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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.
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.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?
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?
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
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.
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
... 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?
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 took Einstein many tries to arrive at the correct fomulation for general relativity. I guess according to you, he should have just given up after his first failure?
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 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
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
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.
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??!)
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!
I don't it is THAT big a deal. Remember, no there are no knwon practical applications for this proof. It's like proving Fermat's Last Conjecture--- cool but ultimately unimportant. Now if someone came along and proved that Riemann's Hypothesis was a corollary of General Relativity then THAT would be earthshaking. Sort of like finding a jpeg of a circle embedded in the digits of pi.
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.
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.
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.
mmmmmmmm......infinite pie..!
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.
I think you are going a bit overboard here. The Riemann hypothesis is the greatest open problem in mathematics right now and solving it would be HUGE :-). However, famous open problems usually do not advance mathematics that much and I suspect that a proof of the Riemann hypothesis would not introduce new techniques which would have wide (or even slightly wide) use in math. Look at some of the Fields metal papers (e.g. restricted Burnside problem - Zelmanov - 1994 metal) and tell me how they changed mathematics.
For influences on math, consider Dirac (crazy British scientist who predicted to existence of the positron) whose ideas led L. Schwartz, L. to write "Théorie des distributions. Tome I,II"; distribution theory has had a huge influence on analysis.
Thank god, I used to lie awake at night worrying about that
Help fight continental drift.
hehe I'm nearly 40 (where did the time go...) so I'd say I'm the present rather than the future. Hopefully my kid(s) will be the future. And will support me.
Now it's back to work, or my job will be in the past.
When they came for the communists, I said "He's next door. Take him away. Goddam commies."
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
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..."
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
"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!
And the first attempt of Andrew Wiles to prove Fermat's Last Theorem also failed, but he managed to patch it.
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?
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
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.
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.
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
Math does not rely on the scientific method. Math relies on rigorous proof based on axiomatic definitions, i.e. logic. Proofs can be flawed, i.e. wrong, but we can never at a later date say, "Hey, it turns out that x^3 = y^3 imples x = y is just not true this time."
Unless, of course, you think that logic could have some holes in it. But let's not go down that road.
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...
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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.
Q.
Insert Signature Here
But there is not enough room in this posting.
99 bottles of beer in 175 characte
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.
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
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.
Could someone capable in the apropriate math(s) please explain how the proof works?
Posters recognized by their sig,
but unfortunately it was censored by the Slashdot lameness filter.
You guys all have it wrong .. the apology is not referring to the proof, it's for having linked to a pdf ..
Don't you mean that know the real answer but have no room to write it down here?
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.
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