Slashdot Mirror
Mathematician Claims Proof of Riemann Hypothesis
TheSync points to this press release about a Purdue University mathematician, Louis de Branges de Bourcia, who claims to have "proven the Riemann hypothesis, considered to be the greatest unsolved problem in mathematics. It states that all non-trivial zeros of the zeta function lie on the line 1/2 + it as t ranges over the real numbers. You can read his proof here. The Clay Mathematics Institute offers a $1 million prize to the first prover."
It's that mathematicians love to exaggerate! Like infinity is infinite, or pi goes on forever! Those guys are always talking big.
Apology for the proof of the Riemann hypothesis (in pdf format).
"We humbly apologize for the complete illegibility of this proof. The mathematician responsible has been sacked."
It's too bad that most of society does not recognize truly great achievements like this. I, for one, admit interest but not enough knowledge of the details to read and understand the proof. I'm sure most people here on /., as representatives of the intelligent future of sentient life, have the interest as well.
-I am an elective eunuch.
...but, oh you know the joke.
They really should make mathematics more like pokemon, it would get more people interested in the subject
Riemann-chu, I prove you! Then bust out the paper.
I read through his proof and...nope, it's wrong. I know the real answer, but am leaving it as an exercise for the interested student.
Karma-whoring free.
Ha! They've already found an error in the proof! All that he posted was his apology! :-)
Yes, I was actually confused at first. For the non-math geeks like myself, who are feeling stupid, look at definition 2a of apology.In a time where funding for many non-practical research is being cut, it's nice to someone established accomplish something.
The paper is called, Apology for the proof of the Riemann hypothesis (in pdf format). To find the apology you have to read through to page 4 where he talks briefly about the problems that the solution of a celebrated problem creates for others who weren't expecting it. Basically the title is, "a form of Mathematical smack talk" (to quote a co-worker).
Most of the paper appears to be history, and the results leading up to his proof. Only a few pages at the end make up the actual new proof, so the novel material is far shorter than 23 pages.
I wouldn't be surprised if there is a fairly final verdict on his proof very quickly. This is not like Wiles' proof of Fermat that was very long and nobody had the background to understand. This proof looks reasonably short and straightforward.
Cheers,
Ben Tilly
I don't want to give it away, but you'll see it.
"If I were to awaken after having slept for a thousand years, my first question would be: Has the Riemann hypothesis been proven?"
David Hilbert
You know you're in trouble when you don't even understand the question.
When they came for the communists, I said "He's next door. Take him away. Goddam commies."
... 42?
Apology - 2: a formal written defense of something you believe in strongly
This should at most have earned a "Funny", or is there something I'm missing here?
um, he says in the paper what he'll do with it. (And actually, it's not the only time it's ever challenged. The whole field of mathematics is nothing but this sort of thing; this one only had big money attached to it because it has eluded the world's best mathematicians for so long.)
This theorem is a theory of how prime numbers are distributed...so does it's proof have any impact on crypto? Does it make it any easier to find prime numbers?
That's what separates you from the football watching zombies. You are the future.
-I am an elective eunuch.
Bull. There are thousands of mathematical researchers. Most don't have hefty salaries, and most aren't working on money-prize problems.
Mathematicians are never in it for the money.
Wonder what he'll do with the money?
Seems like he wants to restore the old family castle:
I must say that at he seems a bit full of himself, or at least, getting a bit ahead of himself. Given how many have tried and failed witht his problem.
Poor Nash is either going to find a mistake in this guy's work or go insane trying to ...
OpenSource.MathCancer.org: open source comp bio
Try looking up the definition of "apology."
The Riemann Hypothesis, among other things, implies that the Prime Number Theorem is off in the distribution of primes by no more than O(sqrt(n)*log(n)). However even without the full result, we already had very good error bounds for the approximation of the prime number theorem for "small" numbers, including numbers far larger than any which come up in cryptography.
By John Derbyshire... It's a great read and covers it in detail.
Does this affect prime based public key schemes at all? How does it affect them?
Need a Python, C++, Unix, Linux develop
I knew it was a hoax when he started discussing his Paley-Wiener space...
Support FSF: Stop thinking with your wallet, and think with your imagination. (cc/non-commercial)
Will the media keep publishing claims of extraordinary mathematical findings without checking the facts forever?
Just like this one over again:
Swedish Student Partly Solves 16th Hilbert Problem
That's what I like about /. If the article is wrong, there is always the comments there to solve it.
Although I hope de Branges has found a proof, I'm not too optimistic. It seems that de Branges has a reputation among mathematicians for going off half-cocked. He does have the Bieberbach proof under his belt, though, so you never know.
It seems that the proof hasn't been reviewed yet. He may have it -- but lots of good folks have tried, without success. This from Science Daily: http://www.math.purdue.edu/~branges/ . While mathematicians ordinarily announce their work at formal conferences or in scientific journals, the spirited competition to prove the hypothesis - which carries a $1 million prize for whomever accomplishes it first - has encouraged de Branges to announce his work as soon as it was completed. "I invite other mathematicians to examine my efforts," said de Branges, who is the Edward C. Elliott Distinguished Professor of Mathematics in Purdue's School of Science. "While I will eventually submit my proof for formal publication, due to the circumstances I felt it necessary to post the work on the Internet immediately."
huh?
