (and when it is warm too, I hear society demands it for some strange reason), some bandwidth and electricity, given a bit of sports equipment, and an occasional trip to interesting places on earth. Then, I need interesting and hard problems to work on, and I'll be a very happy creature.

I could probably do this at below average income, but right now, it seems very interesting stuff very seldomly pays even that...

Re:He'd post AC

[Tony-A]

One thing I've learned is that if I can stand to live with myself, if I like myself, nothing else really makes that much difference.
"A musician must make music." I'd strike the "If ...". It's essential, but probably has little to do with being at peace with oneself. In fact, the drive toward getting it right is very much not being at peace with oneself.

Regarding the "homeless" Paul Erdos, who wouldn't go to more than a little trouble to have him as a house guest? Seems like he'd have the advantages of the very rich with many homes and none of the disadvantages.

To add a smallish fly to your ointment, somebody had to use a couple of mod points to bring your post up to the same level of visibility as this one.

Re:He'd post AC

[Almost-Retired]

All money is, is slavery to a bank, which gives permission for someone to transfer real property to you.

Humm, but what if the loan has been paid off, for long enough you've forgotten that you once made house payments?

You see, I wasn't about to be scratching to make a mortgage payment when my income was reduced to the social security (gawd, what an oxymoron that is for some folks) levels in my old age, so the house has been paid off for 8 years now, and I've been almost-retired for 2.5 years.

That little detail makes it so that I still have some "discretionary" income, keep 2 vehicles running and can play with a little woodworking (I found some cherry a few days ago for less than $1 a bd ft) and these damned computers, and still afford a couple of beers a day. And oh yes, take my boat out on the lake and fish if I get otherwise totally bored. It aint new, it aint fancy, but it keeps my butt dry unless its raining, and gets me around the lake at about 5mph with its 10hp motor.

Think about it... Its called managing your money for you, not some faceless loan shark or bank (is there a difference at the end of the day?).

But, it was easy to pay it off in a short time when both of us were working full time, so we didn't really miss a nearly $700 a month payment while we were paying it of in 7 years instead of 30, and we saved about 60,000 USD in interest doing it. Now all we owe are utilities and taxes.
Its a nice feeling, and those we can handle, or at least till oil hits $100 a barrel.

So no, you don't have to owe your soul to the money lenders. Way the hell and gone too many of you do though.

To those who will never get ahead because they owe their soul to the company store, I have sympathy, but the message is the same. Look at how you are handling your money now and see if there is any room to cut waste. Doing so will pay hundreds of thousands in future dividends once you get into the habit of making every dollar that comes out of your pocket buy something worthwhile. The "just gotta have it" attitude doesn't count at the end of the day if theres nothing left to invest in tomorrow at the end of the day.

Cheers, Gene

Re:He'd post AC

[andreyw]

That would be an Erdos number of 1. And btw, holy shit thats awesome. You have an Erdos number of 2.

Re:He'd post AC

[idesofmarch]

Maybe he believes that by not claiming the award, he insures that the $1 million stays where it will do the most good.

Re:He'd post AC

[DAldredge]

About the time that the electric company starts taking bullshit instead of cash.

Re:He'd post AC

[toiletmonster]

i agree with that.

Re:He'd post AC

[Anonymous Coward]

Not really, since the field of electrodynamics was only in its infancy at that time, a few years after the publication of maxwell's theorems. And it was almost exclusively applied to fixed bodies rather than moving bodies...

So it would be like publishing a paper called "on datastructures" if you were the person that invented datastructures....

Re:He'd post AC

[mollymoo]

Actually, the title: "On the electrodynamics of moving bodies" is exceedingly boastful.
[...]
What an oddly broad topic to choose, unless you are claiming to be saying something rather profound.

Exceedinly boastful? The title is an accurate description of the content - it was a new model for the electrodynamics of moving bodies. There is no indication of merit or pride in the title, it's you who ascribes those attributes. You then attempt to denigrate Einstein for describing what he has done, apparently purely on the basis that his ideas were novel and better than those which went before.

Perhaps if you ever achieve something noteworthy you'll realise that stating what you have done in an appropriate forum is not boasting. Saying something profound is not boasting. If you think it is the problem lies with your self-esteem.

You may have a tiny penis, but that doesn't mean those of us with a monster dick should hide the fact.

Re:He'd post AC

[Phragmen-Lindelof]

If I remember correctly, the American Mathematical Society has about 30,000 members; I would guess that 5%-10% of them "become specialized enough to create anything significant." 1500 "martyrs" is a moderately large number; how many martyrs (not crazy suicide bombers) do you hear about in a year?

I agree that Ricci flows are very specialized; I believe Hamilton and Perelman are the experts (with possibly Yau, Tian, Donaldson, or a few others). Many mathematicians get a lot of enjoyment from "solving a difficult (mathematical) puzzles" (i.e. mathematical research); getting solutions published is also fun.
Hormel has come to our campus to recruit math majors for 20-30 years. One faculty member asked a Hormel recruiter what mathematics the recruits would be doing; he was told "None; math majors just make really good, hardworking employees". A few specific examples of companies who have hired BS, MS or PhD graduates in Math: Ernst & Young, the Bank of Toronto, Hormel, Boeing. Money is not the motivating factor for mathematicians who do "real" research; they could get much higher paying jobs in "industry".

Re:He'd post AC

[tlord]

> So it would be like publishing a paper called
>"on datastructures" if you were the person that
> invented datastructures....

Your analogy sucks except for that, yes,
modern physics was a very young field back
then, just as CS is a very young field now.

Re:He'd post AC

[Barlo_Mung_42]

I agree but I don't think it is as simple as a choice. I think most people who achieve greatness in anything are driven to it. They often (always?) suffer for it but I don't think they feel they had a choice. The same is true for the people who achieve mediocrity only in reverse. They don't feel driven but still don't see any other choice, or if they do it is only later in reflection.

Re:He'd post AC

[GaussianInteger]

Er.. What modern physics? Classical mechanics? Been around for a long long time (hundred of years... Newton anyone?). Don't tell me CS has been around that long. If you mean quantum theory, which is what most people mean by modern physics, it hasn't even been completely developed yet. In fact, development had barely started.

Re:He'd post AC

[tlord]

hehe. By "modern physics" I meant QM, relativity, plus all subsequent theories that hope to subsume/replace/unify those. -t

Re:He'd post AC

[NonSequor]

If we weren't talking about Erdos, I'd agree with you. The thing about him, is that he wasn't just a great mathematician, he was a great collaborator. In addition to that he was generally good natured and his many quirks were (mostly) endearing. He brought out the best in the people he worked with. Erdos didn't need money because he was held in such high esteem that he could go anywhere and people would be willing to pay for his meals and give him a place to sleep just for the opportunity to work with him.

Re:He'd post AC

[skraps]

I wonder about that choice most days. It may sound pretentious to assume that I am even capable of achieving something significant, but I do recognize the choice.

Be a martyr, achieve something great, maybe even advance the science (whichever one). That is a gamble. You may or may not achieve anything great, and in that case it isn't called "martyr", it's called "waste". Achieving mediocrity is easy, and presumably enjoyable. Most importantly, it is immediate. There is a little known third option: not being able to choose a path. The worst parts of both options, and the best parts of neither. :-)

Re:He'd post AC

[CaptainCheese]

The thing about pure mathmatics is, it's a pastime that essentially costs nothing. You don't need any special equipment or a formal higher education.

This means you can do it on welfare from your trailer park home, or from a cardboard box under a bridge if that's your thing. Significant mathmatical breakthroughs have, in the past, been made by incredibly poor persons with little schooling to speak of. Admittedly this is rare, but not unheard of.

You really just need access to a library of some sort and that rarest of commodities, an inquiring mind of your very own...

Re:He'd post AC

[DSP_Geek]

Real Erdos numbers apply to mathematical collaborators producing papers dealing with what some might say are imaginary worlds, so Real Life contact with Erdos must therefore be quantified with an imaginary number. Obvious, really. She has an Erdos number of i.

Re:He'd post AC

[Anonymous Coward]

I'm not certain, but I think Bruce Kleiner is doing a significant portion of the checking of the proof.
(This is what I heard in the U of U math lounge.)

Re:He'd post AC

[chl]

I have always understood "On [some general subject]" to mean "here are some thoughts about this subject, I do not claim to provide an exhaustive treatment, maybe someone finds this interesting." So this would be the opposite of boastful.

On the other hand, maybe he was using false humility and was really doubly boastful.

chl

Re:He'd post AC

[Alesha]

This post is completely trollish. The second comment in the thread explains the real meaning of the title extremely well. (Beeing really insightfull). The analogy for the Einsteins' title in the modern computer science will be f.e.
"On the data distribution in the p2p networks", or
"Stability of the Internet networks".
And these are the _real_ titles of the modern CS papers.

Re:He'd post AC

[JohnPM]

Rubbish. The use of the word "on" removes any claim to comprehensive explanation. The paper could contain either a minor observation or a complete theory.

Re:He'd post AC

[RWerp]

I'm pretty sure that when it turns out he's correct, his friends and relatives will say to him: "Look Grigori, don't be a fool, take the money". If he's interested in research, it will be hard for him to ignore the comfort and security the money would give him. Or the amount of good he could do with that money, to other people. Probably the guy doesn't want to feel disappointed if his solution is wrong, that's why he doesn't care now.

It is all nice and dandy, being a scientist who doesn't give a dent about money, but when you have a wife and kids, things turn out to be more complicated. Eordos was a lonely man, this was the price he had to pay for his style of living. Other math geniuses (von Neumann, for example) had wives who were far more practical than them, and probably quite shrewd when it came to money matters.

Re:He'd post AC

[RWerp]

A lot of people seem to more-or-less weigh the possibility of being significant against the 6+ billion people on earth, and decide against being a martyr.

Most people have no chance of becoming significant in the first place.

Re:He'd post AC

[Dolly_Llama]

See also: A New Kind of Science"

Re:He'd post AC

[kahei]

You're completely correct; I think my comment was mistaken.

Woah, that's weird! I thought I was reading Slashdot but it must actually be some other site.

Re:He'd post AC

[RWerp]

I think most people who achieve greatness in anything are driven to it.

"[...] some are born great, some achieve greatness, and some have greatness thrust upon 'em."

Re:He'd post AC

[some guy I know]

"A musician must make music, the artist must paint, a poet must write, if he is to be ultimately at peace with himself."

This explains why I am ultimately at peace with myself when I'm lying around doing nothing: "A lazy slob must lounge.".

Re:He'd post AC

[fucksl4shd0t]

About the time that the electric company starts taking bullshit instead of cash.

You mean the?{'}[];'{

NO CARRIER

Re:He'd post AC

[AGMW]

True math genius
and from one of the links ...
A reclusive Russian may have solved one of the world's toughest mathematics problems and stands to win $1 million (560 million pounds)

Shurly shome mishtake?

explain the behaviour of multi-dimensional shapes in space - CHECK
multiply 1 by a 0.56 - Vladivostok, we have a problem

Re:He'd post AC

[TuringTest]

No; that was the old way that money used to work, before monarchy started to forge coins. When money meets authority, the theory changes: money is a procedure, distributed among people and accounting software (different kinds of "agents"). In our modern society money isn't a physical object that can be traded, is a promise of the money "owner" to act in a planned, foreseeable way. Money keeps its value because there is an authority warranting that the correct procedures will be kept (before those were the governments, nowadays the banks have more power).

In this "generalised" theory of money, there is nothing that implies that the planned acts should be that of exchange. For example, slashdot moderation points are a kind of money certified and managed by the /. site owners; but these points are not tradeable and are not useable outside of this web.

Re:He'd post AC

[16K Ram Pack]

Good thinking.

I think about the luxuries in my life, and I keep them to the life enhancing stuff - better coffee, better beef to cook with, a few more movies, more comfortable shirts.

Really, ask yourself if you need that 20GB iPod or that PC upgrade. If it helps you get the boring stuff done so that you can watch a few more movies, that makes sense. If it doesn't it's just something to own, not to improve your life with.

Cars are probably the best example of something that's about ownership over benefit. I'm not talking about not owning a car, but not owning a brand new car. You'll be stuck behind that car in front in a traffic jam whether you have a brand new 5-series BMW or a 10 year old Honda Civic. OK, the 5-series will be more comfortable, but how much are you paying for that comfort? And if you didn't have to pay for that comfort, how many traffic jams would you not have to sit in?

Re:He'd post AC

[littlem]

Perelman just casually posted his solution out to the web in much the same way that some of the most brilliant posts on /. come form "anonymous cowards" sitting in their offices at MIT. What a god.

Yes, that's the way maths works - people share their ideas online rather than wait years for the refereeing process. (Though the briefest browse through the "general" section of the arxiv will convince anyone that refereed journals are still necessary.)

Wasn't this sort of scientific openness one of the inspirations and models for OpenSource software?

Re:He'd post AC

[strider44]

Don't worry, I'll take the money for him (if it's for the good of maths!)

Re:He'd post AC

[Almost-Retired]

Good thinking. We have 2 vehicles, a 97 Dodge Caravan with 106K miles on it, wrote a $12k check for it 4 years ago and its running quite well yet, and of course the obligatory 4wd since this IS West Virginia, but its an 88 Nissan 3L V6 with the automatic, with a bit over 200k miles on it. Hasn't used a drop of oil yet, runs great.

Rated at a half ton, I've had a ton of rock or sackrete in it several times. But we have vehicle inspection laws here, and the rust is beginning to be a problem, so I may not be able to get a sticker on it in another 1-2 years without major bodywork. I paid 3k for it 3 years ago, so replacing it is a "shrug" and write the check. I asked the missus a couple of days ago if she would mind driving a pickup and she said no, so I guess when it comes time to unload one of them, the van could be tradein materiel.

Cheers, Gene

Re:He'd post AC

[NoMoreNicksLeft]

Only so much money was ever issued. Let's make that $1 million, to keep things simple. The Fed is a private corporation, yet issues this money to the entire United States, as a loan. They'll want interest, so now we all owe $1.05 million. Even if we all take up a collection, and give it all back... we still owe the $0.05 million... lather, rinse, repeat.

So, you may be able to pay off your individual loan to the bank... but doing so leaves even less money for others to pay off theirs.

Re:He'd post AC

[Paradise Pete]

Erdos didn't need money because he was held in such high esteem that he could go anywhere and people would be willing to pay for his meals and give him a place to sleep

So in a sense, that high esteem that he'd earned was his currency, albeit a less fungible one. But it still was value previously earned, stored in some other form.

Re:He'd post AC

[DrXym]

Einstein said "If I would be a young man again and had to decide how to make my living, I would not try to become a scientist or scholar or teacher. I would rather choose to be a plumber or a peddler in the hope to find that modest degree of independence still available under present circumstances."

He was then granted an honorary membership of the Plumbers and Steamfitters Union.

Re:He'd post AC

[CrimsonAvenger]

But, it was easy to pay it off in a short time when both of us were working full time, so we didn't really miss a nearly $700 a month payment while we were paying it of in 7 years instead of 30, and we saved about 60,000 USD in interest doing it. Now all we owe are utilities and taxes. Its a nice feeling, and those we can handle, or at least till oil hits $100 a barrel.>/I>

I agree. House has been paid off for two years now. Cars for longer than that. So nice not to have to write those checks to the bank anymore.

Re:He'd post AC

[orasio]

I don't think money has the same value in the US that it has in Russia.
In the US, money is first in everyones life, because you need to be a money-making member of the society in order to eat. As it is the first priority, of course for many people it becomes the most important, and they live happy with it.
Russia still has some remainings of socialist ideology, where if you can do something better than make some money to support yourself, you are supposed to do it, and the society is supposed to take care of you. Or in practice, you are just poor, but people admire you for your achievments instead of despising you just for your low annual income.
Of course, it had many practical problems, but it has the potential to a kind of motivation unthinkable in the every-man-on-his-own scheme of things. To each his own, some people like money, some people like something higher.
In the most capitalist countries, you can't do much without money, but that is just a characteristic of that kind of system, not an inherent problem of human society. Every system has pros and cons.

Re:He'd post AC

[2TecTom]

Sure, that sounds real great, doesn't it? The problem is that the statement "monetary reward can enhance" becomes a justification commonly used to fuel massive materialism. So, go ahead, ask for another raise so you can spend even more. Oh, and keep telling yourself that it's real joy you're feeling, and that current global pay levels are fair and justified. It really allows you to feel much better about the situation, doesn't it?

In truth, far too many first-worlders rely on consumerism as their main sense of gratification and primary source of self-worth. This is based on the mistaken belief that buying something is as emotionally gratifying and rewarding as actually working to produce something directly. Think about it honestly, since so many people have so much, why aren't they really any happier for it? For instance, just look at divorce rates. Hmmm, funny, you'd think most very rich people would be happily married, wouldn't you?

Money doesn't provide happiness, it impedes it. Yet people will do almost anything in order to ignore all the clear evidence that demonstrates this.

