Slashdot Mirror
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.
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).
/. come form "anonymous cowards" sitting in their offices at MIT. What a god.
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
"...all the labours of the ages, all the devotion, all the inspiration, all the noonday brightness..." yada yada
RTFA. He published another paper on it recently.
Think nothing is impossible? Try slamming a revolving door.
"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!
Open Source Sushi
1,000,000 USD is about equal to 560,000 GBP, not 5.6 million GBP.
English is easier said than done.
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.
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)
Is it just my observation, or are there way too many stupid people in the world?
His answer to the problem was "42".
- Greg
Start a happiness pandemic
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.
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.
READY.
PRINT ""+-0
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.)
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.
- sm
I'm joking, but you're still an idiot.
"A language that doesn't affect the way you think about programming, is not worth knowing" - Alan Perlis
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.
What's your damage, Heather?
...we must not have a poincare conjecture gap!
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.
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.
Emacs: for people who just never know when to
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.
John McAfee 'It was like that time I hired that Bangkok prostitute; to do my taxes, while I fucked my accountant'
sure, but can you ski through it?
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.
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.
I want a new world. I think this one is broken.
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...
Read my blog: HansMast.com
"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...
Maybe what we have here is just the impending lapse of the Clay Math. Inst.'s required two years of scrutiny...
"But all your emitter and collector are belong to me!"
As Balzac said, "there goes another novel."
"...all the labours of the ages, all the devotion, all the inspiration, all the noonday brightness..." yada yada
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 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.
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.
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...
My UID is prime is yours?
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.
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.
In Soviet Russia...
they prove conjectures.
For an accessible math article on this, try http://mathworld.wolfram.com/news/2003-04-15/poinc are/
This comment was written with the intention to opt out of advertising.
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
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.
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.
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.
Karma: Bad (mostly due to all those "In Soviet Russia" jokes)
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
DVD Ripping, Divx, VCD, SVCD under Linux
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?
Karma police, I've given all I can, it's not enough, I've given all I can, but we're still on the payroll.
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.
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.)
paintball
You just made all that up, didn't you?
paintball
(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.
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.
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
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
This, by itself, isn't particularly enlightening to the non-topologist, but what it actually boils down to is:
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
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)
...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 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.
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
-- Qu'est-ce que la propriété intellectuelle? It is thought control.
Oh, I've followed your link and now I understand why you've been modded flamebait: this is just anti-semitic bullshit.
-- Qu'est-ce que la propriété intellectuelle? It is thought control.
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."