Mathematicians have been working on this for a long time. it is not like one day this guy woke up and said "oh, 1 million dollars for it eh, well I better get to work."
I am the Alpha and the Omega-3
Well if you bothered to scan his Apology you would see that he already gives a suggestion for what the money could be used for.
This proof, if it turns out to be valid, is likely to be more important the Wiles' proof of Fermat's Last Theorem. The Riemann hypothesis touches many areas of mathematics and some areas of physics.
His earlier attack on reimann hypothesis was disproven: http://www.aimath.org/WWN/rh/articles/html/40a/
This is very cool for me because I'm planning on going to Purdue next year for computer science/math =)
Whoever dies with the most toys wins.
... shows that he's been offering "proofs" since July 1989. I see from MathSciNet that he has 87 papers from 1958 to 1994, but isn't this a bit like the boy who cried wolf?
It is interesting that a mathematical proof such as this, which is an exercise in logic, can't yet be verified by typing it into a computer program to verify that all the steps make sense.
I saw this last year. If you look in the header at the top of the even pages in the PDF of the proof, "Apology for the proof of the Riemann hypothesis", you will see that it is dated March 18, 2003.
I think I speak for all non-mathematicians when I say:
what?
I am a filthy pirate.
There are no practical applications of knowing that the Riemann hypothesis is true.
.. mechanical simulations will be easier, we'll have better material science, drug discovery and design will be easier and better, CPUs will get faster (due to efficiency in layout) .. Etc.
Sorry but I dont agree that this is "the most important math problem"
Not to take away from the brilliant work of this guy, and I'm sure his work will have generated some good math on the way. But just knowing whether the Riemann hypothesis is true is not of much help (people have been assuming it to be true for a while).
Math problems that do have direct practical application:
fast N-body calculation
P=NP ?
Factorization.
Solving the above (especially the first two) will have immediate positive impact on society
-Johan
It's 42
The question... we'll have to wait and see (barring any intergalactic space route development)
The Neo-Bohemian Techno-Socialist
What's he going to do with the money? Go into the building trade it would seem ...
From the final page of the apology...
The ruin of the chateau de Bourcia overlooks a fertile valley surrounded by wooded hills.
The site is ideal for a mathematical research institute. The restoration of the chateau for
that purpose would be an appropriate use of the million dollars offered for a proof of the
Riemann hypothesis.
Don't you mean Mathematician?
Sorry to burst the bubble, but some usenetting shows:
The same guy claimed to have solved the same problem at least 4 years ago.
The guy has a reputation for sometimes getting it wrong.
(Probably because he has published flawed proofs of other well-known problems.)
He could be right, but I wouldn't get my hopes up.
"The most important algorithm of cryptography, which is in use today, uses the factorization of primes as its basis. This algorithm called the RSA will be in jeopardy if method to find the distribution of the primes is devised. All the mathematicians now believe that a proof of the Riemann Hypothesis would lead to a great understanding of this distribution. This would then in turn put the whole system of Internet security in danger."
So basically, a valid proof of the hypothesis will give mathematicians an edge in finding methods to breaking encryption based on prime number algorithms.
The problem is simple enough to understand, assuming you know some math basics. As most of you know, any function f(X) where f(Xo)=0 is said to have a zero at Xo. For functions of complex numbers f(z) where z=x+iy and x,y are real numbers, you obviously have the function taking on different values for every x and y, so the zeros can be anywhere on the x-y plane. For the zeta function, "trivial zeros" occur at the negative even integers (z=-2+i0,-4+i0,...) and also at points on the line x=1/2 (i.e 1/2 +iy for certain y).The Riemann Hypothesis says that all zeros that aren't negative even integers lie on this line.
Most of you have who have taken basic calculus courses have probably seen a simplified definition of the zeta function for real intergers greater than 1. when z=n, a natural number, the zeta function reduces to the infinite series Zeta(n)= SUM (k=1-->inf) 1/k^n
Dammit! I kept meaning to prove the Riemann hypothesis myself but keep putting it off for "just one more game" of UT2004.
At the end of the article it states that he wants to use the $1 million to restore the "Chateau de Bourcia" in France, and turn it into a mathematical research institute. Sounds like a nice gesture, when can I visit?!
It's like reading a Knuth book :)
(B) + (D) + (B) + (D) = (K) + (&)
Fermat, eat your heart out.
For those of you who don't know, a proof of the Reimann Hypothesis is THE HOLY GRAIL OF MATHEMATICS. It is like a room temperature superconductor for engineering, a quantum computer for computing, or a Theory of Everything for physics. There have been many false proofs, but considering that Fermat's Last Theorem was proved, this might be too.
they figured out how to get more beers in a case? AH!...well shit....
http://jayceecorder.blogspot.com
...proof by obfuscation.
Yeah, I think you missed:
Equivocation - \E*quiv`o*ca"tion\, n. The use of expressions susceptible of a double signification, with a purpose to mislead boneheaded moderators, especially when you are just making a joke.
Boom Shanka
"Wonder what he'll do with the money? Replace the stack of pencils he depleated, or the batteries in the calculator?"
Actually, he proposes to restore a chateau in France owned by the man who helped spur his interest in number theory (Irenee du Pont).