One of the most difficult things to accept as you grow is that the path to self gratification is diametrically opposed to the path towards self actualization.

Re:He'd post AC

[AbbyNormal]

Or supporting our families and paying taxes? Just my $0.02

Re:He'd post AC

[Wescotte]

Amen brother! Let's all set an example by giving your money away to oh say me. I've yet to learn that money isn't everything. I've never had any so maybe I need to have some in order to learn this lesson?

Re:He'd post AC

[Paradise Pete]

To each his own, some people like money, some people like something higher.

Your own words betray you. :-)
You shrug and say to each his own, and then in the same breath belittle those who you see as different.

Re:He'd post AC

[Travis Fisher]

But in the event that Perelman's is incorrect, his humility and lack of hubris regarding his solution definitely earns him my respect, and undoubtedly that of many others in the field.

I think its more likely that the sheer brilliance of his work earns Perelman the respect of others in the field. I've been to a couple of talks by people who had spent months wading through Perelman's papers. Their opinion was that regardless of whether or not some error was found preventing the work from being a full proof of the Poincare conjecture, the research was undoubtedly brilliant and would greatly advance the field.

There are plenty of arrogant bastards in mathematics who still earn lots of respect for their work. Perelman goes a step farther and, with his humility, earns some admiration as a person as well. At least from those of us who are watching the process at some distance...

Re:He'd post AC

[brufleth]

Not a direct reply but the parent post mentioned MIT. In Boston the homeless people have to make more than $15K a year or they end up pidgeon food.

Re:He'd post AC

[mollymoo]

> There is no indication of merit or pride
> in the title,

Really? Perhaps I have misunderstood something....

Why didn't he title it as something like "A minor correction/reinterprtation of the Lorentz transformations"?, for example? Or "The Ether, Considered Harmful"?

Perhaps "A reinterprtation of the Lorentz transformations" would be a suitable title, but I really don't see why you think he should call it "minor". That judgment should be left to the scientific community.

I think neither pride nor modesty have a place in scientific papers. They should simply be a statment of your research. The title "On the electrodynamics of moving bodies" was an accurate, unemotional description of the paper. It was a paper on the electrodynamics of moving bodies, after all.

Perhaps you meant "boast" as a transitive verb merely describing a feature, as in "this switch boasts 5 10/100 ethernet ports", but I doubt that as you wrote "exessivley boastful". Boasting implies excessive pride, self-admination and glorification. I simply don't see that in the title.

p.s. I apologise for the, ah, slightly rude tone of my previous reply. I stand by the points I made though. I blame the wine...

Re:He'd post AC

[johnnyb]

Even worse, let's say that everyone started to be financially responsible and start paying back their loans, and only buying things they had money for. Sounds good, right?

Well, as loans are paid back, the amount of money in the system will decrease dramatically. This will cause a HUGE deflation in the economy, which would cause everyone who hasn't paid their debts to suddenly be unable to pay -- because they wouldn't be able to get enough money.

The problem with a debt-based economy is that if everyone pays off their debts, then the economy comes to a dead halt.

Re:He'd post AC

[johnnyb]

I think what he was saying was that the ONLY way money comes into circulation is through loans. Therefore, although some can pay back there loans, it is physically impossible for the entire country to ever pay back their loans, because not only are we responsible to pay back the loans, but we also have to pay back interest! But the banks only created enough money for the _principle_ of the loan, not for the interest. So, while you and me can pay back our individual loans, it is physically impossible for the whole country to pay off its debt, because the money supply would be gone, and there would be nothing left to pay with.

Let's say that there is a small economy. I am a central bank. Right now, there is no money. Therefore, you take a loan out for $10, and I charge $1 interest. Frank takes out a loan for $10, and I charge him $1 interest. The whole economy has $20 in it, but they owe $22. There's no way this can be paid off. Now, one of you could handle their money better than the other, and get a $1 advantage to pay off their loan, but that would leave only $9 in the economy to pay off a remaining $11 loan. One of you would be fine, but there is no way in this system for everyone to pay back their debts. So, eventually, the banks own nearly everything.

This is why the founders of our country hated central banks, and was one of the primary reasons for the revolutionary war.

Re:He'd post AC

[NoMoreNicksLeft]

The trouble I have with this, is that I still can't believe it. It's all the worst conspiracy-theory bullshit that I've laughed at over the years, with an extra side of "simply unbelievable".

And yet, the more I read, the more I try to research all this, the less I can find to dispute it.

Re:He'd post AC

[johnnyb]

If it makes you feel better, it's mitigated to a large extent due to inflation. Therefore, it's easier to pay back yesterday's bills today, because money is worth less than it was. However, inflation can only come about from a nation that is more and more riddled with debt...

Re:He'd post AC

[William Tanksley]

The Fed doesn't create value; they create money. Every dollar they print (or otherwise produce) is paid for by lowering the price of all the other dollars, and that process happens automatically, whether they want it to or not.

So your accounting is wrong.

Now, the Fed profits by billing the gov't; the gov't profits by being the first to spend the new money, and since the value of all money doesn't go down until after the new money is on the market, the gov't not only gets to spend nearly free money, it even gets to spend free money that's worth more now than it will be after it's spent.

-Billy

Re:He'd post AC

[William Tanksley]

This behavior (paying off all loans) wouldn't be "financial responsibility"; rather, it would be a total change in people's evaluation of the future value of money. You get a loan if the money NOW is worth more to you than the money THEN.

Quite simply, it couldn't happen; the market interest rate would go to 0%, and it's ridiculous to suppose that anyone's going to pass up loans with anything close to that rate.

However, ignoring the math, there's another detail you've missed. The problem with a lot of people paying back loans is that most loans now are made through the fractional reserve system, which means the money being loaned didn't exist before the loan was made. Thus, when the loan money was spent, inflation happened; then, when the debtor saved up money to pay the loan back, deflation happened. The actual payback causes a minor hiccup as the money is "destroyed" (since it most likely had been in the debtor's saving account earning interest for the bank), but the major adjustments are already made.

There is a problem here, but it isn't with paying back loans or with debt-based economies. It's with fiat money.

-Billy

Re:He'd post AC

[LPetrazickis]

s/the Bank of Toronto/Toronto Dominion Bank/;

Most people just call it TD. I've never heard it called Bank of Toronto in my life.^-^

Re:He'd post AC

[tlord]

Your reading of my use of the word "boast" is a good one. I think that it describes *authentic* human boasting (in the colloquial sense) as well. There's the human emotions associated with boasting, on the one hand, and there's the objective measurable sense on the other. I see those as varying shades on the same underlying color. Pride and modesty have *every* place in scientific papers. A good paper *reaks* of the pride of an author who had the good fortune to get to write it. A good author in possession of a good idea is modest enough to know the importance of putting aside his fears of speaking in public and his opportunities to maximize personal gain. A good author does those things when, with as much pride as he can afford, he presents the paper in the academic forum.

Re:He'd post AC

[Phragmen-Lindelof]

Thanks for the information. A friend (& coauthor) of mine at the University of Waterloo had a PhD student who went to work for the "Bank of Toronto". Although I like visiting Toronto, I do not know the local (or even the actual) names of the banks. I will refer to it as "TD" in the future. (Look, TD! Was it the 49ers or the Chiefs? No, the bank in Toronto. Oh, so they scored?)

Re:He'd post AC

[Javagator]

I work for the good of all mankind, but my wife makes me pick up the checks.

Re:He'd post AC

[orasio]

I thought everybody believed that direct self-realization (being a painter, a writer, an mathematic theorist) was a higher goal than self-realization through money (working and earning money so you can paint/write in your leisure time, or maybe working as an engineer where you can use math), but the latter was more feasible, because of practical issues, and thus is the most popular.
It could be paraphrased like this: some people are more practical, some are more idealistic.

Re:He'd post AC

[johnnyb]

Actually you are not quite right.

First of all, wealth has little to do with labor, but a lot to do with value. But that distinction isn't very important. You are correct in that the value of money is basically the value of what is produced divided by the amount of money in circulation. However, that isn't what we're talking about here. When you deal with banks, you are not dealing with "money as a wealth equivalent" but rather, specifically, with money. Because banks have a monopoly on the creation of money, no matter how much value is produced within an economy, the fact is you cannot pay off your debts with the amount of money in circulation, no matter how much or how little that money is worth.

Let's go back to the banking example. Let's say I borrow $10 from the bank and Frank borrows $10, each at $1 interest. Let's say I harvest 1,100 oranges and Frank harvests 900 oranges. That means that the value of the $20 in the economy is 2,000 oranges. Had I produced 600 oranges and Frank produced 400 oranges, then the value of the $20 would be only worth half of what it was in the previous scenario. IN BOTH CASES, WE CANNOT REPAY THE BANKS IN FULL. Even if the next year we produce more or less, and cause inflation or deflation, or if more people join the economy and get more loans to increase the money supply, the result is the same, there is not enough money in circulation to repay all of the loans.

If you can find a scenario that allows all of the individuals to repay their loans, please post it.

Re:He'd post AC

[cfuse]

Anyone that brilliant would see how pointless it is to worry about money.

Yes but babes, what about the babes?

Re:He'd post AC

[bronsinbound]

You sure are going to be singing a different tune when you put on some age. And when you see all those you used your labor and ideas retire in luxury while you and your family worry about the next meal and apt/house payment, you are going to eat those words just like did. Bon Appetit!

Re:He'd post AC

[NoMoreNicksLeft]

I'm more concerned with book loans, I think. Say that there is no money in the system yet, but the first think i need is a house, which will cost $80,000. I go to the bank, they loan me $80,000. But I don't withdraw that as cash, it's simply wired to the contractoor's/realtor's account. He doesn't withdraw it either, just sits on it.

You can talk all you want about money and creditworthiness, and all that bullshit... but it boils down to that bank giving permission to someone else, to give me a house. Tell me how it's anything different from that, please. On the scale that it happens in real-life, what it means is that the banks control our day to day lives (even more so now that they've addicted the populace to credit cards).

Re:He'd post AC

[fingerfucker]

That's bullshit.

Money in your example was a means of representing something worth a house. You made up that it is the 'permission' for one person to give the other a house. If the reputation of money as a representation of value goes away because of banks, people will tell them good by and switch to some other way of representing value that WILL be respected.

Don't make stuff up and learn about some fundamentals of economics first.

Re:He'd post AC

[NoMoreNicksLeft]

If it were money, and not entry in a book, that might be the case. Not only is it not cash, it's money that has been loaned to someone else already. Calling it money is a little dishonest, in that this bank gets to create it out of thin air. Nothing tangible is ever exchanged, just numbers in a ledger...information in effect. Sounds like permission to me

Re:He'd post AC

[fingerfucker]

And what do you think money is? Money is only an entry in a book. Even the fact that printed money exists is just something that is happening out of necessity - to faciliate smaller transactions where it would be cost-prohibitive to bring a bank into the picture.

Banks are "financial intermediaries". This is not a fancy word that "experts" made up, it is actually the most accurate description of what a bank is.

Money is a comodity. How valuable money is is assigned by people out of free will.

It is true that all money that ever shows up in bank ledgers comes from a loan, and it comes at an interest rate. But that interest rate is nothing more than the cost of using money as an intermediary.

In your scenario, no money is present first. Then XYZ borrows $80,000 from a bank (let's say at 1%) and when he buys ABC's house, XYZ's money is crossed out in the bank record and ABC's balance is increased. The house changes hands and now, the situation is such that XYZ is paid interest by the bank for keeping the money there - let's say 0.5% (this is the incentive for ABC to keep the money "on the market" and contribute to the supply of money). On the other hand, XYZ who owns a house is still charged 1%, because technically, he has a loan.

Now, understand that XYZ never had goods or services worth one entire house. He "borrowed". He did not get the house for free! He will either have to keep on paying the interest (and never pay back the loan), or he will have to come up with $80,000 plus a few year's interest. If he keeps on paying just the interest and never the principal, chances are, he will end up paying a LOT more over the long term than paying the principal plus (some) interest sooner.

In either case, he owes "money" to the bank and he has to come up with the money somehow -- he can make an arrangement with the bank that he will mowe the lawn in front of their branch every week and for every lawn mowing, they will forgive $30 of his loan balance. Or, he could go out to the public and sell his lawn-mowing services to people who don't want to / can't mow their lawn in exchange for money. Every time he mows the lawn, the money he receives will be the representation of the value he has created.

See, XYZ didn't get the house for free. He had to create value to make up for it because neither ABC nor the bank is a charity. The only use of the money was to represent value so that XYZ doesn't have to come up with something worth $80,000 all at once, but he can do it in smaller "chunks" of value.

The interest cost of money to XYZ is essentially the cost of convenience of using money (and the bank) as a transactional intermediary. Do you think ABC would sell XYZ a house for 2,667 mowings of the lawn? (I obviously came up with 2,667 by dividing $80,000/$30). I don't think ABC would want mowings of the lawn in return for the house, because in reality, ABC's needs are not for mowing the lawn, but maybe he wants bread. It would be very difficult for ABC to go about convincing other people that they should be selling him bread in exchange for lawn mowings by XYZ. In addition to all that inconvenience, there is risk that XYZ will be unable to perform the mowings (since mowing is a service delivered by human labor) in the long run - ABC certainly doesn't like that.... XYZ will not be able to buy a hosue from ABC if he doesn't use some better form of representation - maybe instead of lawn mowings, he could offer something tangible, probably 2,000 kilos of processed birch wood. Now ABC doesn't have the risk of not getting compensation for the house, but has a different risk, the risk of the fact that the birch wood that he now has to store somewhere will catch a mould. So ABC would have cost associated with storing all the wood. And we still haven't addressed the question of ABC's ability to get other goods (like bread - which he wanted in the first place) for pieces of wood.

You see, the banks are used by people out of convenience and out of need to have a financia

Re:He'd post AC

[NoMoreNicksLeft]

Well, you didn't say much that I didn't already say, except to try and cloud things with details.

Maybe we do need someone to give permission for one person to get a house. I just feel that there are better ways to appoint people to do that, other than allowing the welathiest families from 500 years ago to set up an entire sham of a system.

Barter doesn't work. We can agree on that. But allowing the bank to earn interest on the same money 9 times over, allowing a private corporation to issue our money, just seems really dumb. But hey, you like it. Maybe when they finally own everything, they'll make your grandchildren pampered little lapdogs, I dunno.

Re:He'd post AC

[fingerfucker]

You don't seem to know what you want. You didn't menition anything that shows that you have clear-cut criteria for evaluating this matter and you didn't propose anything, just insist on the same thing over - "corporations are bad", "freedom for private enterprises are bad" and other things (pardon me if I skewed any of your claims in the above-quotes, but that's what it sounds like when you say it).

"I just feel that there are better ways" - it's nice to have a feeling like that, but WHAT are those better ways?
"[...] just seems really dumb" - if something only "seems" to you to be one way or another, and you don't back that up with any reason, then this discussion won't work.

"But hey, you like it" - It's not a matter of liking it or not. If I see that using a financial intermediary and money issued by them is a cheaper way for me to achieve my goals of exchanging goods and services over barter, I'll do it. That's what it's all about.

Good luck to you.

Re:Duplicate?

[Disevidence]

RTFA. He published another paper on it recently.

The "free" internet bubble never burst

[poofyhairguy82]

But there's a snag. He has simply posted his results on the Internet and left his peers to work out for themselves whether he is right -- something they are still struggling to do.

"There is good reason to believe that Perelman's approach is correct. But the trouble is, he won't talk to anybody about it and has shown no interest in the money," said Keith Devlin, Professor of Mathematics at Stanford University in California.

I'm always amazed how much free stuff is on the internet. Free million dollar solutions! Good luck with em!

Re:The "free" internet bubble never burst

[MyHair]

I'm always amazed how much free stuff is on the internet. Free million dollar solutions!

Just think of how many free flatscreens that would buy...

Re:The "free" internet bubble never burst

[cfuse]

"There is good reason to believe that Perelman's approach is correct. But the trouble is, he won't talk to anybody about it and has shown no interest in the money," said Keith Devlin, Professor of Mathematics at Stanford University in California.

Does this mean if I can show a proof I can get a million dollars?

Don't get me wrong, after having to look at 5 web pages (none of which was the article of course) to even get a grasp on what the Poincaré conjecture actually was, I would think that if I could prove it I would have certainly earnt those dollars.

On the subject of him being unmotivated by the money, has anyone bothered to offer him a new problem in exchange for the proof? He obviously likes solving them, and there must be some new ones around.

Math?

[hunterx11]

1,000,000 USD is about equal to 560,000 GBP, not 5.6 million GBP.

Re:Math?

[fireman sam]

the GBP is a new currency.

GBP (George Bush Pound) - The dollar unit associated with the search for WMDs.

Re:Math?

[rand()0]

Now why would he do that? He gets 10 times the money otherwise.

Re:Math?

[AuMatar]

In that case it should be 5.6*i, since we all know the WMDs were imaginary.