I came up with this proof weeks ago aqnd submitted it, but Slashdot rejected it.
Wonder what he'll do with the money? Replace the stack of pencils he depleated, or the batteries in the calculator?
He states in the proof on page 23 that he wants to use the money to restore the chateau de bourcia as a mathematical institute.
Kind of like Wolfram... He got a huge grant, and used it to develop an awsome math package.
Sorry, my dog ate it.
I think I might as well write my epitaph now:
Doesn't it make you feel good to know that our freedoms are protected by politicans, lawyers and journalists.
it is not like one day this guy woke up and said "oh, 1 million dollars for it eh, well I better get to work."
Yeah, no shit. I mean, that would be more the style of Bill Gates. It would go something like this:
Wake up
say "1 million dollars for it eh, well I better get to work."
fart
say "ah, easiest million I ever made, at least since yesterday morning"
Dude, what the fuck are you talking about?
Mathematicians tackle difficult problems all of the time, regardless of the (lack of) money involved.
I don't know why you say that interest in "theoretical" mathematical proof is waning. It certainly isn't where I come from. (And what is ultra-math??!)
Yeah, poor poor Pluto Nash.
Then the IRS will send de Branges a huge bill for the 45% tax rate on "winnings."
Then his ex-wife will sue for 50% of the million dollars because "he used to moan 'oh, Riemann' while we were doing it."
Then de Branges will spend 25 years opening letters from the poor and destitute who desparately deserve a chunk of his newfound yet nonexistent wealth.
Then eventually he will take his place in an unmarked mass grave reserved for all the great mathematicians who died peniless and unloved.
Well, that's my guess anyways.
>Mathematicians are never in it for the money.
You got it! They are in it for the chicks!
many mathematical theories being with the assumption of the riemann hypothesis being true. yay for those theories
This usage of "apology" is fashionable in math circles; a prime example is the title of G. H. Hardy's memoir : A Mathematician's Apology.
See Jeff Lagarias's paper "An elementary problem equivalent to the Riemann hypothesis (.pdf)"
The 23 page "apology" is not the actual purported proof, contrary to what the article and press release say. The actual proof is the manuscript "Riemann zeta functions", the third link on de Branges' home page, which weighs in at 124 pages!
So if his "proof" isn't obviously wrong, it'll likely take quite a while for the experts to verify.
http://www.maths.uwa.edu.au/~berwin/humour/invalid .proofs.html
A long time ago, in the distant past, there were Finders. Dedicated individuals that wandered around outside the camps and found stuff. Over time, it became more difficult to find stuff, and the Finders became the Searchers. Many times the Searchers would return empty handed. As technologies improve and new insights are gained, the same fruitless searches of the past were repeated. Sometimes with a new results, sometimes as fruitless as before. Regardless, it was this not giving up on an idea just because it failed once that led the change in title from Searcher to Researcher.
Most reseachers I know produce one magnificent failure after another on the quest for a new piece of knowledge. Everything that is easy to find has probably already been discovered, and mathematics is no different. So the guy made a few failed attempts at solving the puzzle, this doesn't make each sucessor to the first attempt a garaunteed failure.
He'll use the money to restore a family castle. It's written at the end of the latest page of his proof.
RTFA. From the Apology, p.23. "The restoration of the chateau (de Bouricia) for that purpose would be an appropriate use of the million dollars offered for a proof of the Riemann Hypothesis." He wants to convert an old ruined chateau into a mathematics institute.
Why not digitally sign the manuscript and send the signature over to a PGP Digital Timestamping Service? Keep the timestamped signature just in case somebody beats you to the punch and you're right, and save yourself the embarassment if you're not.
Please mod this post up... it's incredibly insightful and a beauty to behold. Just made my day.
I looked at de Branges' "Apology for the proof of the Riemann hypothesis" and found no proof. Perhaps the proof is in another document?
Even though he is a kook, I root for him; no one believed him when he claimed he had proven the Bieberbach conjecture. I believe, however, that he has claimed to have proven the Riemann hypothesis previously. One should check carefully before trusting his claim.
Sorry, but I find parent exceedingly funny.
I am poor and destitute of mod points and would ask for contributions to my beloved parent.
...except that all of those other things you mentioned would actually be useful. This thing has been taken for granted for decades.
mmmmmmmm......infinite pie..!
Purdue will take the money, because he works there. It will be used to build a new scoreboard for the football stadium.
I think the scoreboard is covered by the large numbers of football tickets sold. The elevators in the Math building, however, could use a little re-vamping.
-- SNS
Mathematicians are never in it for the money.
Well, maybe some of them. Though that's being awfully charitable with the definition of 'mathematician'...It's 42.
Besides, I think he forgot to carry the one.
If you do what you always did, you get what you always got.
http://64.233.161.104/search?q=cache:NMJzXzKh1-0 J:www.math.purdue.edu/ftp_pub/branges/invariantban ach.pdf+Cardinality+And+Invariant+Subspaces+(in+pd f+format).&hl=en
See, the man of steel has some finite strength. It would be more correct to say that everyone here is undefinably strong.
Is it ok if we just go back to articles about bio? At least I understood those :P
Thank god, I used to lie awake at night worrying about that
Help fight continental drift.
man with that prizemoney hes gonna have soo much fun.
surrounded by babes behaving all irrational all over him, a big line of them stretching out to infinity...all in their prime
and as much pi as he can eat.
The elevators in the Math building, however, could use a little re-vamping.
Bah. Take the stairs.
Most mathematicians need all the exercise they can get.
"Nine times out of ten, starting a fire is not the best way to solve the problem." - my wife
From, http://www.math.purdue.edu/ftp_pub/branges/apology .pdf :
:-)
"The ruin of the chateau de Bourcia overlooks a fertile valley surrounded by wooded hills. The site is ideal for a mathematical research institute. The restoration of the chateau for that purpose would be an appropriate use of the million dollars offered for a proof of the Riemann hypothesis."
I guess when you work with numbers as big as he does one million is no big deal.
The 23-page "Apology" referred to in the press release is also apparently mentioned in this 1996 Usenet post. So is there a new proof? No one seems to know yet.
I have another proof Of Riemann Hypothesis but this text area is too small for it, anyway /. comments doesn't allow math symbols.
The package said "Windows XP or better. Pentium Class Processor or better"... So I got a Mac with OS X
A cool overview of why this is such an interesting hypothesis.
If nothing else check out the animation.
mind-boggling
sorry? did somebody say something?
The Riemann Hypothesis is a pain to explain before getting into some complex stuff about complex analysis (calculus involving complex numbers; IE numbers involving i = sqrt(-1)). I'm going to show the Riemann Hypothesis in the simplest terms possible, something that calculus students could understand (though not prove, of course!).
The Riemann hypothesis states that if this function:
sum from n=1 to infinity ((-1)^(n+1) / n^(x+iy))
equals zero, then x = 1/2 . x and y are variables; x+iy is a complex number normally labeled "z".
If you don't want to deal with complex numbers, you can use the equivalent statement about real numbers: If the following function:
(sum from n=1 to infinity ((-1)^(n+1) * cos(y*ln(n)) / n^x))^2 + (sum from n=1 to infinity ((-1)^(n+1) * sin(y * ln(n)) / n^x))^2)
equals zero, then x = 1/2 . The following URL is a picture of the above in normal notation so it's easier to read:
http://www.geocities.com/myriachan/riemann.png
Melissa <3
OK, I'm no mathematician and although the Clay Mathematics Institute is offering $1 million to anyone who proves this theory. I'm offering a case of beer to anyone who can make sense of any 3 words after "It states that..."
This should at most have earned a "Funny", or is there something I'm missing here?
Uh, yeah. I'm going to assume that the thing you missed was "Monty Python and the Holy Grail." Or, at least the opening credits.
I signed this
Great minds have already tried and failled on proving Riemann Hypothesis, including John Nash and John Von Neumann, both from Princeton Advanced Studies Center.
If this proof were accepted by the mathematician community I belive Louis the Branges will be considered one of the greatest mathematicians of this new millenium.
Doesn't it make you feel good to know that our freedoms are protected by politicans, lawyers and journalists.
it'll be one more thing they'll make you learn in school! :D
First: complex numbers, explained. You may have heard the question asked, "what is the square root of minus one?" Well, maths has an answer and we call it i. i*i = -1. If the real number line ...-4, -3, -2, -1, 0, 1, 2, 3, 4... is represented as a horizontal line, then the numbers ...-4i, -3i, -2i, -i, 0, i, 2i, 3i, 4i... can be thought of as the *vertical* axis on this diagram. The whole plane taken together is then called the complex plane. This is a two-dimensional set of numbers. Every number can be represented in the form a+bi. For real numbers, b=0.
Right. Now the Riemann Zeta Function is a function/map (like f(x)=x^2 is a function) on the complex plane. For any number a+bi, zeta(a+bi)will be another complex number, c+di.
Now, a zero of a function is (pretty obviously) a point a+bi where f(a+bi)=0. If f(x)=x^2 then the only zero is obviously at 0, where f(0)=0. For the Riemann Zeta Function this is more complicated. It basically has two types of zeros: the "trivial" zeroes, that occur at all negative even integers, that is, -2, -4, -6, -8... and the "nontrivial" zeroes, which are all the OTHER ones.
As far as we know, *all* the nontrivial zeroes occur at 1/2 + bi for some b. No others have been found in a lot of looking... but are they ALL like that? The Riemann Hypothesis suggests that they are... but until today nobody has been able to prove it.
qntm.org
Mathematcian finally picks up at university bar!
In breaking news today the, now millioaire, mathematician who proved the Riemann hypothesis was finally able splash enough money around at the university to attract the ladies. Rumour has it the whole evening went sour when he got stuck trying to prove the things in the bed room worked.
And who do you think is going to manage and live in the wonderful chateau doing all this research?
"It states that all non-trivial zeros of the zeta function lie on the line 1/2 + it as t ranges over the real numbers."
So what. My wife proved to me that there are no (and never will be) any non-trivial zeros on the left side of the decimal point in my checking account!
The race isn't always to the swift... but that's the way to bet!
"proven the Riemann hypothesis, considered to be the greatest unsolved problem in mathematics.
Cool! Now that this one's been done, I guess all of the other hypothoses'll be proven||disproven in a snap!