Re:Math?

[pfriedma]

"world's toughest mathematics problems and stands to win $1 million (560 million pounds) -- but he doesn't appear to care."

Re:Math?

[Anonymous Coward]

1,000,000 USD is about equal to 560,000 GBP, not 5.6 million GBP

Yes, it is, for small values of million.

Re:Math?

[cs02rm0]

In uk they call 100 000 a million.

Oh no they don't. Colour, pavement, football, 1 000 000 = a million tyvm.

Re:Math?

[Bitsy Boffin]

You are confused.

100 000 is one hundred thousand wherever you are
1 000 000 is one million wherever you are
1 000 000 000 is one billion in America and primarily one thousand million elsewhere.

Re:Math?

[I confirm I'm not a]

1 000 000 000 is one billion in America and primarily one thousand million elsewhere.

Currently this meaning [10^9 == 1 billion] is the preferred meaning in financial world (it looks more); therefore most English-speaking countries, such as the United Kingdom, South Africa, and Australia, now use this value.

I'm with the USA on this one. Now if we can just get you guys to put a "u" in color, and we'll be sorted ;)

Re:Math?

[fucksl4shd0t]

I think you misspelled sourted.

Re:Math?

[beef3k]

Actually the article says "560 million pounds" (!). Guess someone was out drinking last night.

Re:Math?

[strider44]

I know on all university papers a billion means 10^9. They list it's definition at the start of many courses.

But for everything else, we speak English, you speak American. Everything else, incidentely, except for colour in my course of software engineering, which is always spelt color.

Look at his method for solving this!!!

[Anonymous Coward]

He's trying to integrate homeomorphic convergence using a Baxter-Bates supermodality, which Krause clearly explained is impossible for T(s) in a non-linear progression. Fantastic thought process on this complex differential geometric problem.

Just kidding! I have no clue what the hell this is. I got lost after the word conjecture.

Re:Look at his method for solving this!!!

[Anonymous Coward]

And if you hadn't added that last paragraph, you'd be +3, Informative by now.

Re:Look at his method for solving this!!!

[Zone-MR]

So my astrophysics bullshit generator at http://zone-mr.ath.cx/?act=bullshit consistently generates $1 million explanations?

Re:Look at his method for solving this!!!

[andreyw]

Hey, it got me through my High School discussions. I kid, I kid... but I like your BS generator.

Re:Look at his method for solving this!!!

[Tony-A]

translate matheese-to-english and summarize in a way we can understand?

Disclaimer: MS Mathematics and I'm not about to claim I understand it, but this is Slashdot so here goes anyway.
There are a couple of fundamental ways of viewing something like a circle or a sphere, that can be generalized to an arbritrary number of dimensions. These ways are now known to be equivalent except for one lone holdout. What makes 3 so special that it can hold off our best mathematical minds?

This conjecture was subsequently generalized to the conjecture that every compact n-manifold is homotopy-equivalent to the n-sphere if and only if it is homeomorphic to the n-sphere. The generalized statement is now known as the Poincaré conjecture, and it reduces to the original conjecture for n = 3.

The n = 1 case of the generalized conjecture is trivial, the n = 2 case is classical (and was known even to 19th century mathematicians), n = 3 has remained open up until now, n = 4 was proved by Freedman in 1982 (for which he was awarded the 1986 Fields Medal), n = 5 was proved by Zeeman in 1961, n = 6 was demonstrated by Stallings in 1962, and n >= 7 was established by Smale in 1961 (although Smale subsequently extended his proof to include all n >= 5).

manifold. a space that is locally Euclidean.
compact. every open cover has a finite subcover.
So a compact manifold is like a bounded chunk of Euclidean space.
The surface of the earth as a sorta spheroid is a compact manifold.
The surface of the "flat earth" is a compact manifold if there is an edge you would fall off of
Just looking at you immediate surroundings, you cannot tell which you're on.

Two objects are homeomorphic if they can be deformed into each other by a continuous, invertible mapping. Like a donut and a coffee cup are homeomorphic. So there exists f:DONUT->COFFEE-CUP (and if there's one there's many more).

Not content to leave things well enough alone, mathematicians start playing with the functions.
f:X->Y and g:X->Y
A homotopy between two functions f and g from a space X to a space Y is a continuous map G from (X,[0,1]) -> Y such that G(x,0)=f(x) and G(x,1)=g(x).
Two mathematical objects are said to be homotopic if one can be continuously deformed into the other.

Seems obvious and it should be easy to prove but intuition is not very reliable and should doesn't imply does.

f:UNIT-INTERVAL -> Euclidean-2-space. f is continuous. The image ought to be 1-dimensional. However, there are continuous functions which have 2-dimensional images.

Cantor's Perfect set. Uncountable number of points but has measure zero. Measure is a generalization of length. The measure of the rational points on a line is zero, but that's only countably infinite.

Triangle A B C. Bisectors of angles ABC and ACB are equal length. Prove the triangle is isocoles. It's provable but I've never managed it.

Four-color theorem. Finally proved with very many special cases solved by computer.

Euclid's fifth postulate. Despite a few people who thought they'd proved it, I think the current state of affairs is that if any of the geometries has a problem, then the other two geometries also have a problem. However all the geometries are "locally Euclidean".

Re:Look at his method for solving this!!!

[Tony-A]

Sorry, shoulda quoted.
Although it seems pretty obvious that the intelligent well written parts are NOT MINE. Just the stupid paraphrases are mine and those stupid paraphrases should not be blamed on the author of the linked article.

Re:Look at his method for solving this!!!

[baggins2002]

Did you happen to note that the description of the problem makes reference to a 2 dimensional sphere? When I went through these types of problems 20 yrs ago, I recall that a definition of a 3 dimensional object can be used to describe and object in higher dimensions, but not a lower dimension.
But then again maybe I'm wrong and this is a 2 dimensional sphere _________________________.

Re:Look at his method for solving this!!!

[Tony-A]

I'm probably rustier than that, but seems like you can embed a lower dimensional object in a higher dimensional space without difficulty. The idea of n-dimensional sphere is to be valid for any n, but now that I start trying to think about it, I'm not at all sure exactly what a 2-dimensional sphere is. I do remember, as a side issue of something in algebraic topology, an arbitrary dimensional generalization of Greene's and Stoke's theorems expressed in a grand total of 4 characters.

Re:Look at his method for solving this!!!

[Smallpond]

What non-mathematicians like us mistakenly believe to be a 3D sphere is a 2-dimensional surface in 3D space. So the mathematicians seem to refer to this surface as a 2-dimensional sphere. The hypersphere of interest to Poincare is the 3-dimensional surface in 4D space. He would call that a 3-dimensional sphere, had he been writing in English. But then, the first floor in French building is what Americans call the second floor, so we're off to a bad start anyway.

Re:Look at his method for solving this!!!

[fingerfucker]

Did you check for etymology of the french word 'étage' ("floor")? Because you're probably using a bad example there and I'd like to know too.

In several other languages, the word used for a floor would actually be literally translated into English as "after-the-stairs area". The English word "floor" really means simply a "platform" (which could obviously be on any level), while the foreign words for "floor" are more specific and refer to an "elevation level" (which is any floor that is no longer on the ground level).

Re:If he doesn't want the money

[Anonymous Coward]

They should give it to me so I can buy a 200,000,000 page Slashdot subscription.

Damn...

[Overzeetop]

I read all the links, and I'm pretty sure they were all in english, but I didn't understand a word of it. No wonder all the mathematicians are nuts.

(I wonder if this is what some of my non-engineering clients think of my work sometimes)

Yes but...

[gbulmash]

His answer to the problem was "42".

- Greg

Re:Yes but...

[dynayellow]

Makes sense, as I have no idea what the question is.

Re:Yes but...

[Anonymous Coward]

Makes sense, as I have no idea what the question is.

Hm... Let's see what the article tells us about it:

If we stretch a rubber band around the surface of an apple, then we can shrink it down to a point by moving it slowly, without tearing it and without allowing it to leave the surface. On the other hand, if we imagine that the same rubber band has somehow been stretched in the appropriate direction around a doughnut, then there is no way of shrinking it to a point without breaking either the rubber band or the doughnut. We say the surface of the apple is "simply connected," but that the surface of the doughnut is not. Poincaré, almost a hundred years ago, knew that a two dimensional sphere is essentially characterized by this property of simple connectivity, and asked the corresponding question for the three dimensional sphere (the set of points in four dimensional space at unit distance from the origin). This question turned out to be extraordinarily difficult, and mathematicians have been struggling with it ever since.

Ah. Poincaré understood to ask a simple question like "what is six multiplied by seven" in such a profoundly stupid way that it puzzled the world ever since if and why the answer was 42...

Re:Yes but...

[HoldmyCauls]

Aw, I was going to guess that!

Re:Yes but...

[rand()0]

But see it actually makes sense, unless you think it originally showed up in hitchhiker's guide.

Re:Yes but...

[thebudgie]

If i had mod points, I would give them to you. That's the best laugh i've had all day. It's only 3:34am too.

Re:Yes but...

[big_a]

We say the surface of the apple is "simply connected," but that the surface of the doughnut is not.

"Mmmm doughnuts..."

$1 million USD?

[Anonymous Coward]

From the article:

A reclusive Russian may have solved one of the world's toughest mathematics problems and stands to win $1 million (560 million pounds) -- but he doesn't appear to care.

Heh. Last I checked, $1 million dollars was not quite equal to 560 million (British) pounds. (560 thousand, sure ...)

In an article on mathematics. Of all things.

Re:$1 million USD?

[bullitB]

That's a British million. A million is only 10^3 over there.

Re:$1 million USD?

[NotQuiteReal]

Heh. Last I checked, $1 millon dollars was not quite what it used to be anyhow.

You can barely buy what used to be a nice house in many markets for a millon. And if you did, you'd have to feed the property-tax man a couple of thousand USD a month just to keep it.

Anyhow, I saw that the article said "he didn't seem interested", but what does that mean? Is there some form he didn't fill out? Some protocol not followed? What? Will he not just be offered the prize after two years of scrutiny or did he not really complete the proof?

It wasn't really clear to me. Give me a rigorous proof that he won't take the 29-some-odd-million roubles, if offered?

Re:$1 million USD?

[PetoskeyGuy]

It refers to weight. The prize is payable only in quarters.

Re:$1 million USD?

[timeOday]

So Dr. Evil was only demanding $1K?

Re:$1 million USD?

[XO]

what's really funny, is that bullitB is technically correct, and he's scored 5 Funny here ... doh.

Bad moderators, no donut.

Re:$1 million USD?

[Anonymous Coward]

bullitB is certainly not correct. I've yet to hear million defined as thousand, even in the UK.
The UK 'million' is the same as the US 'million'.
The difference he may have been, in a twisted way, trying to recall was billion - a US billion is 10^9, a UK billion 10^12.
But a million is not, never had been, and hopefully never shall be 10^3

Re:$1 million USD?

[danila]

Of course it is! Million comes from latin "mille" which meant thousand, as in "Millenium". So every educated person should know that 1 million = 1000.

The Whocares conjecture

[Neo-Rio-101]

Whocarés Conjecture If we stretch a g-string around the surface of somebody's buttocks, then we can shrink it down to a point by moving it slowly, without tearing it and without allowing it to leave the surface. On the other hand, if we imagine that the same g-string has somehow been stretched in the appropriate direction around someone's face, then there is no way of shrinking it to a point without breaking either the g-string or suffocating the person. We say the surface of the buttocks are "simply connected," but that the surface of the person's face is not. Whocares knew almost hundred years ago, knew that a well shaped pair of cheeks is essentially characterized by this property of simple connectivity, and asked the corresponding question for the rest fo the people still reading this, as to why they were doing so. This question turned out to be extraordinarily difficult, and slashdotters have been struggling with it ever since.

Riemann hypothesis reportadly also solved

[jm91509]

According to the Guardian another clever Maths dude has proposed a solution to another of the 7 "million dollar" problems.

This particular problem has big implications for online cryptography as it deals with the distribution of prime numbers. Apparantly.

(I'm no mathematics person BTW.)

Re:Riemann hypothesis reportadly also solved

[Anonymous Coward]

That's a great link, with a wonderful human-readable summary of the 7 problems.

For those too lazy to click:

Seven baffling pillars of wisdom

1 Birch and Swinnerton-Dyer conjecture Euclid geometry for the 21st century, involving things called abelian points and zeta functions and both finite and infinite answers to algebraic equations

2 Poincaré conjecture The surface of an apple is simply connected. But the surface of a doughnut is not. How do you start from the idea of simple connectivity and then characterise space in three dimensions?

3 Navier-Stokes equation The answers to wave and breeze turbulence lie somewhere in the solutions to these equations

4 P vs NP problem Some problems are just too big: you can quickly check if an answer is right, but it might take the lifetime of a universe to solve it from scratch. Can you prove which questions are truly hard, which not?

5 Riemann hypothesis Involving zeta functions, and an assertion that all "interesting" solutions to an equation lie on a straight line. It seems to be true for the first 1,500 million solutions, but does that mean it is true for them all?

6 Hodge conjecture At the frontier of algebra and geometry, involving the technical problems of building shapes by "gluing" geometric blocks together

7 Yang-Mills and Mass gap A problem that involves quantum mechanics and elementary particles. Physicists know it, computers have simulated it but nobody has found a theory to explain it

Re:Riemann hypothesis reportadly also solved

[HorsePunchKid]

Mathworld had this to say about his "proof":

A June 8 Purdue University news release reports a proof of the Riemann Hypothesis by L. de Branges. However, both the 23-page preprint (from 2003) cited in the original release and a 124-page preprint (from 2004) cited in a back-dated modified release seem to lack an actual proof. Furthermore, a counterexample to de Branges's approach by Conrey and Li has been known since 1998. The media coverage therefore appears to be much ado about nothing.

I believe that came up in the previous Slashdot thread about the RH.

Re:Riemann hypothesis reportadly also solved

[Hao Wu]

3 Navier-Stokes equation The answers to wave and breeze turbulence lie somewhere in the solutions to these equations

Out of curiosity, is there potential for supercomputer predict weather pattern via these (as in hurricane, wind, etc.)?

Re:Riemann hypothesis reportadly also solved

[Kiryat Malachi]

Not likely, but not because of these equations - more because of something called sensitive dependence (part of chaos theory, which is very applicable to weather prediction).

However, to my understanding, solving Nav-Stokes would allow us to improve the aerodynamics of bodies moving through fluids, possibly increasing fuel economy for cars, planes, and ships. Should also be applications anywhere there's fluid thermodynamics.

Re:Riemann hypothesis reportadly also solved

[FrostedChaos]

3 Navier-Stokes equation The answers to wave and breeze turbulence lie somewhere in the solutions to these equations

"The answer, my friend, is blowing in the wind, blowing in the wind."

Re:Riemann hypothesis reportadly also solved

[danila]

This "summary" doesn't help anyone understand what these problems are - it only helps to create an illusion of knowing.

Re:Duplicate?

[terrymaster69]

According to Wikipedia, his proof of this surfaced around 2002 and he was lecturing on it in 2003. I guess it's not new news per se, but a Millennium prize problem is a big deal no matter how you look at it.

He wouldn't care to post

[Janek Kozicki]

oh well.. he wouldn't care to post here, I guess. There are more interesting things around to do, for a methamatical genius, than to hang around with nerds. (btw, I love his books)

The Millenium Problems

[shadowmatter]

Since a great deal of discussion and awe comes up anytime one of the millenium problems is mentioned (solved?) on Slashdot, I'd just like to say that any layman interested in learning more about the millenium problems should run to his/her library/bookstore and pick up The Millennium Problems: The Seven Greatest Unsolved Mathematical Puzzles of Our Time. Although, perhaps, for the layman, the end may become a bit tricky (the problems are explained simply in order of increasing difficulty), it's a book worth sticking with, and ultimately worth a read.

- sm

Re:The Millenium Problems

[Deraj DeZine]

So how much money do you get when someone orders the book from your link? Well-played, though.

Re:Problems with the Millenium Problems

[jericho4.0]

You're an idiot. The Poincare Conjecture has direct application to streching rubber bands around apples.

I'm joking, but you're still an idiot.

Just like Linux configuration forums

[Brento]

But there's a snag. He has simply posted his results on the Internet and left his peers to work out for themselves whether he is right -- something they are still struggling to do.

Okay, so tell me how this is any different from every l33t user that tells me how to get my dual flat panel setup working under Xandros without editing the X files manually? Sounds like these kids just tried their hands at mathematics, too.

Re:Just like Linux configuration forums

[Compuser]

1. This is important for all humanity so this is not
the case of: it's too complicated, I'll just get a
Mac. This is a case of if you build it they will
come.

2. He probably wants the verification to happen
double blind, without his input which could make
things easier to understand but also could make it
easier to skip over errors. This simply is a way
to nudge each reviewer to think for themselves.
We know getting YetAnotherDistro to run SomeDriver
is possible, it's just a matter of how. Not so here.

3. Whether or not he is right, this guy _is_ 1337.
Think K&R writing a blurb on how some driver is to
be written letting you code up the rest.

Mr. President...

[cerberus4696]

...we must not have a poincare conjecture gap!

Re:Mr. President...

[ScrewMaster]

Okay, Mr. Kubrick. That's quite enough of that.

Hopefully he has better luck than de Branges

[DeepRedux]

A few months ago Louis de Branges published his proof of the Riemann Hypothesis on the internet. This is also a Millennium problem. Apparently, no mathematician has read it.

It is not that de Branges is unqualified: he settled Bieberbach's Conjecture. Interestingly, much of the validation of de Branges work on Bieberbach's Conjecture was done by a team at the Steklov Institute, referred to in the MathWorld link in the article.

Re:Hopefully he has better luck than de Branges

[agentpi]

I go to Purdue, and de Branges is unable to explain himself at all. He has attempted to explain his process to other professors at a seminar here, and has only confused them. He also kicked first year grad students out of his seminar, stating they were to inexperienced. From these grad students, I have learned that he is pretty much and hotshot and an asshole. I'm thinking about going to his seminar on wednesday just to see how long it takes him to kick me out. (I'm a first year undergraduate). A note about his proof of the Bieberbach Conjecture. While de Branges did prove the conjecture, he overcomplicated it, as he does many things, and everybody and their thesis advisor has simplified his proof in some way. Mathworld really discredits his "proof" for one, it contains no proof, and his method was proven flawed by counterexample in 1998.

Re:Hopefully he has better luck than de Branges

[pi_thagoras]

Except, of course, that mathematicians have read it, and it seems, in all those pages, there isn't actually a proof. (See the bottom of the front page of Mathworld)

As opposed to Perelman, who appears to have actually proved a larger conjecture, of which the Poincaré conjecture is a specific case.

Re:Hopefully he has better luck than de Branges

[swillden]

someone needs to prove that this counterexample applies directly to the way this assumption is used in his theory (and is not a special trivial case)

No, Branges needs to prove that the counterexample does not apply to his theory.

someone needs to prove that the presumable false assumption makes the whole theory false.

No, if he can't show that the counterexample doesn't break his proof, then Branges needs to show that his proof doesn't require that particular lemma.

So as long as nobody can prove the above de Branges theory stands as the only known proof.

That's not how it works. Proofs aren't considered valid until proven wrong, they're considered speculation until reviewers have painstakingly analyzed them and not found any flaws. Any flaws discovered put the burden back on the author to revise the proof and either eliminate the flaws or demonstrate more clearly why they are not flaws.

Re:Hopefully he has better luck than de Branges

[agentpi]

yeah, its right on mathworld's front page. http://mathworld.com its the 3rd story on the bottom: The 2004 Wolfram Technology Conference invites authors, students, educators, and developers who use Mathematica and other Wolfram products to participate. This year's conference will include contributed talks, a new student presentation forum, an art gallery, tutorials, hands-on workshops, and problem-solving clinics. Twin Prime Proof Proffered A May 26 preprint by Vanderbilt University mathematician R. F. Arenstorf appears to come close to settling the long-standing question of the infinitude of twin primes. While a hole has recently been found in the proof, mathematicians remain hopeful that the proof can be corrected. Riemann Hypothesis "Proof" Much Ado About Nothing A June 8 Purdue University news release reports a proof of the Riemann Hypothesis by L. de Branges. However, both the 23-page preprint (from 2003) cited in the original release and a 124-page preprint (from 2004) cited in a back-dated modified release seem to lack an actual proof. Furthermore, a counterexample to de Branges's approach by Conrey and Li has been known since 1998. The media coverage therefore appears to be much ado about nothing. I don't really mean to completely insult his proof of the BIerbach conjecture, it is just that simplifications came so much sooner after his proof than normally come, at least that is what I have been lead to believe while I could be wrong, My main point is that he is pretty much an asshole. He holds a seminar which is supposedly open to the public, and Kicks out pretty much anyone he doesn't think is advanced enough. I am going to go to his seminar tomorrow morning, just to confirm that he is indeed an asshole. Please email me with any thoughts on this. agentpi@mac.com

Re:Hopefully he has better luck than de Branges

[agentpi]

How do you split comments into different blocks, the obvious answer doesn't work! maybe its a problem with Safari.

Re:Hopefully he has better luck than de Branges

[agentpi]

Thanks anonymous coward, I didn't notice that you posted so my reply is long and redundant, but you said it well!

Re:Hopefully he has better luck than de Branges

[danila]

No, Branges needs to prove that the counterexample does not apply to his theory.
It's not a court, Branges doesn't need to do anything - someone needs to prove it one way or another for the science to progress.

Re:Hopefully he has better luck than de Branges

[bill_mcgonigle]

I use "Plain Old Text" format and returns.

It even interprets some html tags in Plain Old Text Mode.

Saves lots of typing over HTML mode.

Re:Hopefully he has better luck than de Branges

[agentpi]

thanks, I am an idiot

I hope this worked..... ...It did, YAY!!!!!

Re:Hopefully he has better luck than de Branges

[babbage]

The first link on the chap's homepage is entitled "apology for the proof of the Riemann Hypothesis".

Yeah, I skimmed his paper, and noticed that as well. Apparently, "apology" in this context means a proof that has not yet been subjected to peer review, but which the author is deeply convinced is correct. Pasting some output from a dict apology, it seems:

1. Something said or written in defense or justification of
what appears to others wrong, or of what may be liable to
disapprobation; justification; as, Tertullian's Apology
for Christianity.

[....]

Usage: An apology, in the original sense of the word, was a
pleading off from some charge or imputation, by
explaining and defending one's principles or conduct.
It therefore amounted to a vindication. One who offers
an apology, admits himself to have been, at least
apparently, in the wrong, but brings forward some
palliating circumstance, or tenders a frank
acknowledgment, by way of reparation. [....]

[....]

2: a formal written defense of something you believe in
strongly [syn: {apologia}]

Clearly, de Branges is using the term in this sense.

It doesn't really matter though, because if you actually read his paper, the first third is all incomprehensible background nonsense about the nature of the problem, while the last third is all incomprehensible arrogant nonsense about what he wants to do with his prize money. The actual meat of the paper is buried somewhere in the middle, but it's like that's all just an afterthought to the guy's mad ravings about his place in history and his imminent wealth.

He couldn't be more different than the person that seems to have solved the Poincare conjecture. Where Perelman is silent behind a paper that seems to concretely prove not just the problem at hand, but a whole broader class of problems, de Branges has this ridiculous paper that goes on and on about what a big shot he is, while stomping around his university like a little tinpot Napoleon. I'm no math whiz, but hot air isn't always hard to recognize...

Re:Hopefully he has better luck than de Branges

[danila]

This is a useful quote, but don't take that "require" too literally. Yes, you are perfectly justified not to believe that the conjecture is solved, until you read about it in Science - this is reasonable. What is not reasonable is to think that de Branges is somehow required by someone or something to provide extra proof or something else. He doesn't have to if he doesn't want to.

Just like Perelman, de Branges can just sit and wait. Hopefully, someone will eventually read the proof thouroughly and see whether there are any significant errors. And then everyone will benefit from knowning whether the proof exists and if yes, what it is and that the conjecture is true.

abstract- not complicated at all!

[Anonymous Coward]

This is a technical paper, which is a continuation of math.DG/0211159. Here we construct Ricci flow with surgeries and verify most of the assertions, made in section 13 of that e-print; the exceptions are (1) the statement that manifolds that can collapse with local lower bound on sectional curvature are graph manifolds - this is deferred to a separate paper, since the proof has nothing to do with the Ricci flow, and (2) the claim on the lower bound for the volume of maximal horns and the smoothness of solutions from some time on, which turned out to be unjustified and, on the other hand, irrelevant for the other conclusions.

Re:Duplicate?

[EulerX07]

Think nothing is impossible? Try slamming a revolving door.

Place a 2 by 4 on the floor in the door.
Slam the revolving door.

Another impossible problem solved.

One thing he overlooked...

[HoldmyCauls]

Solving a Millenium Problem carries a reward of $1M, but apparently Perelman isn't interested...

He does realize that's as good as *money*, right???

Re:One thing he overlooked...

[TheLink]

He was working on "A special theory on winning a million dollars with math". Being a real mathematician since he has proven to himself he can get the reward, he is satisfied.

Just like the joke about the mathematician who woke up and discovered a fire in his room. After working out exactly how much water to use and what direction to throw it, he said "There is a solution" and went back to sleep (without putting out the fire - that's a job for the physics/engineering folks).

Re:One thing he overlooked...

[mikeee]

No, no. A physicist would calculate how much water was required; a mathematician would only demonstrate that the fire would go out after a suffient quantify of water was poured on it.

Re:Duplicate?

[Derg]

isnt that slamming the door against the 2x4? not, slamming the door itself, as compared to a standard door, door against jam...

An apple is simple connected a donut is not.

[HornWumpus]

Therefor a butt is not simply connected.

However you stated 'We say the surface of the buttocks are "simply connected"' buy that do you mean to ignore all the plumbing associated with the butt while recognizing the thru and thru nature of the mouth/nose hole.

I NEED more information. I'm strangely fascenated by the topography of butts. Perhaps I can get a grant.

Re:Duplicate?

[pchan-]

sure, but can you ski through it?

Wake me up when it's peer reviewed and accepted

[Anonymous Coward]

I'm tired of seeing these 'please make me famous even though I didn't really prove it' threads. The little boy has cried wolf too many times. We don't care unless it's really solved.

Editors, I'm talking to you.

Re:Duplicate?

[Paleomacus]

Depends on the definition of 'slamming' a door I would guess. Still...the 2x4 is probably against what you would call a door jam for a revolving door. It might even be arguable that a revolving door has a jam...

Great philosophical questions of our age :P

Re:Duplicate?

[John Courtland]

Let the lock hang loose on the revolving door. When it turns and the pin falls into the floor - BOOM.

Racist title

[Fjornir]

I can't believe slashdot would run a story with that title. "Perelman May Have Solved Poincare Conjecture" would have been much more dignified. You would never see "Muppet May Have Solved Poincare Conjecture" would you? Please, Perelman is a mathematician first, Russian second.

Re:Racist title

[Anonymous Coward]

Oh, good, now Russians are Muppets. You've helped.

Re:Racist title

[Cytlid]

I don't see where there's a problem. The guy lives in Russia, right? You know, people go to work (non-tech people let's say, defnintely not slashdot-fodder), and gather around the watercooler and say "Hey, did you hear about that Russian guy who solved that math thing?".

No harm in that. Now if they said "Pinko May Have Solved..." or better yet "Whitey May Have Solved..." (or Honkey, etc), there could have been a slight problem. (No insult intended, perhaps I'm a white guy from Russia.)

Would it have been racist if it said "American May Have Solved..."? Probably not. I actually thought it was cool and hope it's true.

Re:Racist title

[Fjornir]

Dude... You missed this comment...

Chill out. It was a joke.

So, to quote Trek, "Double dumbass on you."

Re:Racist title

[saitoh]

Interesting (and valid) observation, but Russian is a nationality, not a race.

Re:Racist title

[bill_mcgonigle]

I don't see where there's a problem. The guy lives in Russia, right?

The only important part about him being a Russian is that he was able to live off a U.S. savings account by living in Russia to get this done.

Besides that it's of little importance to the subject at hand. What's the point of saying "New Jersian Solves Fermat's Last Theorem"? Maybe "Princeton Professor solves Fermat's Last Theorem"? I prefer "Wiles solves Fermat's Last Theorem". Yeah, you have to be informed about the players (which I'm not) but it's not like computer mags talk about "Finn releases new kernel".

Re:Racist title

[Fjornir]

Here's an interesting (and valid) observation for you: a bit more than two hours after I clarified this joke you dropped the same comment as the first person who needed the joke explained.

I'll admit - it was a lame joke. It would've come across much better if I'd included an "Oh wait - look here" link to the (joking)post I was basing my joke off of, but man... Two hours later? Did you not happen to check if this point had been raised?

Re:Wake me...

[RedWizzard]

Wake me when someone verifies his work. I can claim to solve anything, but it doesn't mean much unless the community says I'm right. Right off the bat it seems fishy: no journal submission, just a web post? No referee? And he's not answering questions about his work? He's either a genius or a nutcase, possibly both.

The claim has been around for a while. From the referenced MathWorld article:

Almost exactly a year later, Perelman's results appear to be much more robust. While it will be months before mathematicians can digest and verify the details of the proof, mathematicians familiar with Perelman's work describe it as well thought out and expect that it will prove difficult to locate any significant mistakes.

That was in April 2003. It's now over a year later again and it hasn't been disproven.

Paincare conjecture

[starrsoft]

Wow! Someone finally solved the paincare conjecture... wait, didn't morphine do that? and the Christian Scientists?

A Christian Scientist from Theale
Said, "Though I know that pain isn't real,
When I sit on a pin
And it punctures my skin
I dislike what I fancy I feel".

Oh! It's poincare... forget it...

Re:Well, at least the Russkies are good at math...

[DAldredge]

Yes, and we grew out of it.

Getting Maried Bad for Math?

[students]

It's well known that mathematicians and scientists are less productive past the age of 40 or so. The conventional wisdom is that they are simply getting old, but one article in Science News indicated that perhaps maried scientists were less productive, just like many criminals reform when they get maried. Perhaps Grigori Perelman knows this. One problem with my suggestion: The mechanism suggested by the article was that scientists are motivated by "babes" and that once they are maried they don't need more. So if Grigori is intentionally lying low, his carreer should still end.

Re:Getting Maried Bad for Math?

[SYFer]

As Balzac said, "there goes another novel."

Re:Getting Maried Bad for Math?

[NichG]

Well, it could just be that the drive to do math, or whatever, is a subtle emergent thing, so when a stronger pull exists, like the time requirements due to a family, the drive towards academics becomes diluted. Plus, theres the peace and quiet of no kids/spouse running around, which is much more conducive to spending time thinking about a hard problem than constant ruckus.

Re:Getting Maried Bad for Math?

[Madcapjack]

I think that they become less productive mostly because with academic success comes more responsibility- to graduate students, to running an academic department, etc. There is simply less time to devote to work. Also, if one has already made a valuable contribution to the field, and established a career, there is substantially less pressure to really push yourself. Professors trying to receive tenure work damn hard and the pressure is on- they gotta be productive.

But this does not imply that all researchers should be kept at that peak level for their entire career (to maximize productivity). I think that would be counterproductive, and physically and psychologically harmful. Pressure adds a lot of stress, and stress can really kill you. ( :

I have my own pet theory about why that russian dude doesn't want the money- he doesn't want to get a visit by the Russian Mafia.

Re:Getting Maried Bad for Math?

[bikiniAtoll]

A counter example to your claim:

Leonhard Euler had 13 children, lived to be 76, published over 800 papers, half of which were in the last 17 years of his life (after he went blind), according to wikipedia .

Re:Getting Maried Bad for Math?

[students]

Not my claim. The article also gave counter examples (like Andrew Wiles). It compared the exceptions to career criminals, who continue to steal even when they don't need to.

Riemann was covered this summer on Slashdot

[ajna]

The purported proof of the Riemann conjecture was reported and discussed in June 2004 here on slashdot. Incidentally the comments contain what I feel is the funniest math-related lines I've ever heard: Riemann-chu, I prove you! (credit to foidulus).

meh, important, but not that important.

[cryptor3]

Not really. There are already a lot of people who believe that the RH is likely to be true.

Just because the hypothesis hasn't been proven doesn't mean someone can't start working on an application that only works if it is true. I'm pretty sure there's guys already working under this assumption. Don't know anyone personally, but that's what I'm told.

Quantum computing is a nice, related example. When Shor came up with a factoring algorithm, no one had proven that quantum computing was possible. But that didn't stop him from working on his algorithm.

I think the article's intro is a sensational piece of crap. Until someone justifies the author's introduction paragraph, he (Tim Radford) has lost my respect.

tr/Russian/Grigori Perelman/ ..?

[etheriel]

Why doesn't this article's title read:

"Grigori Perelman May Have Solved Poincare Conjecture"

I've noticed that these kinds of announcements often make a point of appending a nationality to the name of the person involved in the discovery. Surely this proof builds on mathematical knowledge from around the world. Or was Grigori Perelman standing solely on the shoulders of "fellow Russian" mathematicians? I highly doubt it...

Re:tr/Russian/Grigori Perelman/ ..?

[Scrab]

Possibly because many people won't have the faintest scooby who Grigori Perelman is....

At least we know who the Russians are, and from there we can specify....

Re:tr/Russian/Grigori Perelman/ ..?

[nihilogos]

Russian mathematicians are a special breed. If you ever do any original mathematical research, especially a high powered area like analysis, the chances are some Russian did it in the 60s.

I suspect it's the long winters.