Quod scripsi, scripsi.
This review of Karl Sabbagh's book The Riemann Hypothesis contains some background on De Branges. http://www.maa.org/reviews/sabbaghRH.html He sounds like quite a character, from that and from his "apology"... given recent trends, I wonder if someone might write a novel or play about him?
What ramifications would this have on the world if it was solved? What possibilites would it unveil?
Anyone care to mention the apology he posts on his web page...? Another faker. Click the damn link.
Mathemetician Claims Proof Of Riemann Hypothesis. First of all, to "prove" a hypothesis (or thorie or law) would not be with the scientific method. The sci. method is to have refinment etc. etc. if you "prove" that the stars circle the earth, what would happen when you find moons of jupider orbiting it?
The heading should read, Mathematician Claims Strong Evidence Of Riemann Hypothesis
He appears to be 72.
Who do you get to be an expert to tell you something's not obvious? The least insightful person you can find? -J Roberts
I always thought it was a rhetorical Hypothesis
Not really. He says it would be a good use, not will be. I don't see that as counting his chickens before they're hatched.
Good, inexpensive web hosting
Prime Obsession: Bernhard Riemann and the Greatest Unsolved Problem in Mathematics
This is a very informative book about Riemann's work on the hypothesis, as well as the work of many other mathematicians. You probably need a solid college-level understanding of math to follow most of the technical explanations, but the historical parts of the book are very interesting.
Most mathematicians need all the exercise they can get.
The ones with offices on the ninth floor seem pretty fit.
Subject says it all.
Of course we all know what happened to the last supposed proof that appear on Slashdot (regarding twin primes).
In case you *don't* know, the paper was withdrawn as a result of a "serious error in lemma 8." I can only hope that this proof fairs better, though I'm not betting on it.
Nothing disturbs me more than blind loyalism towards some unrealistic and over-idealistic notion of one's nationality.
I thought the string theory was the hardest and most useful theory to prove or solve.
Dr Michio Kaku has set out to prove or disprove it and says if solved would allow time travel, teleportation, and agelessness.
Yell & scream & rant & rave... it's no use... you need a shaaaave ~ Bugs Bunny
Naw, it's gotta be the pie... at least that's all I ever hear them talking about...
And so it came to pass, Gentle Reader, that some of the Finders did find their fruit, and these were known as Keepers. But a few still lost their newfound fruit on the way home, and these poor souls were thenceforth known as Losers, unless they wept, in which case they were also known as Weepers.
"He who throws mud, loses ground." - proverb
"So when mumsie and I fled that nasty war on the continent, we set up home in Delaware, and I soon found myself attending a snooty boarding school (where they incidentally filmed Dead Poet's Society) and caddying for father and the former CEO of DuPont, who I sure showed a thing or two, proving my mathematical genius at the tender age 17. I later attended MIT, where in my free time as an undergrad, I pointed out several flaws in pre-publication versions of famous math texts, and was generally an astounding genius. Yet when applying to Math graduate programs, I hadn't done enough coursework for more presitigious institutions, so I applied and went to lowly Cornell. However, I eventually got my PhD, and accepted an associate professorship at Purdue, followed immediately by a full professorship. Of course.
Also, I rule. Kiss my aristocratic ass, you pretenders."
Being a researcher is far more fulfilling than sitting in your parents basement posting on Slashdot about how Linux is ready for the desktop.
...now what am I going to do with all of my free time. I guess it's back to video games... *sigh*
LilMikey.com... I'll stop doing it when you sto
You had me at "scoreboard".
See "Riemann Zeta Functions" lower for the actual paper in question. The bibliography has a date of May 25th, 2004 at the top. This looks like a modification of a previous paper he had posted there for several years (his previous attempt.)
I wonder how John Nash is doing? From the book "A Beautiful Mind", it seems he was working on the Riemann Hypothesis in his later years at Princeton. I wonder how far he got.
The movie and book were completely different. I think the book was more in depth, considering the movie didn't even mention Nash's first illegitimate son. But Jennifer Connelly is HOT.
http://github.com/gbook/nidb
The reasons why most specialists doubt that his approach can ever yield the result are well described in this paper from 1998:
(i.e., despite the name, the "generalized RH" proved by de Branges actually did not include the standard RH as a special case.)This is...
O
U
T
R
A
G
E
O
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Hah!! I'm waiting for some slashdotter to explain how the proof would've progressed faster had the good mathematician used a stack-based, RPN methodology to write it.
-- Posted from my parent's basement
Double. You. Tee. Eff.
I wanted that million bucks. How else can my math dgree earn any money?
Mathematics is made of 50 percent formulas, 50 percent proofs, and 50 percent imagination.
There's the occasional post that deserves to be modded to "+10 -- Best Damn Thing I've Read On Slashdot This Year".
Thanks!
You are not a beautiful or unique snowflake -- but you could be if you got off your ass.
Get ready to get butt-raped.
My Panasonic remote controller doesn't even have a zeta function, let alone a way of zeroing it. It's got some real numbers, though. Is there a way to hack a zeta function in? Can I interface it with a learning remote?
Got time? Spend some of it coding or testing
But just for you, I'll rewrite my epitaph:
Doesn't it make you feel good to know that our freedoms are protected by politicans, lawyers and journalists.
mathematician.
Now here are some words to keep this from being modded down as too short. Note how none of them are misspelled? Wooooo
The man is brilliant at what he does, and deserves to dream like the rest of us. I say good luck to him, and to the vistor go the spoils.
For those of us who've taken philosophy, it might be interesting to note that this particular use of the word apology may stem from Socrates' Apology wherein he defends himself from his accusers.
Q.
Insert Signature Here
No serious mathematician would suggest that de Branges is a kook or crank. He has solved important and difficult problems in the past by introducing creative approaches and developing new tools. When he first announced that he had proved the RH, he was taken seriously.
As I understand it, his first attempt was awfully written, and it took quite some effort to figure out what he was saying, let alone if it was correct or not. A hole was found, the hole was patched. Another hold was found, another hole was patched. Like a bubble under the carpet, each correction created another error. At this point, no serious mathematician thinks that his attack on the RH is viable. Not because committees didn't plan for it, as he suggests, but because it has been looked at and simply doesn't work.
Enough about the Riemann Hypothesis. What we need is more talk about Riemann noodles.
But there is not enough room in this posting.
99 bottles of beer in 175 characte
In which case, I dearly hope that he has indeed found a proof. Again, however, it is best to remain skeptical until peer review has signed off on this paper.
This sig space intentionally left blank.
Mathworld has a link to a paper which claims de Branges' method of proof is invalid. Here is a direct link to the site with the paper.
Berkeley Groks has an interview that aired today with John Derbyshire discussing the Riemann Hypothesis. He states that after talking with many mathematicians in the field, the prospects for a solution any time soon are quite low.
If true, does this proof also prove that the sequence of primes does not terminate? And if so, does this mean that the primes can't be used as an example of Goedel's thm any more?
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He looked to be in his mid 50's when I took a math course of his 10 years so, so around 70 is about right.
mathworld.wolfram.com
Riemann Hypothesis "Proof" Much Ado About Noithing A June 8 Purdue University news release reports a proof of the Riemann Hypothesis by L. de Branges. However, both the 23-page preprint cited in the release (which is actually from 2003) and a longer preprint from 2004 on de Branges's home page seem to lack an actual proof. Furthermore, a counterexample to de Branges's approach due to Conrey and Li has been known since 1998. The media coverage therefore appears to be much ado about nothing
In the apology, he states that "the existence of an infinite number of primes was known" in antiquity, but he doesn't say specifically whether it was proven.
Now, for some reason I had the impression that we believe there are an infinite number of primes, but it has never been proven and may be impossible to prove, making it a possible example of Goedel's thm. But this seems to imply that I was completely wrong, and the existence of an infinite number of primes was proven by the Greeks. So what's up with all this?
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It's 42 isn't it?
Never thought there'd be big money in mathematics...
;)
(Go, Flo!)
Free PC version of ChipWits at http://www.breueronline.de/klaus/chipwits/
The proof (or, better said, the sketch of the proof) actually starts at the end of page 21, very close to the last page. The original work is actually pretty hard to find since it is buried in so many unrelated side notes.
/. until now :-)
Here is the general outline:
1) At the end of page 19 he mentions that "The positivity condition which is introduced implies the Riemann hypothesis if it applies to Dirichlet zeta functions."
2) After some introduction of the quantum gamma functions that lasts two pages, the actual proof starts at the end of page 21 with the phrase "A quantum gamma function is obtained when is nonnegative. A proof of positivity is given from properties of the Laplace transformation."
3) The proof ends in the middle of page 23 with the a verification that W(z) is a quantum gamma function with quantum q = exp(-2*pi), obtained from a spectral theory of the shift operator.
Overall this is just a very brief sketch of the whole proof.
BTW, to add gas on fire, here is an exceprt from mathworld.com, which surprisingly was missed by
http://mathworld.wolfram.com
Riemann Hypothesis "Proof" Much Ado About Noithing (sic)
A June 8 Purdue University news release reports a proof of the Riemann Hypothesis by L. de Branges. However, both the 23-page preprint cited in the release (which is actually from 2003) and a longer preprint from 2004 on de Branges's home page seem to lack an actual proof. Furthermore, a counterexample to de Branges's approach due to Conrey and Li has been known since 1998. The media coverage therefore appears to be much ado about nothing.
The counterexample to Brangles approach can be reached here: http://arxiv.org/abs/math.NT/9812166
Don't try to use the force. Do or do not, there is no try.
You're confusing MR with another primiality test (whose name I don't recall). MR is guaranteed to run in poly time, but it's not guaranteed to give the right answer. There's another test which runs in poly time and gives the right answer, but only if GRH is true. Of course now we have AKS, which runs in poly time and always gives the right answer without relying on any unproven hypothesis.
And in the real world, MR is still your best practical choice.
Xenu loves you!
I'm waiting for an apology from you!
- "They misunderestimated me."
Why couldn't he just write a three page proof with no rambling. Talk is cheap, but maths sticks! P.S. I wonder will this have much of an impact on RSA encryption?
May the Maths Be with you!
But I suspect that brute-forcing the function isnt really going to work, but it is useful for calculating primes i think...