Re:tr/Russian/Grigori Perelman/ ..?

[eric.t.f.bat]

$EDITOR just wanted to invoke the Russianness of the story to head off complaints about his inability to spell "Millennium" in the summary.

Re:tr/Russian/Grigori Perelman/ ..?

[pjt33]

Your tr turns the title into "Grggori Mry Hrve Solved Pooicrre Coijectrre". Did you mean s/Russian/Grigori Perelman/?

Re:tr/Russian/Grigori Perelman/ ..?

[guacamole]

Well, the title is still wrong. When I hear "Russian" instead of say "Russian Professor", I expect the guy to be an ethnic Russian which Mr. Perelman obviously is not.

dammned practical?

[way2trivial]

perhaps true math genius is, as you mention, an exclusive trait from womanizing and acquisition mentality..

maybe we should be looking for the monomania gene in all these 'idee fixee' folks...

Re:Well, at least the Russkies are good at math...

[DAldredge]

But we grew out of it. It is the 21st century and they should be way more advanced than they are. But they are not becauase those in power are scared by educated followers. Look at the way the treat women and girls in their own countries like that 16 year old girl that was just hung in Iran or all the honor killings that happen because a woman was raped and that makes it her fault.

If they do not wish to be judeged by their actions...well tough shit.

Re:Duplicate?

[Y2]

Yes, yes, but googling "Grigori Perelman" gets you a 17-month-old article at Wolfram saying, "Poincare conjecture solved, this time for real."

Maybe what we have here is just the impending lapse of the Clay Math. Inst.'s required two years of scrutiny...

Re:Well, at least the Russkies are good at math...

[DAldredge]

No, we brought some of them over with us, (Pat Robinson, Raulph Reed, Others) ;->

The "reclusive nut's" picture

[Anonymous Coward]

http://www.wordiq.com/definition/Image:Perelman.jp g

The guy is a bit scary..

Re:The "reclusive nut's" picture

[CTalkobt]

>> The guy is a bit scary..

Aren't they all?

Interesting View

[a3217055]

This is all very interesting and I like the way Perelman has gone about working out this whole genius and fame, and money. I wonder what if movie stars ever found out or the RIAA or the music industry, they might license him. Interestingly there was also a breakthrough in the Riemann Hypothesis, I wonder if anyone has ever heard of Louis de Branges de Bourcia at Purdue and his paper on the Riemann Hypothesis . The person who posted the news article did not tell use what Poincaré Conjecture is? Well this is slashdot not, mathdot :) { Just Kidding Dawgs, aite } . Anyway Perelman has a very ascetic way about him, maybe he sees beyond the materialsitic, and media oriented consuermism. Anyway interesting it is to see someone who sees beyond himself. Just because google news bot picked this up don't make it that great of a post. It was known for the last 6 months that Perelman and colleagues had been working on this. PS ::- buying != happiness Saw this at NYC Penn Station {not a good sign}

Perelman and the prize

[NimNar]

Perelman was unemployed for 10 years while he worked on the problem. His last job was in the States in the early 90s, where he saved enough money to live in Russia for the whole time he worked.

So think about his perspective: he's a complete loner who was ignored by the mathematical community for 10 years! Now that he's going to be a "certified" genius (with the $1M prize) why exactly should he care.

Also, it's worth pointing out that like Wiles (who solved the Fermat Conjecture), Perelman's work develops a theory that has the Poincare conjecture as a corollary which is interesting but not of central importance.

Re:Perelman and the prize

[doublegauss]

Perelman was unemployed for 10 years while he worked on the problem. His last job was in the States in the early 90s, where he saved enough money to live in Russia for the whole time he worked.

What I find particularly interesting is that this guy was able to devote 10 years of his life to solving a problem so complex that there was no intermediate output. The same happened to Wiles, who took 7 years to get hold properly of the Fermat theorem.

Obviously, in both cases it would have been impossible to reach such great results if the authors had had to keep a steady pace of lesser publications. But this is the rule in the academic world: "publish or perish". You must prove yourself "productive" year by year, otherwise you're out.

I've always thought that applying industrial methods of prouctivity measurement to research is utter madness (I am an academic myself). IMO, Perelman's and Wiles' cases show it clearly.

Re:Perelman and the prize

[Knetzar]

Wiles did create some great theorems while solving the Fermat theorem. One of his earlier failed proofs had many proofs in it that could be used in other areas of mathematics.

Re:Perelman and the prize

[Alomex]

Obviously, in both cases it would have been impossible to reach such great results if the authors had had to keep a steady pace of lesser publications.

Wiles proved Fermat's Last Theorem while employed as a professor at Princeton University. In other words, it is possible to engage in such reclusive work while in academia (see Louis de Brange work on the Bieberbach conjecture, for another similar data point).

Re:Perelman and the prize

[stud9920]

But this is the rule in the academic world: "publish or perish". You must prove yourself "productive" year by year, otherwise you're out.

Or have your PhD students put your name on the paper. That's what my PhD friends do anyway.

Re:Perelman and the prize

[Anonymous Coward]

Obviously, in both cases it would have been impossible to reach such great results if the authors had had to keep a steady pace of lesser publications. But this is the rule in the academic world: "publish or perish". You must prove yourself "productive" year by year, otherwise you're out.

Umm, no. That's the whole point of tenure.

Before tenure, you do have to prove yourself, but after that you are free to spend years working on something, with no prospects of intermediate output. Sure, your salary could stagnate, but if you're in academia for the money, you're a fool.

Wiles was a full professor with all the trimmings before embarking on that 7 year project.

Math and Language

[Fractal Dice]

I prefer to think of math as "the language of patterns" (with a lot of regional dialects).

Our ideas are the same up to an isomorphism.

Re:Math and Language

[xoran99]

Our ideas are the same up to an isomorphism.

Probably only semi-conjugacy... Some ideas are pretty twisted :P

Poincare Conjecture link sucks!

[t'mbert]

Can someone explain this better? That link to the conjecture is plain awful.

Here are my questions (in parens):

If we stretch a rubber band around the surface of an apple, then we can shrink (huh? what do they mean by "shrink" here?) it (rubber band or apple?) down to a point by moving (huh? again, what does "move" mean here) it (rubber band or apple) slowly, without tearing it and without allowing it to leave the surface (okay, must mean rubber band doesn't leave the surface of the apple then?). On the other hand, if we imagine that the same rubber band has somehow been stretched in the appropriate direction (what direction would that be?) around a doughnut, then there is no way of shrinking it (rubber band again I assume) to a point without breaking either the rubber band or the doughnut. (why? the writer made a big leap here, but it's not obvious)

Re:Poincare Conjecture link sucks!

[Anonymous Coward]

Ok, imagine an apple with a rubber band around it. You can slide the rubber band down slowly, without breaking it, and have it shrink to a point, touching the apple all the while. This is called being 'simply connected.'

Now imagine a donut. It's got a hole in the center. Imagine a rubber band passing through that hole - think of two connected loops. This is not simply connected.

You can't shrink the donut's rubber band to a point, because of how it loops through the donut. You'd have to crush/tear the donut [or break the rubber band] to get it down to a point.

Poincaré's conjecture deals with this, but in one extra dimension.

Re:Poincare Conjecture link sucks!

[Anonymous Coward]

It's very easy. A rubber band around a sphere can slide along the surface so that the circle it forms becomes smaller and smaller, until it converges into a point. But if a rubber band is wrapped around a torus (doughnut) like a link in a chain (so that it goes through the hole in the doughnut), you can't slide it along the surface to make it any smaller than the cross-section of the torus nor can you detach it without cutting the band or the pastry.

The Poincare Conjecture involves hypothetical 4-dimensional shapes with the same properties, and isn't very easy.

Re:Wake me...

[Mr2cents]

That was in April 2003. It's now over a year later again and it hasn't been disproven.

What we need is a 1 Million $ prize for the person that disproves the proof.

Any relation to Yu Perelman

[too_bad]

Does anyone remember the book "Mathematics can be fun" maybe published some 40 years ago
which made learning mathematics as a kid absolutely wonderful ? Wonder if Grigori Perelman
is of any relation to the author of that book Yu Perelman ?

Re:Any relation to Yu Perelman

[Anonymous Coward]

Grigori Yakovlevich Perelman is a son of Yakov Isidorovich Perelman, autor of "Zanimatelnaja Matematika" among other books.

Re:Any relation to Yu Perelman

[helfen]

oh man, I love his books, especially "Zanimatielnaja fizyka" ("Physics can be fun"), this books show that, indeed - mathematics can be fun.

So he can solve it...

[jeephistorian]

I want to meet the guy (or gal) who came up with a question worth $1 million!!!!

Fritz
__________

Re:So he can solve it...

[DrEasy]

He must be easy to find, doesn't he work for a famous TV game show? He/she even comes up with a few every week!

Re:Duplicate?

[Derg]

again, the lock is not technically part of the door, it is an independant member, attached to the door to perform some function. in your standard door, you have a case, jam, and the door itself, attached to the formers by means of hinges. this is all a door is. knobs, 2xn's and locks are all addons. is a computer any less a computer without multimedia capabilities? is a door any less a door without a lock? to let the door slam against the lock is valid, but not when your asking for the door to slam against itself. therefore i argue, slaming a revolving door is quite impossible.

Re:Problems with the Millenium Problems

[Ibag]

If I'm not mistaken, the N-body problem was shown to have no solution in elementary functions like 100 years ago, or something like that. Possibly by someone really famous (as far as mathematicians go). He won a prize from a Danish king by doing so, as the king had made a contest to see who could solve it.

There are a number of reasons why these problems should have prize money attached to them without direct practical applications that are curreently known. First, their results are important from a purely mathematical standpoint. Second, the techniques that must be invented to solve these problems are important in their own right. Third, the mathematical problems that we can't find uses for now could very easily have applications in 100 years. Number theory is being applied to computers, group theory has practical uses now, and I'm sure that many other brahcnes of math have found applications after long periods of having little to no practical value.

What the fuck is up with the world and its instant gratification, "but what does it get me NOW" attitude these days? Oh, if only the 80s had never come....

Turning down the money is nothing special

[Anonymous Coward]

I don't think that there's anything inherently honorable or dishonorable about taking the money. If he wants to take the money and blow it on hookers and Ferraris, that's just as honorable as getting satisfaction because your brain gives you some sweet endorphins because you think you've made the honorable statement that "I'm not about the money, I'm about the math".

Re:Turning down the money is nothing special

[Forbman]

Don't hate the playa, hate the game...

Time

[r2q2]

The main problem with all of these solutions especially in math is that time is the largest factor in determining if the solution is correct. Give you 2 years and its marginally okay. Give you 40 and its accepted as a standard etc...

Re:Duplicate?

[rm -vrf]

of course you can. the real question is, will you make it across intact.

Russian? Brit?

[Anonymous Coward]

http://www.newscientist.com/news/news.jsp?id=ns999 92143

So did the British man or the Russian solve it? April 02 newscientist has the same basic story with the names changed.

Re:Russian? Brit?

[Quaryon]

From the article:

According to the rules of the Clay Institute, any purported proof must survive two years of academic scrutiny before the prize can be collected. A recent example of a proof that did not survive even this long was a five-page paper presented by M. J. Dunwoody in April 2002 (MathWorld news story, April 18, 2002), which was quickly found to be fundamentally flawed.

Q.

Russian may have proved Poincare Conjecture

[Eric119]

In Soviet Russia...

they prove conjectures.

By your own argument...

[memco]

you have proven yourself wrong. You said, "knobs, 2xn's and locks are all addons", and as such the door is the only thing that can be slammed. seeing as how a door without hinges can't be shut, nor can a door without a knob (or latch) be shut, it is imporrsible to slam any door at all. However, since we commonly associate a slammed door with having these items, a slammed revolvoing door is allwed to slam against any external part.

Re:By your own argument...

[Derg]

So close yet so far. A door without hinges has a neutral closed position, whereas the door rests against the jam. This is common when the installing carpenter is worth their weight in 10penny nails. To say that a door without hinges cannot be slammed is inconsievable, as a door without hinges is not a door, it is a board and a door case. Hinges are not accesories, as a knob and lock are. one can still operate the door wihout them, though as I stated before, without the hinges, a door you have not.

swing and a miss, strike 1.

since when did a door that has been slammed need either a knob (or latch, as you say) or lock? I have on the front of my home, a door. it is a screen door. It has no latch, and no lock. it has a spring however, which keeps it in a neutral closed position. Are you saying this door cannot be slammed, as it has not a lock or latch?

swing and a miss strike 2

A slamming revolving door is allowed to slam against any external part? Fine, but that is not what the original post stated. it said to slam the door. not against a board, or against your head, it said to slam the door. Now when I slam a door, I do it against itself, thusly slamming the door against the door, but as that is doubly redundant, we just say I slammed the door. You can surely slam it against a 2xn, but that is not slamming the door, it is slamming the door against something else. So again, I say, You cannot slam a revolving door.

swing and A miss, strike three, YOUR OUTTA HERE!

note: not to be a dick, but i Know of a way to slam a revolving door, that satisfies all arguments, and does not involve any external items, latches or otherwise. Interested in how? reply and I shall reveal.

Re:By your own argument...

[John Courtland]

Either you break it in half, or you dislodge it from the pivot (I've actually seen the latter twice from some drunkards :p)

If he doesn't care about the money

[ickypoo]

... then maybe he should consider donating it to the town of Beslan. I'm sure they could use the help.

Good!

[jb.hl.com]

Now that's what I call altruism.

Totally

[apankrat]

Agreed, but I believe the name is Stallman, not Erdos :-)

Re:The Poincare Conjecture?

[dosun88888]

You're thinking of the Bourne Again Christian Conjecture.

Good article here

[mrthoughtful]

For an accessible math article on this, try http://mathworld.wolfram.com/news/2003-04-15/poinc are/

Thomson quote

[Jafa]

Um, just to point out, because this is a common mistake, but Thompson didn't pen the phrase "feed the body or the head will die". Not sure who said that.

But, Rob Marr coined the phrase 'Kill the body and head will die' in a horrible movie. Some info here.

I'm not sure the quote 'Kill the body and the head will die' is the quote you're looking for here for your argument, though.

J

Re:Duplicate?

[radicalaxis]

Um, unless I have a huge blind spot, the article says no such thing. In fact, this article makes it clear that the latest article he has published was in March 2003, and although a further paper is forthcoming, it is believed that the first two papers contain a correct proof.

As far as I can tell, it seems the fuss is rather about the distinguished mathematician (math popularizer, rather) Keith Devlin saying that he thinks it is correct... but as far as I can tell, he has no special authority on the problem and hasn't looked it over in the details

isn't interested?

[bani]

what a twat.

i mean really, if you don't want the money, then take it and give it to charity .

Re:He does not make more than $4-5k/year

[mrak018]

few hundred? Rotfl.
Here in Russia he probably earn no more than 1 or 2 hundred.

Our scientists has 0 money and infinte amount of time to work, because our scientific institutes give them office space and not enough money to spend it for anything other than food.

Comment removed

[account_deleted]

Comment removed based on user account deletion

Do NOT believe in Riemann Hypothesis proofs

[glMatrixMode]

Hi, i'm a mathematician, i attendend one of the most "promising" talks by someone pretending to prove RH, and there was no reason to believe that he actually proved it. So please be sceptical when it comes about RH

RH seems to be one order of magnitude more difficult than the other 'Millenium problems'.

David Hilbert once said
"If I were to awaken after having slept for a thousand years, my first question would be: Has the Riemann hypothesis been proven?"

More specifically RH is about the structure of the set of prime numbers. One can formulate it as a statement on the distribution of prime numbers within the real numbers, but that's probably missing the point of the story. The set of prime numbers 'behaves' like the set of orbits of a dynamical system (a dyn. sys. is anything that evolves with time), and the real progress towards RH consists in attemps to concretely describe this dynamical system. See the work by Connes, Deninger... you have free papers on arXiv. If you want to have a look, I recommend especially the paper math.NT/9811068 on arXiv. here's an URL :

http://www.arxiv.org/abs/math.NT/9811068

But the serious people like Connes don't pretend to solve RH. Actually most people don't expect it to be solved within decades from now.

Re:Do NOT believe in Riemann Hypothesis proofs

[glMatrixMode]

oops, i should have said 'closed orbits' instead of 'orbits'. The dyn. sys. will also have non-closed orbits and they won't correspond to a prime number. Also there will be one fixed point, and it won't correspond to a prime number.

Re:Problems with the Millenium Problems

[Ibag]

How? There are many branches of mathematics and mathematicians who deal in practical work and will decry the relevance of this type of work.

The results of different mathematicians, some big and some small, are put together by the next generations of mathematicians to derive new results. Many people who deal with the practical are content to buil on fairly old results. They can decry all they want, but most likely even they use somee result which was initially a solution waiting for a problem. General relativity is a good example of mathematics that had no application at first. Einstein needed the tools of differential geometry (beyond just surfaces in 3 dimensions) to formulate and express the theory. I might needd to check my math history a bit, but I can't think of any major mathematics which were developed for a specific practical purpose since about Gauss. There have been serveral that have been applied, though.

What new "techniques" were invented to (suposedly) solve this problem?

I don't quite understand the details as I have only taken a single class in differential geometry and I don't think a paper has been released yet, but Perelman gave a lecture on his results at MIT and my unerstanding of it is: By doing something studying the Ricci flow in a new way, spawning some new field that I heard refered to as "Geometrization" or some such, he created a theory which solves a large class of problems. The poincare conjecture is just a special case of his theory.

In general, though, all the really hard problems in mathematics have spawned many theories and techniques as people attempted (and failed) to solve them. While Andrew Wiles proved and important conjecture in the process of proving Fermat's last theorem, 250 years of mathematicians created all sorts of wolderful results along the way. If I told you them, would you appreciate them, or even understand them?

They were the base foundations for the research and development of what we have today

And things like this will be the base foundations for the research and development of what we have tomorrow. But when things like that were being worked on, they had no practical use outside of mathematical puzzles and other bits of mathematics. I believe that Hardy once said that he loved number theory because he knew he was working on something with no applications. You don't know what results will be based upon this work and for you to use hindsight to justify the work that became important while dismissing all work that doesn't have immediately obvious applications is at the very least illogical. You don't know the future, and its pretty clear that you don't know the past. Don't pass judgement on a major achievement before it has hadd a chance to bear fruit.

In Russia

[EachLennyAPenny]

Poincare Conjectures solve YOU. SCNR

Re:Confused

[Anonymous Coward]

You are forgetting that this is about an Apple, so obviously there's a Reality Distortion Field at play somewhere. Anything is possible. Including 2D fruit, 4D donuts, and G5 sunflowers. Oh wait, the last one isn't.

I wonder if this Russian fella used RDF as a factor in his equations?!

Re:Confused

[xoran99]

A better analogy would be to continuously move a circle on the surface until it becomes a point. In the case of a donut, you could draw the circle through the middle hole and around again, so you can't "shrink it to a point" my continuously moving it anywhere; it goes around the donut anywhere you put it. With a sphere, though, you can continuously move the circle to a "pole," where it becomes a point. This property is called simple connectivity.

It's pretty easy to see that all simply connected 2-manifolds (in 3 dimensions, at least) are homeomorphic to the shell of a sphere, i.e. they may be stretched and contorted to look like it. The question answered here is whether the same is true in the next dimension.

PC gone mad.

[jotaeleemeese]

I normally roll my eyes in despair when somebody complains about politicial correctness gone mad (because normally the complainer is a little racist wishing for times gone by).

But now I am absolutely flabbergasted that somebody may find such title racist.

Honestly man, where is your common sense?

Russian is not used in a derogatory manner, don't be mentally anal retentive for goodness sake.

Do you know the work context?

[jotaeleemeese]

Find it in a dictionary, it may help your jokes in the future...

Two yars to prove this.

[the cleaner]

According to this article he published the proof in 2002 and as of August 2004 was still being checked.

Seems to be not that easy stuff, if it takes a world full of Mathematicians two years to check a single proof...

Billions - Spanish / English

[Guiri]

Well, there are actually differences between numbers in different languages: 1 Billion in english is 10^9, while 1 Billion in spanish is 10^12.

Cheers

Re:Billions - Spanish / English

[pjt33]

Nonono. You're confusing English with American. 1 billion in English is 10^12, whereas 1 billion in American is 10^9. However, to ensure everyone is confused the Houses of Parliament switched to using American billions in the 1970s.

Re:Billions - Spanish / English

[njj]

No, a British billion is 10^12, too (although the American definition seems to have largely supplanted the British one in popular usage). We have a (now obscure) word `milliard' which means 10^9.

Presumably this means that Bill Gates is actually a `milliardaire' when visiting the UK.

For a nation which often claims to be the greatest country in the world, I must say that American billions are a bit, well, small...

Re:Billions - Spanish / English

[Ibn al-Hazardous]

Actually, IIRC the difference is between the European and US'ian definitions of Billion, Trillion etc. So, the Brittish Billion equal the Spanish and the Swedish Billion, while the one the talk about in the US is 10^3 times smaller. That's what made the parent funny... :)

Now, all I wonder is - which standard does the Canucks follow?

Re:Confused

[XO]

Mods:

You suck, this is not Flamebait. Someone mod me as flamebait, and mod this something Positive.. beacause I guarantee 95+% of slashdot does not understand the description.. As someone else earlier said, the page linked makes a HUGE leap, and doesn't take anyone with it, in the explanation of the conjecture.

This proof has been around for a while

[zoum]

http://www.findarticles.com/p/articles/mi_m1200/is _17_163/ai_101339488
The paper link is inside.

Re:Problems with the Millenium Problems

[chthonicdaemon]

This sounds remarkably similar to an "Engineering vs Mathematics" argument that is heard in Universities all around the world. The mathematicians are not generally interested in solving real world problems. They are interested in generating math. Engineers are not interested in math, but need it to solve the 'real problems'.

My Solution to Number 5

[JohnPM]

I've solved it:

5 Riemann hypothesis Involving zeta functions, and an assertion that all "interesting" solutions to an equation lie on a straight line. It seems to be true for the first 1,500 million solutions, but does that mean it is true for them all?

Answer: NO it doesn't mean it's true for all of them. You would have to prove that.

Where do I get my money?

Re:My Solution to Number 5

[Phleg]

Well, theoretically speaking, a proof of the Riemann Hypothesis could depend upon the hypothesis being true for the first 1.5 billion solutions, so it would mean it's true for all of them, as long as the proof could be stated as a consequence of that condition.

Old news?

[Anonymous Coward]

Extracted from: http://www.nacho.unicauca.edu.co/Maticias/0309ConP oi/0309ConPoi.htm

Translated for better reading (I use to speak spanish):

Robinson, S., Russian reports he has solved a celebrated math problem, New York Times, 15 April 2003, F3

In November, 2002 appeared a rumor on the Internet saying that the mathematician Russian Grigory Perelman, from the Institute Steklov of the Russian Academy of Sciences in Saint Petersburg, had published in arXiv a preprint presenting a proof of Poincaré's Conjecture.

Trivial to prove / the description must be wrong.

[Anonymous Coward]

Uhm maybe that link describing the Ponticare conjecture described it incompletely, because the question as described is trivial to prove. I can see it geometrically.

Cut a 4 Sphere with a plane right down the center.

The cross section is a 3 sphere. Consider that section to be the section wrapped with your 3 sphere "rubber band".

Now move a short distance perpenducular to the this slice and take another slice. It will be a smaller sphere. You've just slide your "rubber band" down the apple a bit.

If you keep doing this the 3 sphere slices get small and smaller, converging to a point.

Viola, it's simply connected.

Re:Problems with the Millenium Problems

[chthonicdaemon]

I understand that it's supposed to generate "good mathematics" that will supposedly help us solve practical problems eventually .. but why not offer the reward for actual practical mathematics

Because practical mathematics already has a monetary reward?

How do you get your jollies?

[raehl]

If you're a math geek, you'll do things that let you sit down and work on problems.

If you're a sex fiend, you'll spend your time in the gym, and maybe convincing people to pay you hefty consulting fees to tell them things they already know.

If you're a musician, you'll be in a band, even if you'll never make more thana hundred bucks a gig.

If you want to be the richst man in the world, well, if I knew the answer to that I'd be the richest man in the world.

But if you're a guy who actually does like solving math problems, and someone comes along and offers you $1 million, it's probably pretty useless to you, sine it doesn't help you solve math problems.

(Ok, in reality, that's kinda short-sighted, as you could buy $1 million of computer time, but maybe he doesn't like computers.)

Re:How do you get your jollies?

[julesh]

But if you're a guy who actually does like solving math problems, and someone comes along and offers you $1 million, it's probably pretty useless to you, sine it doesn't help you solve math problems.

Yes it does. You invest it wisely and it means that you never have to worry again about whether someone will give you a grant to work on the problems you want to work on. The money represents freedom.

Re:How do you get your jollies?

[TuringTest]

But that assumes that your mathematician have the will and the knowledge to "invest it wisely"; it is perfectly possible for the matematician that the "invest money" is not at all an interesting one and that the imposed burden of following stock prices and market trends would make it a pain in the ass. If that is case a grant will be much more desirable since it will be given to you for achieving results in precisely the math problems that you like.

Re:How do you get your jollies?

[TeknoHog]

But if you're a guy who actually does like solving math problems, and someone comes along and offers you $1 million, it's probably pretty useless to you, sine it doesn't help you solve math problems.

I'd probably have written "cos it doesn't help you solve math problems." ;-)

Anyway, I for one would gladly take the million bucks. Spend it on musical instruments and computers to help me in things I'm interested in. Oh yeah, and pencils.

Re:How do you get your jollies?

[Ryan Amos]

Didn't we learn anything from Pi? Mathematicians shouldn't play the market. It makes them put a drill through their skull. Please, help save a mathematician today.

Re:How do you get your jollies?

[JayDoggy]

If you want to be the richst [sic] man in the world, well, if I knew the answer to that I'd be the richest man in the world.

That reminds me of my favorite Citizen Kane quote: "Well, it's no trick to make a lot of money... if all you want to do is make a lot of money."

Re:How do you get your jollies?

[AxelBoldt]

You invest it wisely and it means that you never have to worry again about whether someone will give you a grant to work on the problems you want to work on. The money represents freedom.

Every tenured math professor has that freedom. Luckily, math research is cheap, so all you need is some travel money, and that comes with the job.

Re:He's probably not even Russian

[varjag]

Russia is a heavily anti-semitic country.

Heavily? To the same extent that the USA is heavily anti-african-american, perhaps.

So tell the truth...

[raehl]

You just made all that up, didn't you?

This is Slashdot.

[raehl]

So the Whocarés Conjecture is obviously hypothetical.

sheesh

[Merovign]

Somebody needs to slap this guy and scream "TAKE THE MILLION BUCKS!!!!"

I cannot stand people who rub a lamp, get a genie, and then can't think of anything they want.*

It's like buying the last orange cream soda in the Gobi Desert Gift Shop, deciding you don't want it, and pouring it out.

If you think the money can be put to better uses, well then DO THAT.

* I'm not implying that this was luck. This behavior is worse than when it's luck and you're unprepared.

Book title?

[advocate_one]

At first glance I thought that a Russian had finally managed to read one of those holiday books and make sense of it... you know, those with titles like "The Bourne Identity", "The Omega Sanction"...

Computer Time

[appleLaserWriter]

(Ok, in reality, that's kinda short-sighted, as you could buy $1 million of computer time, but maybe he doesn't like computers.)

Computer time will only help with P problems, or P elements of NP problems. Great mathematicians seem to be NP-solving machines. A hundred years of computing time on the best computer might releive some of their tedium but would actually have an insignificant impact on their ability to solve problems.

The rest of us lesser beings might consider spending out time building a super-high resolution MRI machine. We'd want to be able to image every atom in a person's brain and record a year's worth of data at something like 100k samples per second. The MRI should be light and comfortable so our test subject could wear it comfortably for that year.

Once the suerp-MRI machine is ready, we manufacture it into a comfortable yet stylish (to the eyes of mathematicians) hat, and invite a prize-winning mathematician to wear it for a year.

At the end of the year, we need to locate some prize-winning neuroscientists to help us decode our brain scans and prize-winning computer scientists to help us build it.

Millennium, not millenium

[Stephen]

Just remember, it's from the Latin "annus", not "anus".

RTFA yourself?

[BACbKA]

I've just re-RTFA, and saw no new refs to anything from 2004 (care to quote what you're talking about?). Looks like a duplicate to me, although I am only for this kind of publicity for the proof - maybe another person would venture into verifying the proof based on this posting. Judging by the comments on this /. article, a lot of folks have seen the mention of Grisha's proof for the first time.

Re:RTFA yourself?

[Disevidence]

For fucks sake....

April 15--Russian mathematician Dr. Grigori (Grisha) Perelman of the Steklov Institute of Mathematics (part of the Russian Academy of Sciences in St. Petersburg) gave a series of public lectures at the Massachusetts Institute of Technology last week. These lectures, entitled "Ricci Flow and Geometrization of Three-Manifolds," were presented as part of the Simons Lecture Series at the MIT Department of Mathematics on April 7, 9, and 11. The lectures constituted Perelman's first public discussion of the important mathematical results contained in two preprints, one published in November of last year and the other only last month.

Read the things in bold. They might help you. The first slashdot article was about the first paper. This second paper has more details on the solution, hence the slashdot story is not a dupe. Next time you tell someone to RTFA, make sure your right.

Re:RTFA yourself?

[Disevidence]

WHOOPS. Scratch that last post.

I'm completely wrong. His last thing WAS last year, my bad.

Mod me down now.

Re:He'd post AC (OT)

[balloonpup]

Off topic, I know, but wow...where do you live that you can have a $700/mo payment on a house? My husband and I rent a loft for just a little over that price! *is indeed willing to move!*

Re:Confused

[BollocksToThis]

Thanks xoran, that's helped quite a bit. I think the summary on that page does a very poor job of explaining the problem. I imagined wrapping a rubber band around the donut like this:

O o

the small o is the donut, hole facing you. The large O is the rubber band - put your face against the scree and cross your eyes until they merge for the interactive ascii art version. It didn't occur to me to loop the rubber band THROUGH the hole. How could you do that without destroying the donut first? It all sounded like madness.

P.S: Mods, I was being half serious, half humourous - I don't know where you got troll and flamebait from, but I would like to suggest getting laid. Thank you.

1 billion = 1 yard

[horace]

In the good old days britain used the following system for large number naming:
10^(6*2^(n-1))= n=llion
so that
million = 10^6
billion = 10^12
trillion = 10^24
etc which has the advantage of making it easy to know whether you should say a million billion, a thousand trillion or a quadrillion. It is also far more economical with the use of names.

Official usage now is the much less pretty American usage 10^3(n+1) = n-llion so:
million = 10^6
billion = 10^9
trillion = 10^12
and so on.

In the financial world the word milliard still lives on in the abbreivated form "yard" or perhaps "'iard" to refer to a billion. It is quite disappointing when you learn that a trader talking about a yard of yen does not mean a three foot stack of bills.

Why aren't proofs verifiable via software?

[grumbel]

One thing I don't get is why isn't there some software out there to verify the proofs? I mean math follows rules and these rules should be convertable into a piece of software, shouldn't they? So why do I always read that somebody might have proofed this and that, yet nobody has yet verified it and often there are even just a few people with enough knowledge to verify the proof at all so it takes quite some time until a proof get verified.

I am not talking about having a computer generate the proof itself, which can be difficult of course, I am just talking about verifing a given proof.

Re:Why aren't proofs verifiable via software?

[Carewolf]

The same reason you don't prove every program you write is mathematically correct. It is not very compatible and a lot of hard boring work.

(In fact it is usually so much work, the chance of an error in the proof-reader is greater than the chance of an error in the proof)

Re:Why aren't proofs verifiable via software?

[stevelinton]

A lot of work is done on proof-checking in AI, but even so, writing up your proof with enough detail and formality to be machine checked typically increases its length by a factor of 10, sometimes more. A very complex program can then convert this into a MUCH longer, but really fully detailed proof. A rather simple program can then check this final proof. Then, if the premises and conclusions are correct, and you believe the simple program then you really have checked your theorem.

Re:Why aren't proofs verifiable via software?

[narcc]

I am just talking about verifing a given proof.

The real bitch about the whole thing is proving that your program is valid. (That's no fun for even trivial programs.)

Of course, you then have to show that the process was carried out without error. (Computers aren't 100% accurate all the time. Any number of unknowns can "creep in and flip a bit" [so to speak] and ruin your calculation.)

There are a good number of papers, iirc, that mention the problems with the computer "proof" of the four-color theorem.

Re:Why aren't proofs verifiable via software?

[TeknoHog]

The real bitch about the whole thing is proving that your program is valid.

I agree; IANAM but I believe it's a problem with higher levels of abstraction. You need to have a metamathematics to deal with a proof in mathematics. Then your program is actually a problem of metamathematics, and you need metametamaths to prove that...

Re:Why aren't proofs verifiable via software?

[Phleg]

How exactly would you go about proving, in a purely structural language, that one statement or at worst one "concept" implies another?

Re:Why aren't proofs verifiable via software?

[praxis]

I might use Prolog or another logic programming language to go about proving that one statment implies another, but only if the statements may be codified using set theory. If by "purely structural" you mean procedural, then my suggestion is invalid, but if you mean simply deterministic, then try out Prolog.

Re:Why aren't proofs verifiable via software?