95% of all computer errors occur between chair and keyboard (TM)
I hope so. I've been to that stadium and the scoreboard is a bit antiquated. I'm glad to see this geeks work actually turn into something useful.
I see it, I see it....
He forgot to carry the 1!!
Could someone capable in the apropriate math(s) please explain how the proof works?
Posters recognized by their sig,
Step 3: Profits.
If he teaches in Indiana, why is the phone number on his web page 011-765-494-6057? The 7 is Russia, with the 65 as some city code. Is this whole thing a scam to get us to call a Russian 900 number?
Hmm, must not be much of a teacher.
The safest way to approach lava is to have another person with you and he goes first.
Am I the only person who has noticed that Mathematician has been spelled incorrectly in the title. I know /. hires educationally sub-normal editors but when they can't run a spell checker you know the Ramen has addled their brain cell.
-- Be careful what you say. Someone might remind you about it another day.
but unfortunately it was censored by the Slashdot lameness filter.
Mathem a tician!
They will never know the simple pleasure of a monkey knife fight
I have a proof too, but this comment entry box is too small.
If you are interested in the problem, read the book Dr. Riemann's Zeros: The Search for the $1million Solution to the Greatest Problem in Mathematics by Karl Sabbagh. It includes a fair bit about Louis de Branges, including an appendix with a high-level version of this proof.
De Branges is perhaps best known for solving another trenchant problem in mathematics, the Bieberbach conjecture, about 20 years ago. Since then, he has occupied himself to a large extent with the Riemann hypothesis.
You know, we mathematicians sure don't look like pathetic losers when we have this wonderful characterization.... "In the last 20 years, he's done nothing but examine this hypothesis".
You guys all have it wrong .. the apology is not referring to the proof, it's for having linked to a pdf ..
He forgot to carry the 7.
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 cited in the release (which is actually from 2003) and a longer preprint from 2004 on de Branges's home page seem to lack an actual proof. Furthermore, a counterexample to de Branges's approach due to Conrey and Li has been known since 1998. The media coverage therefore appears to be much ado about nothing.
Of course, What is not proven by Wolfram himself might not get attention from them, but you would think Mathworld (http://mathworld.wolfram.com) is a pretty authoritative site on this
--- "I didn't think anyone would understand it" -Prof. Bob Muller
Don't you mean that know the real answer but have no room to write it down here?
"greatest unsolved problem in mathematics"
How does the author come to that conclusion? For instance, Fermat's problem is much more widely known and at least as famous.
How about some Jack Handey:
When you die, if you get a choice between going to regular heaven or pie heaven, choose pie heaven. It might be a trick, but if it's not, mmmmmmm, boy.
I think it is safe to say that since I don't understand the problem that I probably shouldn't bother trying to understand the (supposed) proof.
I think Purdue must have been expecting the money, because they are just finishing up an extensive rebuilding of the entire football stadium. This proof couldn't have come at a better time!
You know, I used to hate those elevators. But then I graduated, moved to Chicago and met a girl. Who lived on the 16th floor of a building with elevators that were even slower.
I must be cursed.
Well, that's all very well, and indeed, quite good mathematics, sir. However, it says very little about the more infamous, and infinitely more important, Ramen Hypothesis.
In short, this theory states that:
All non-trivial zeroed-out accounts of the bank function lie on their backs while consuming large amounts of artificial flavors with real noodles. Don't forget the water.
To date, this is the only one of the acclaimed Menial Problems from the Claypot Mathematics Institute that has not been solved. The Pointcare Conjecture was thrown out, because no one cared about the point. The Hodge-Podge Conjecture was also thrown out as it was revealed to be nothing more than an aggregation of previous "mathematical refuse".
Sorry, but...
.... Now, this is where I admit that I do not really understand that area of math, and have not been closely following the status of (alliteration alert) Perelman's proposed proof. Still, Perelman is a real mathematician, and even if the proof is (was?) wrong, it has real ideas of value in it.
It is not proved; he is not at the top of his field; this "paper" will be quickly forgotten among professional mathematicians; and I doubt any professional mathematician is going over the proof with any sort of comb.
L. de Branges first achieved fame for proving the Bieberbach conjecture. His proof went through strange and abstract methods. He went on the road to present his proof at various seminars in France, Russia, etc; IIRC a bunch of Russian students got very excited and basically rewrote his proof. Their new proof was much shorter and avoided the use of strange methods. Nowadays, their proof is remembered and his is not, but the proof still bears his name, since after all he was the first to come up with *some* kind of proof, and their proof did more or less come out of his.
So he deserves credit for that, and it was quite an achievement to prove the Bieberbach conjecture. But even then he was using unwieldy proofs with unnecessarily abstract methods.
For many years he has been claiming to have a proof of the Riemann Hypothesis. Professional mathematicians stopped listening a long time ago.
This guy is washed-up.
I whole-heartedly agree that this short article is hilarious, but I would like to add the adjective condescending. What kind of asshole apologizes for solving a problem? Does he think he lives on some higher plane, and therefore must take direct, personal responsibility for every aspect of our lives?
Look at how G. Perelman submitted his ideas on proving the Poincare conjecture just a little while ago. He didn't waste anyone's time by rehashing the already-available history of the problem or its wider context in mathematics. Nor did he apologize for having an idea. Rather, he submitted his ideas for consideration, with the full awareness that there may have been a mistake.
de Branges is so full of crap, it makes me sick.
zach
"HUH?"