[voodoo1man]

Even though mathematicians like to claim that all their proofs are "formal," there's really no such thing. The amount of background lemmas, axioms and facts needed to prove even elementary mathematical statements is so large that even 1st year maths students use arguments based on abstractions, previous results, and plain old assumptions ("it's trivial to see that..." is a favourite statement). As BrotherZeoff has recommended, take a look at GEB - you'll see pretty quickly that even the most obvious of facts takes pages to prove in a formal logic system. This is why it so frequently happens that proofs are rejected after peer review - the author neglected the validity of some lemma or made assumptions that were incorrect, and he missed them in proof-reading or their consequences didn't even occur to him. The amount of background knowledge needed to machine-verify this particular proof is immense, and would take many times longer to represent than it would for a committee of expert mathematicians to peer-review the proof (and as others pointed out, you'd need to verify that no mistakes in representing that knowledge were made!). Even though you can generate the knowledge from the axioms of topology, that would be akin to generating the proof, and as you pointed out this is far from feasible (it's basically a giant tree search - there's really no shortcut for these things). I guess someone could try to build a mathematical (or at least topological) version of Cyc - a giant ruleset of relevant mathematical theorems. But if even you could find enough mathematicians (and money to pay them) to do this, chances are it still wouldn't contain all the lemmas needed to prove this or that particular theorem.

However, this does bring an interesting idea to mind - a wikipedia-like, distributed theorem database and prover. Anyone can add theorems and their proofs to it, like wikipedia, which would be verified by distributed clients, like SETI, and then added to the database as lemmas for future proofs. If you start with enough true theorems, new ones can be accumulated pretty quickly, while the fact that all of it follows formal logic means that no false facts can ever be added (although the possibility for DOS attacks is pretty significant).

Re:He'd post AC (OT)

[Almost-Retired]

In one of the nations poorest states, in one of the hardest hit by loss of jobs recently, Lewis County, West Virginia. When I met and married my current wife 15 years ago, she had a house, on a 30 year contract at about 400 a month, doing that on a school teachers salary. When I finally got my own head above water financially (the 2nd ex left me a hell of a mess with the irs, but as a tv Chief Engineer, I made quite a bit more than she did teaching school) the first thing I did was refinance it for 7 years at 6%, at a hair under 700/mo. Been paid off now for about 7 or 8 years.

West Virginia can use a few selected people who are willing to come here. Jobs can be had, but may not be everyones cups of tea. With oil back up, well drilling has started up again, which has taken up most of the slack from the closeier(sp) of several glass making operations due to far eastern imports cutting the market for our higher priced hand-blown products. Basicly, he who is willing to work, can usually find work. It may not be at what one would call the prevailing scale, but then neither is the cost of living here (older places in bad need of some sweat equity can be had for under $20k) other than its almost de-rigor for the first vehicle to be a 4wd. There is one thing we've got planty of, and thats hills. Right up in your face hills.

I seemed to have fit right in when I came here as I am essentially self-educated in electronics and have been making my living making electrons do interesting work since the late 1940's. My highest 'formal' education is the 8th grade. But in local tv broadcasting, I am a very big frog in a quite tiny pond, spending the last 20 years in that office/workshop. With all the perks added in, I was making more than $60k when I retired.

To give you an idea of the climate here for technical jobs, about 10 years ago I gave a 10 explanation of how tv works to a bunch of 8th graders touring the station as an end of the school year perk. I finished up by saying that my job keeping all this working was an interesting job, but that someday I would retire, and I wanted one of them to be nipping at my heels wanting to replace me. 30 some 8th graders laughed their collective asses off, they didn't understand that like shoveling shit out of the cowbarn, somebody has to do it. I'm an old Iowa farm kid, so I know about shoveling shit out of the cowbarn too. So I wrote that possibility off and never mentioned it again to an end of the school year tour group. AFIAC, it was their loss, not mine. I rather enjoyed being the old man on the mountain, the guru if you will, that when things went to hell, got the phone call. Of course, 2.5 years after I retired, I still do. No one knows that 40 year old GE transmitter (locally anyway) like I do. OTOH, I get paid to answer the phone too, which helps in the health insurance dept. :)

To put something in here thats not OT, I would hope that this russian does take the money, and that he has more sense than to turn into a russian version of Jack Whitaker, who won the lottery here for about 140 mill 2 years ago, and has had nothing but legal problems since. He's also been mugged & left for half dead several times since everyone knows he carries several hundred $K around with him as he frequents the bars. IMO, thats not what winning the lottery should be about.

The russian would be similarly targeted as one to be taken advantage of if he had that kind of money at his disposal. Because of this, he may see it as a less than ideal situation. If he was smart, he'ed open an account here, and have a regular funds transfer to there of maybe 1 or 2 hundred a month setup in perpetuity. That amount would go a long way in raising his standard of living I'm sure. As to how to assure he got it when the russion mafia probably owns the local bank there, I don't know.

Cheers, Gene

Millenium Problems ?

[RomanTotaleXVII]

Solving a Millenium Problem carries a reward of $1M

Is one of them spelling millennium correctly ?

some terminology

[njj]

I'll try and explain what the Conjecture is, because it's not entirely obvious. First of all, I need to explain what the 3-sphere is.

The n-sphere (which mathematicians generally denote by S^n) can be thought of as `all points in (n+1)-dimensional space which are at unit distance from the origin'. So S^2 is the surface of a solid 3-dimensional ball. This sometimes surprises people, who expect this to be S^3 but the key observation here is that the 2 refers to the intrinsic dimension of the object, rather than the extrinsic dimension of any space you might happen to put (`embed') the object in. The fact that we often think of the 2-sphere as being embedded in 3-dimensional space doesn't change the fact that it's inherently a 2-dimensional object. An ant wandering around on it still only has two degrees of freedom.

The 3-sphere (S^3) locally looks like ordinary, flat, Euclidean 3-space, but on a larger scale it kind of doubles back on itself - if you keep walking (or floating) in a `straight line' (well, actually the 3-dimensional analogue of a `great circle', but never mind) in any direction, then you'll eventually get back to where you started.

The Poincaré Conjecture says

Any homotopy 3-sphere is homeomorphic to the 3-sphere

This, by itself, isn't particularly enlightening to the non-topologist, but what it actually boils down to is:

Any closed, compact, simply-connected 3-manifold is homeomorphic to the 3-sphere

What does this mean?

Well, an `n-manifold' is a space which locally looks like ordinary, flat, Euclidean n-dimensional space. So a 3-manifold is a space (like S^3) which locally looks like ordinary 3-space (but which might twist back on itself in a peculiar way on a larger scale).
`Closed' means that the 3-manifold doesn't have a boundary - no matter how far you walk, you're not going to run into a brick wall, or fall off the end. `Compact' is a bit more technical, but in this context essentially means you don't get odd shooting-off-to-infinity stuff you have to deal with.

And `simply-connected' means that the first homotopy group (the `fundamental group' of the space) is trivial. What that means is that any closed loop (of string, if you like), in the manifold, can be continuously shrunk down to a point. Here `continuous' means that you're not allowed to cut or glue the string while you're doing it.

To use a 2-dimensional analogy, the 2-sphere (the surface of the 3-dimensional ball, remember, or alternatively a British doughnut) is simply-connected, because given any closed loop in the surface, you can shrink it down to a point without it getting snagged on anything. Whereas the 2-torus (the surface of an American doughnut) isn't, because you can't shrink all closed loops down to a point - one which goes all the way round the central hole, for example, can't be shrunk.

Finally, `homeomorphic' is basically a technical word for `topologically equivalent' - we allow continuous deformations (stretching, twisting, etc, but not cutting or pasting), rotations, reflections, or any combination of these.

So, the (classical) Poincaré Conjecture is essentially a technical way of saying ``If it looks like a 3-sphere then, basically, it is''. (For certain definitions of `is', and `looks like'.)

The analogous conjecture in n-dimensional space is known to be true for n=1 (trivial), 2 (pretty simple), and 5 and above (the 5-dimensional case was proved by Zeeman, who is my PhD grandsupervisor - my supervisor was one of his students). The 4-dimensional case is weird, and there are three different forms to consider - the `piecewise linear' and `topological' cases have been proved, but the `smooth' case is still unproven.

As I understand it, what Perelman claims to have done is prove Thurston's Geometrisation Conjecture, which implies the Poincaré Conjecture as a special case - rather lik

Re:some terminology

[tengwar]

Can you give some idea of why n=3 is hard?

Re:some terminology

[njj]

I don't understand the finer details myself, but here goes. The 1- and 2-dimensional cases are relatively easy to prove, but the case n=3 is sufficiently complicated that those methods aren't sophisticated enough.

Similarly, although the higher-dimensional (n>4) cases are progressively more complicated still (with weirder and weirder behaviour possible), more sophisticated techniques become feasible, which don't work in lower dimensions. Also, a lot of interesting questions in 3- or 4-dimensions become trivial in higher dimensions.

For example: You can knot a (1-dimensional, embedded) string in 3-dimensional space - and indeed there's a rich branch of mathematics which is devoted to studying the different ways you can do this. But you can't knot a string in 4-dimensional space, because there're are sufficient degrees of freedom to allow you to untie it.

This is tricky to visualise, but think of the 3-dimensional `slice' of 4-space which the knot is resting in. Take a small section of the string and push it slightly in the fourth direction. In the main 3-dimensional slice, there's now a gap in the string, which we can use to untie the knot - pass the knotted bits of the string through this gap until we're left with a straight length of string with a gap in it. Now push the `missing' bit of string back down into the main 3-dimensional subspace. At no point have we cut or glued the string, but we've untied the knot.

(There's an excellent and very readable book on higher dimensions: The Fourth Dimension (And How To Get There) by Rudy Rucker.)

Basically, what's happening here is that there's enough `room' (for want of a better word) in 4-space to make the interestingly nontrivial behaviour we see in 3-space (namely the possibility for knotting 1-dimensional strings) fail to happen.

And, from what little I understand of the details of the Poincaré Conjecture, there's an analogous thing happening there - the techniques which enable the solution of the higher-dimensional versions of the Conjecture aren't applicable in lower-dimensional space (specifically 3-space) because (in some hand-wavy, technically imprecise sense, at least) they rely on having a little bit more room to manoeuvre.

This is why 3- and 4-dimensional topology is quite a popular field - lots of interesting nontrivial things happen which don't happen in higher dimensions.

No, he is a Russian (or St. Petersburger) first

[hughk]

after all, didn't he choose to return to Russia?

Actually where the Steklov Institute of Mathematics is, St. Petersburg, is a beautiful city and he decided to return from the US to live there. Others would too, if it wasn't for the idiots currently running the country.

Lastly, it is useful to remind people that there are excellent mathematicians and software developers there and you don't always need to go to India for offshore solutions.

Clearly you've never watched...

[Disc2]

...who wants to be a millionaire.

MODERATORS - plagiarism / karma whore

[Anonymous Coward]

The author of the parent post claims to explain the conjecture from the point of view of a "MS Mathematics". This would be fine if the explanations had not been copied directly from MathWorld.

Quote from the parent post:

The n = 1 case of the generalized conjecture is trivial, the n = 2 case is classical (and was known even to 19th century mathematicians), n = 3 has remained open up until now, n = 4 was proved by Freedman in 1982 (for which he was awarded the 1986 Fields Medal), n = 5 was proved by Zeeman in 1961, n = 6 was demonstrated by Stallings in 1962, and n >= 7 was established by Smale in 1961 (although Smale subsequently extended his proof to include all n >= 5).

Now please compare this with the middle paragraph from http://mathworld.wolfram.com/PoincareConjecture.ht ml. The one that starts with "The n = 1 case of the generalized conjecture is trivial, the n = 2 case is classical (and was known even to 19th century mathematicians), [...]"

This is just an example. Other paragraphs can be found in MathWorld's pages about the Poincaré conjecture, definition of manifold and compact manifold, homeomorphic, etc.

Now I don't mind if some useful information is posted on Slashdot. But some obvious plagiarism like that without crediting any sources definitely deserves some Overrated treatment...

Re:MODERATORS - plagiarism / karma whore

[Tony-A]

MS Mathematics is a degree, not a point of view. MS is better than as BS, but far short of a PhD. It means that I'm not totally clueless, but falls far short of implying that I've got much of an idea what I'm talking about.

translate matheese-to-english and summarize in a way we can understand?

This was an attempt at translating. Translations are not originals.
This was an attempt at making the "matheese" maybe a bit comprehendable to us mere mortals. Of course I'm trying to put down accurate definitions, from the best available source.

Re:MODERATORS - plagiarism / karma whore

[Kardamon]

[flamebait] So, Wolfram gets plagiarized... Cool, it's what he deserves: Wolfram did not give credit to Konrad Zuse (or anybody else) when he made up this nonsense.[/flamebait]

unapologetically off-topic (my post, that is)

[bodrell]

I just have to make a comment about the Dodge Caravan.

This is completely anecdotal, and in this case the expression "your mileage may vary" is especially apt, but the Dodge Caravan is the reason why I will probably never buy an American car. Or van, in this case. My family made the mistake of getting one several years ago. I believe it was a 1985 manual transmission (not many of those made, either). That piece of shit just kept falling apart, piece by piece. The interior plastic crap broke off at the slightest touch. The ceiling fell down (the cloth covering, that is). But the coup de grace happened at the most inopportune time. We were on a family trip, about 1000 miles from home, when the engine exploded. I don't know which part of it broke, but it sprayed oil all over the windshield while we were on the highway. Luckily my dad had plenty of spare oil, and for about 50 miles we would stop every 5 miles, wipe off the windshield enough to see, add another quart of oil, and get back on the highway going 35 mph.

That engine had less than 90k on it. My dad used that incident to illustrate the principle of "built-in obsolescence" and it's a lesson I never forgot. Since that point, my family has not purchased another American car. Exception: until very recently, there were no Japanese full-size trucks, so we did get a Ford F250 to haul building supplies. American trucks do seem slightly more sturdy than the cars. Now we get old Mercedes diesels. You can get one for less than $3000, and they'll run for up to half a million miles if you're careful. It sure seems like a more financially sound strategy than purchasing a Dodge Caravan for four times that amount.

That said, I wish you luck with your Dodge Caravan / Plymouth Voyager. Maybe we just got a lemon, but I've never seen a lemon Mercedes (or Honda, or Toyota, or Nissan . . . ).

Re:unapologetically off-topic (my post, that is)

[Almost-Retired]

Well, this is the 3rd one of them we've had in 15 years. The first, which may remind me of your story, had a 2.2L 4 in it, and so help me God, you had to shut off the air conditioner to get across the intersection before the light turned red again. And, like yours, it self-destructed, but it waited till we'ed replaced the head once at about 120k miles, and then it ran for another 75k miles before the pan suddenly wasn't quite big enough for all the parts as the wife was going bowling one night. But, it had been pretty decent in the mileage dept, and had carried us quite a ways, so whan I went looking, I considered that she was still teaching school as a traveling elementary music teacher who carried about 500 pounds of stuff from school to school every day, and found another van, a 92 to replace that old '85 model. This one had a 3.6L V6 that had at least 5x the giddyup the 4 had, capable of burning rubber on the takeoff should you want to abuse it that way.

It had 50k on it when we bought it, and when the headlights got so yellow we had to check with a flashlight to see if they were lit, I traded it off on this '97 we have now, writing a check for the $12k difference not too long before 9/11/01. It had 60 on it then, and took immediately several dashboard teardowns and a new clockspring in the steering column before all the controls worked right, that item miss-installed at the factory. That dashboard, when fully dissed, takes up the whole front yard! It now has 106k on it, and I managed to muss up the right front corner about 3k worth this spring, (first time I've had to call the insurance folks for something that happened with me behind the wheel since July 1968!) so I had a good excuse to replace the headlight on that corner. So its nice and bright yet while the one on the left is showing signs of yellowing already at 7 years of age. 'twouldn't be so bad but just the replacement plastic headlight, no bulb in it, is $280 from the aftermarket folks, and almost $400 from chrysler. That, pardon my language, is fscking ridiculious. But, instead of having cookie cutter 5x7 glass ones they can sell for $17 at wallyworld, each maker has to put his 'styling' trademark on a different unit each year, and sometimes several different models in a year will use unique moldings. Thats no way to have any 'economy of scale'.

The headlights lesn plastic turning yellow is such a problem for the last 20 years that I've considered mounting a class action federal suit to make all makers doing business in the states replace them with glass lights as a safety recall. A 5 year old set of those things, even with fresh lamps installed, is only half as bright as when new. I've measured them with a light meter.

Couple that with chryslers penchant for a headlamp rated at 45/40 watts hi/lo, (so they don't have to put a bigger, gas hogging alternator on the vehicle) and you got a whole generation of people driving around in the dark, looking for a good place to have an accident.

At my age, with the dark adaptation going to hell in a hand basket (I'm double doomed in that dept, I have excellent color vision, and you can be colorblind and see well in the dark, or have good color vision but can't see at night worth a toot), the temptation to hang extra driving lights on the rig is quite strong. I'm also well aware as an electronics type, that an extra 110 watts worth of H3's, is way more than that puny little alternator can handle and live to tell about it.

Sigh, you used to be able to hit the junkyard and find a good used 75-100 amp alternator for a $50 bill or less, but now its $200-$400 because its rare, and you couldn't make it fit without access to a full-fledged machine shop to make its brackets and get the pulleys to line up. And then there might not be space left for it if its bigger around, they use every millimeter in the engine compartments today. Or how about a 2" longer serpentine belt? Only by accident from some other maker probably. Murphy's Law and all that.

Stop the w

Re:unapologetically off-topic (my post, that is)

[bodrell]

Very interesting. My family's Caravan died before it ever got yellow headlights. Thanks for the response ;)

Re:PoincarÉ

[Anita Coney]

"Is it that difficult to respect international spellings?"

Yes.

Godel, Escher, Bach

[BrotherZeoff]

If this question interests you, you need to read Godel, Escher, Bach: The Eternal Golden Braid.

It's an awesome read, full of theory, exposition, and fables to explain the theory. The main idea behind the book is to explain Godel's proof that there are some things which are true but unproveable. There's a lot more to it, though, and it will stay with you for the rest of your life.

Re:Godel, Escher, Bach

[man_ls]

I just bought the book for $15 based on your recommendation, from Amazon.com. It looked interesting.

Hope it's worth it :)

Re:Can't TAKE ANY MORE!

[love2hateMS]

People, money is good. I repeat, money is good.

The only people who sit around talking about how bad money is are:

1. People who don't have any because they are lazy and not willing to put in the effort.
2. People who have it but didn't work for it and have the luxury of sitting around pontificating about a world they barely participate in. (ie. most of Hollywood)

consequences?

[Darth_Burrito]

Does this have any real world consequences? Like I know if P=NP and P ain't that bad, there could be dogs and cats living together, mass hysteria, giant marshmallow men in new york, etc... What about this?

Einstein & Poincaré

[Kardamon]

Einstein's paper "On the electrodymanics of moving bodies" contains nothing new. It was actually Poincaré who was the first to correctly state the special theory of relativity (the transformation formulas were found by Woldemar Voigt in 1887, H.A. Lorentz in 1892, Sir Joseph Larmor and others)

In 1898, Poincaré attacks the distinction Lorentz and Larmor make between "local time" and "universal time": "Nous n'avons pas l'intuition directe de l'égalité de deux intervalles de temps. Les personnes qui croient posséder cette intuition sont dupes d'une illusion... Le temps doit être défini de telle facon que les équations de la méquanique soient aussi simples que possible. En d'autres termes, il n'y a pas une manière de mesurer le temps qui soit plus vrai qu'une autre; celle qui est généralement adoptée est seulement plus commode. ...Il a commencé par admettre que la lumière a une vitesse constante, et en particulier que sa vitesse est la même dans toutes les directions. C'est là un postulat sans lequel aucune mesure de cette vitesse ne pourrait être tentée. Ce postulat ne pourra jamais être vérifié directment par l'expérience; il pourrait être contredit par elle, si les résultats des diverses mesures n'étaient pas concordants. Nous devons nous estimer hereux que cette contradiction n'ait pas lieu et que les petites discordances qui peuvent se produire puissent s'expliquer facilement. ...c'est que je veux retenir, c'est qu'il nous fournit une règle nouvelle pour la recherche de la simultanéité... Il est difficile de séparer le problème qualitatif de la simultanéité du problème quantitatif de la mesure du temps; soit qu'on se serve d'un chronomètre, soit qu'on ait à tenir compte d'une vitesse de transmission, comme celle de la lumière, car on ne saurait mesurer une pareille vitesse sans mesurer un temps. ...La simultanéité de deux événements, ou l'ordre de leur succession, l'égalité de deux durées, doivent être définies de telle sorte que l'énoncé des lois naturelles soit aussi simple que possible. En d'autres termes, toutes ces règles, toutes ces définitions ne sont que le fruit d'un opportunisme incoscient." (H. Poincaré, La mesure du temps, in Revue de métaphysique et de morale 6 (1898), pp. 1-13)

In 1902, Poincare writes there is no absolute time and no absolute space: "1 Il n'y a pas d'espace absolu et nous ne concevons que des mouvements relatifs... 2 Il n'y a pas de temps absolu; dire que deux durées sont égales, c'est une assertion qui n'a par elle-même aucun sense et qui n'en peut acquérir un que par convention... 3 Non seulement nous n'avons pas l'intuition directe de l'égalité de deux durées, mais nous n'avons même pas celle de la simultanéité de deux événements qui se produisent sur des théâtres différents; c'est ce que j'ai expliqué dans un article intitulé la Mesure du temps; 4 Enfin notre géometrie euclidienne n'est elle-même qu'un sorte de convention de langage; nous porrions énoncer les faits mécaniques en les rapportant à un espace non euclidien qui serait un repère moins commode, mais tout aussi légitime que notre espace ordinaire; l'énoncé deviendrait ainsi beaucoup plus compliqué; mais il resterait possible. Ainsi l'espace absolu, le temps absolu, la géométrie même ne sont pas des conditions qui s'imposent à la mécanique; toutes ces choses ne preéexistent pas plus à la mécanique que la langue francaise ne préexiste logiquement aux vérités que l'on exprime en francais."(H. Poincaré, La science et l'hypothèse, 1902

Re:Problems with the Millenium Problems

[njj]

This sounds like a typical excuse for universities to get more grant (much of which is tax) money - delusions of practical application "if only we get just a little more money, we could do so much!" (the cries of which are repeated every year).

This is a valid concern, and you're certainly not the first person to voice it - indeed, it seems to have become not just ok, but actively encouraged for government education ministers to rant about how taxpayers' money is being wasted on frivolous matters (before getting into their chauffeur-driven Jaguars and heading off to sumptuous gourmet lunches).

It's something I've thought a lot about, myself - I've spent thousands and thousands of pounds of my own, hard-earned and carefully-saved money over the past eight years, funding myself through an MSc and then a PhD in pure mathematics. Not because I thought it would boost my salary, or anything, but because I wanted to learn more about something which interested me. I don't begrudge a penny or second of the money or time I spent doing it - it changed my life, it changed the way I think about everything, and I learned a lot of fascinating stuff along the way.

What it boils down to, I guess, is that if you want to live in a cultured, advanced society (and you should, if only because of the fringe benefits like the general population being healthier and longer-lived, and the crime rate being lower, and so on - but also because it makes life a lot more interesting) then you have to pay people to find out new stuff. Some of this will be practical things like engineering or applied science, some of it will be less practical stuff (like pure science or mathematical research) which might at some point turn out to have practical applications (and both mathematics and `blue-skies' scientific research has a pretty good record in this regard), and some of it will be entirely impractical stuff like art or music.

We simply can't rely on private corporations to fund this sort of stuff - with a few notable exceptions (such as Xerox PARC) they generally have an intensely short-term, practical viewpoint on research - if it's not going to start bringing in hard cash within a couple of years then they don't tend to bother. And there's no particular reason why they should - that's not what they're for.

So what does that leave? Charities and central government, basically. And central government means our tax money.

Do I begrudge my tax money being spent on dubious private finance deals where some private company profits immensely from knocking down a perfectly serviceable hospital, selling off the land, and building a new, smaller, less well-equipped hospital further away? Well yes, actually, I do. Quite a lot, in fact.

Am I irked that a phenomenal amount of UK taxpayers' money is being used to wage a dubious (and catastrophic) war halfway round the world, for the benefit of Texas oil-barons and the Halliburton board of directors? Very much so.

Do I begrudge the Arts Council using (a far tinier fraction of) my tax money to fund Damien Hirst to pickle a sheep's carcass in a tank of formaldehyde? Not for a second. I might think he's a nutter for doing it, and I might not necessarily want to see it when he's done it, but I'm glad to live in a civilisation where people are trying out things like that, for no other reason than they think it might look nice, or interesting, or encourage people to think or look at the world in a slightly different way.

Does a Mozart string quartet directly generate money? No - or at least not much, and not for very many people. But it enhances the world in so many ways, and inspires and motivates the people who listen to it. There are numerous anecdotal cases of important scientific insights being triggered by a piece of music or a painting.

Mathematics is a bit of a hybrid, really. It's `blue skies' research, done purely for its own sake, but it has an unreasonably good track record of turning out to be really useful someti

Ironic

[blackest_k]

That an article reporting on a mathematical problem being solved
equates 1 million dollars = 560 Million pounds!

http://story.news.yahoo.com/news?tmpl=story&cid= 85 7&ncid=757&e=10&u=/nm/20040906/od_uk_nm/oukoe_scie nce_maths

Re:Problems with the Millenium Problems

[Anonymous Coward]

You're right because you can't see anything practical coming from it? *That* makes you right? Someone needs to take some logic courses.

Riemann hypothesis

[irf]

this may also be of interest, it appears that
another one of the so called "millennium problems",
may have just been solved, that is Riemann
Hypothesis:-
http://www.vnunet.com/news/ 1157891
we are all lucky to live in such exciting times.

Re:Ironically it was Poincarré (not Einstein)

[Kardamon]

Oh, I've followed your link and now I understand why you've been modded flamebait: this is just anti-semitic bullshit.

Re:He'd post AC (OT)

[4of12]

I'm glad you've found a way to make it work for you.

But it's a precarious world.

For folks with less mental acuity in West Virginia, they'll spend less time enjoying the beautiful mountains and forests of the state and most of it underground mining coal.

Or making metal in a mill, surrounded by concrete, bad smells, and loud noises

Or on their feet making fast food or cashiering in a convenience store.

But I agree, the key to a lower stress life is to live well within your means.

Except...

[Civil_Disobedient]

What's often overlooked in Maslow's heirarchy of needs is the fact that it is a heirarchy. In other words, it's all well and good to be self-actualized, but you need to have your rent and food bills covered first . You can't just skip from "poor starving genius huddled in an alley scrawling your brilliance in feces on the walls" to "self-actualized."

Re:Can't TAKE ANY MORE!

[Retric]

*I don't think money is BAD*

BUT, while some money is good more money can be almost useless. As a 24 year old making 46k a year who is having trouble finding things to spend money on I can say there is a threashold where it stops being more usefull.
Books LT 200$ a month
Food LT 300 $ a month
Car LT 400$ per month (I live 5 miles from work so it's cheep to have an old car.)
Rent + utils LT 900$ per month have a roomate I like
phone 30$ a month
Everything else LT 300$ a month.
Hmm, mabe I should put more than 8% into my 401k or something but I like having 4k in the bank. Hell mabe I should get my little sister a laptop I mean I got my mother one last year but kate say's she is happy with her desktop so what's the point? While I will soon start making mid 60's or more what am I going to do, dump the roomate and retire early or get a wife and kids?

O well not that far from my next review and if I only get 8k like that time I will probably walk and get a real job after having gotten that ever so important 2 year's exp after college. But, what do I say to those friends making 80k who say I could get you a job just send me my resume it's hard to be motivated when somedays you can't but think "I can finaly undersand my dad's old saying; 'I could do this or that and make a lot more money but what's wrong with 100k?' I mean shure he had kids but we could have made more and we spent more but what would have been the point?"

Re:Duplicate?

[goodydot]

1. slam the revolving door by pushing it backwards 2. disconnect the revolving door and slam it to the ground 3. I don't have a revolving door you insensitive clod! 4. call it names and tell gross stories about the revolving door 5. having sex with a revolving door is publicly humiliating 6. quick quiz: which president had a 'revolving door' policy? 7. have you SEEN the revolving doors of today? 8. all your revolving doors are belong to us 9. ?????? and the number 10 way to slam a revolving door? 10. profit

Bah!

[HungSoLow]

Call me arrogant, call me a troll ..

If he truly had a brain in his head, he would accept the million and donate it to some organization/charity that needs it!

Re:Problems with the Millenium Problems

[sexylicious]

I might needd to check my math history a bit, but I can't think of any major mathematics which were developed for a specific practical purpose since about Gauss.

Well, the Finite Element Method and the resulting analytical techniques were developed int he 1950's at the University of Washington. That type of analytical math is used for dynamic modeling of structures, fluids, electronics, and a few other things. It's calculus of variations at its core, but a more powerful technique in its field.

A better example would be statistics. Most any cutting edge physics involves statistics in some way. Statistics is also the basis for quantum mechanics.



As for Perelman's results, it can be summarized as follows:
Any 3-dimensional surface is made of a superposition of surfaces with loops, and those without loops. (Looped surfaces means that a coffee cup and a torus are the same.)
Out of all the 3-dimensional surfaces known, only the sphere is the simplest.

All surfaces in 3-dimensions consist of a sphere and any combination of looped surfaces. Open surfaces are not included in this new definition.

That last was Poincare's conjecture. Perelman proved that the simplest object in 3-dimensions is a sphere, and successively more complex surfaces are made of a sphere superposed with looped surfaces (donuts).

What this all means for the rest of us? Not much, other than physics has a more stable foundation in math (for 3-dimensions.)

Re:He'd post AC (OT)

[balloonpup]

Well, the technical/non-technical jobs thing isn't an issue, really, for me, nor if I can get a job there. I'm a trucker for a national company and they don't really care where I live -- it just changes where I go when I'm off. I'll have to check it out. Thanks for all the info! *off to ponder*

Muppet

[musselm]

Now that would be news, if a Muppet solved the Poincare Conjecture:)

Re:Muppet

[bill_mcgonigle]

Now that would be news, if a Muppet solved the Poincare Conjecture:)

Thanks for the wonderful mental image of Animal eating Poincare!

Re:Can't TAKE ANY MORE!

[love2hateMS]

Interesting reply. Let me give you something to think about. Concentrate on improving yourself, and let the salary be the vehicle that allows you to do that. I've been taking university courses for years just for the fun of it. I've taken everything from aeronautical engineering to women's literature to philosophy (to political science, history, psychology, sociology, blah blah blah). Money is freedom to constantly grow yourself.

Best of luck!

Re:Duplicate?

[1arkhaine]

But, when you slam a normal door, you are slamming it against the frame of the door, which I would consider to be distinct like a lock would be distinct. It's not like the door just slams onto itself, it slams on to the wood (or whatever) around it that forms a case of sorts. Hmmm.

Claymath explanation not common sense

[ktorn]

Imagine a rubber band passing through that hole

Ah, that's the bit I needed to read.

I kept thinking about the rubber band stretched along the outside ring of the donut, not through the centre. Because it's common sense that you can't stretch a rubber band through the hole without braking it (or the donut) first.

So, now I know what they mean by "somehow been stretched in the appropriate direction around a doughnut".

Thanks! You should be writing the explanations for claymath.org.

In the interest...

[memco]

of thoroughly exhausting all possibilities before you explain you method, let me point out one last detail.

"Think nothing is impossible? Try slamming a revolving door."

This was your original challenge, you didn't specify in what way or any restrictions. Therefore, all the solutions provided technichally fit your challenge, thus all were correct. Each time a new solution was provided you provided a new challenge involving more restrictions, so before you call everyone else's solution invalid, you shouold recognize that this was a result of your being incomplete in presenting the challege. That said, please enlighten us on how to slam a revolving door.

Re:In the interest...

[Derg]

its a matter of pessimism vs optimism. You see a statement that says Slam a revolving door, and you see a slew of options. I see it and see one, slam the door, using nothing but the door. So in essence, we are both correct, just depends on your stance, pessimist or optimist.

as was no doubt pointed out elsewhere, my solution, (though I saw another in another post) is to warp the dimmensions of the door, whilst one of the pannels swings free of the track. I pass a door of this type everyday on my way to work (411 w wisconsin ave, milwaukee... the door, not my job). Nobody ever said the door was made of static materials. Just warp one pannel, out lets say half an inch, or shrink the jam by half and inch, as the door continues to freely swing, BAM! It slams against itself. Slamming a revolving door. (the other solution I will agree falls under the strictest sense of the challenge involves knocking the door off its center post, causing it to tip onto its side.)

any other solutions, not involving foreign and extraneous objects?

Re:He's probably not even Russian

[varjag]

Maybe am mistaken, but isn't "African American" a common P.C. speak for dark-skinned people of African origin?

Anyway, my point was that Russia isn't too antisemitic since about mid-50s. There are people who hate jews, but then there are no less people who hate e.g. russians, or chechens, or whomever there as well. In other words, your typical multi-national society.

wow

[Mika24]

ok (trying) to read and understand the millenium problems makes me feel dumb. but that aside what practical uses do any of these solutions or problems have?

Re:Trivial to prove / the description must be wron

[Tyndmyr]

Note that if you take any 2d slices(where one dimension is the one not applicable to the rubber band) of the 3d sphere and rubber band converging, you'll notice two points converging... This might be over-simplification, but it appears a similar view would be applicable to your solution. So long as one of the dimensions of the 3-d "slice" contains the one the 3-d band is not in, all is well. I see no reason why this would not hold true for an apple of x dimensions, where the band around consists of x-1 dimensions.