You see? You see? Your stupid minds! Stupid! Stupid!
I noticed in his apology that he must be rather old. He should have given the proof to one of his children or grandchildren so as to avoid the inevitable inheritance tax on that million dollars ;-)
Yayyy... Purdue ROCKS.
Hey... if a prof here doesnt get the money.... we atleast got greatt profs like him....
My personal theory is that geeks need to have a sense of Humor. Else......they die young. The more geeky you be... the more you appreciate a joke (Not tell it...only appreciate it)
The composite operator with zeros 0 op 0 does not always give zero.
open4free ©
It raises an exception: Division by Zero.
Is it undefined? Argggghhhh, many headaches!!!
So there is a million dollar prize for proving Reimann - how much do you get if you manage to disprove it?
www.sjbaker.org
yes i am not a mathematician, but a friend who is explained the error to me. I recall he told me "well the funcion beta sigma pi is bla bla bla bla to the logarithmic integral divided by bla bla bla bla which is convergent, although bla bla bla bla is complex it cant be proved, understand?"...uh.... yea.
The apology for the proof is dated March 18, 2003 on page 2, the documents 'riemann zeta functions' is dated May 24, 2004 on page 2, but where is latest proof?
Murphy's Law of Research: Enough research will tend to support your theory.
Just in the general case (disregarding this "proof"), what if a million dollar "proof" is published, is found to have a non-trivial error, and someone else fixes the error and publishes a very similar proof largely based on the incorrect one, which turns out to be correct? Who gets the money? Who decides the triviality of the error?
WWJD? JWRTFA!
Yes! It's nice to hear this once in awhile, since most failures are presented at first as great successes, and when their flaws are discovered, they sort of quietly disappear. A young researcher entering the field sees all around what appear to be amazing, intimidating solutions, and it takes a while to understand that nearly all (or in my field, all) of them have more or less fatal flaws.
There's a balance to be struck between presenting the half-baked and having the guts to present something completely new and only half-understood. It seems like this guy has built up enough "credit" in the community with his earlier work to have the option to throw this up in the air without damaging his reputation too much.
It is a pity that you have to build up credit like that, but given the number of people working in the field, it takes a bit of karma to rise above the noise.
Protect your liberties. Donate to the ACLU
You did notice that his last name is de Bourcia, right? It's his family's ancestoral home. It's only noble in an aristocratic sense.
My other first post is car post.
Doesn't it make you feel good to know that our freedoms are protected by politicans, lawyers and journalists.
Sine, sine, cosine sine.. 3.14159!!!!!!
e, e, is so great.. 2.71828!!!!
Berto
"The ruin of the chateau de Bourcia overlooks a fertile valley surrounded by wooded hills. The site is ideal for a mathematical research institute. The restoration of the chateau for that purpose would be an appropriate use of the million dollars offered for a proof of the Riemann hypothesis."
How curious. Did he actually publish a possible Riemann hypothesis proof, or is it only a day dream of a mathematician about how to spend a million dollars? This dude is strange.
Robert
If I were to be awaken after having been sleeping forever, my first question would be:
"Has Duke-- ah, never mind..."
Sincerely,
Pan Tarhei Hosé, PhD.
"Homo sum et cogito ergo odi profanum vulgus et libido."
I'm afraid this is going to get buried in all the responses about your proof of 0 = 0 x 0, but...
Aside from quantum physics, I like to explain the yearning for "i" as follows:
(1) Start with your arguments for why we might want zero.
(2) In order solve problems like 6 + z = 4, we want the negative numbers. For example, z might be $-2 if we were doing accounting.
(3) Now, we also want to be able to split an orange or a dollar among, say, 5 people. That requires solving 5 * z = 1. Thus, we need fractions, or the rational numbers.
(4) We start thinking about other multiplicative equations, such as z * z = 9/4 where we get z=3/2. That's fine, but z * z = 2 has no rational solution. It seems weird we should be able to solve this only for certain values of the RHZ, and we end up getting ourselves to the real numbers.
(5) But wait! The real numbers only get us solutions for nonnegative values of the RHS. What if we want to solve z * z = -2 ? Bingo, we need irrational numbers.
So basically, you can think of irrational numbers as being a way of "completing" our usual notion of numbers so as to have solutions to equations that "feel" as though they ought to have them.
That said, I suspect most people consider quantum mechanics a better justification.
IAAMSICA [I am a mathematician specializing in complex analysis]
Bonus Proof
Theorem:
A ham sandwich is better than eternal happiness.
Proof:
- A ham sandwich is better than nothing.
- Nothing is better than eternal happiness
- Therefore, a ham sandwich is better than eternal happiness. QED.
The guy was born in 1932 and proved the Beierbach conjecture in 1985, from which we conclude (no higher math needed) he was 53 years of age at the time.
John Nash states that the Riemann Hyopothesis drove him to his extreme problems with schizophrenia, perhaps the Holy Grail of Pure Mathematics has taken another victim to the edge of insanity and beyond. I am reminded of the sage advices of my Calculus teacher, Mr. Jack Albers: "Don't let yourself be victimized by the problem!"