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."

Comments

Hilbert Turns in his Grave?

[kaalamaadan]

"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

Re:Hilbert Turns in his Grave?

[Mark_in_Brazil]

Hilbert may have been referring to the importance of the Riemann Conjecture, and not the difficulty of proving it.

Really, folks, this is a big deal if it's true. It just doesn't get the attention Fermat's Last Theorem did because it's harder to understand what it means and why it's important.

After all, most people don't even know what complex numbers are, much less complex functions. The zeta function, then, is already beyond the understanding of most people, not because they're incapable, but because they're not interested. But the implications of the Riemann Conjecture are far-reaching indeed, affecting things like quantum mechanics and statistical physics.

--Mark

Re:Hilbert Turns in his Grave?

[Tony-A]

"The structure of mathematical journals creates the impression that mathematics is fragmented into unrelated disciplines. The underlying unity of mathematics is however maintained by problems which span these disciplines. ... The Riemann hypothesis is listed as an important link between algebra and analysis."

The significance may be more in the mathematical machinery required to prove it than in the result itself.

Re:Hilbert Turns in his Grave?

[RAMMS EIN]

However important this proof may be to mathematicians, it hardly has any impact on real life. Gödel has already proven that mathematics, or really any complex system at all, is incomplete, meaning that there are true things that cannot be proven. The approach taken in real life, as well as pretty much any science, is to accept a hypotheses tentatively and use it until one that better predicts observations is found. Any "law" of nature that we have now has been used for so long without shocking inconsistencies that the proof or falsification for any hypothesis can only have a very minor impact on it.

Re:Hilbert Turns in his Grave?

[Anonymous Coward]

The significance may be more in the mathematical machinery required to prove it than in the result itself.

No. Large parts of modern mathematics rest on proofs which begin "Assuming the Riemann Hypothesis to be true...". If it turns out to be false, there's a lot of work to do over again (of course, that could be fun, too...)

Re:Proof of theory

[Anonymous Coward]

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.)

Impact on crypto?

[Anonymous Coward]

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?

What are the consequences for cryptography?

[Omnifarious]

Does this affect prime based public key schemes at all? How does it affect them?

de Branges' reputation with other mathematicians

[Anonymous Coward]

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.

A Proof .... Maybe

[BrownDwarf]

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."

quick google search

[cancerward]

... 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?

Riemann hypothesis proof is useless

[Anonymous Coward]

There are no practical applications of knowing that the Riemann hypothesis is true.

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 .. 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.

-Johan

Re:The Reimann Hypothesis

[kylemonger]

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.

For some suggested approaches, see

[elid]

http://www.maths.uwa.edu.au/~berwin/humour/invalid .proofs.html

Re:Apology

[MerlynEmrys67]

Of course if I were to RTFA - and more importantly UTFA (Understand the Article) I wouldn't be able to post this for another 2 years or so...

As it is, it looks like he proposed this solution over a year ago and has been getting it vetted in a tightly controlled community. Now that the cat is out of the bag he will have to get it into a peer reviewed journal (takes 6 months or so) and wait 2 years to see how it is bashed...

Yeah - that is about the time it would take for me to UTFA, except I am not a Mathemetician, so add in another 6-8 years to get that training as well. So I will get back to you sometime around 2120 with an insightful comment after UTFA

Re:Apology

[gniv]

The last paragraph of the article is interesting:

A curious coincidence needs to be mentioned as part of the chain of events which con- cluded in the proof of the Riemann hypothesis. The feudal family de Branges originates in a crusader who died in 1199 leaving an emblem of three swords hanging over three coins, surmounted by the traditional crown designating a count, and inscribed with the motto "Nec vi nec numero." This is a citation from Chapter 4, Verse 6, of the Book of Zechariah: "Not by might, nor by power, but by my Spirit, says the Lord of Hosts." The chateau de Branges was destroyed in 1478 by the army of Louix XI of France during an unsuccessful campaign to wrest Franche-Comte from the heirs of Charles the Bold of Burgundy. The family de Branges performed administrative, legal, and religious functions in Saint-Amour for the marquisat d'Andelot during Spanish rule of Franche-Comte. Francois de Branges of Saint-Amour received the seigneurie de Bourcia in 1679 when Franche-Comte became part of France. The chateau de Bourcia remained the home of his descendants until it was destroyed by Parisian revolutionaries in 1791. The chateau d'Andelot near Saint-Amour, which survived the revolution, was bought in 1926 by Pierre du Pont, an elder brother of Irenee du Pont, for a nephew assigned in diplomatic service to France. This coinci- dence accounts for the interest which Irenee du Pont showed in a student of mathematics. 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.

That's quite noble of him.

Maybe

[Phragmen-Lindelof]

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.

What does this imply?

[pukvete]

What ramifications would this have on the world if it was solved? What possibilites would it unveil?

Good Book about the Hypothesis

[Anonymous Coward]

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.

Track record

[wviperw]

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.

Re:Apology

[dasmegabyte]

This guy is an all around class act. I've always found mathematicians to be kind of standoffish, and while this guy is obviously at the top of his field, he's also on top of the rhetorical game, the very structure of this "Apology" shows that he's having a great deal of fun with his chosen profession.

My favorite selection:

The solution of a celebrated problem creates a disturbance in the otherwise quiet flow of mathematical events. The solution escapes the planning of committees. Colleagues are unprepared because the possibility of a solution has not been included in their research proposals. Students have avoided related thesis topics because of the risk that the work will not be welcome to a prospective employer. Friends are discouraged from research activity by the demands of the situation created by the solution. The manuscript, which is necessarily written at the highest research level, is readable only to a limited audience. An introduction is therefore needed which makes available the opportunities created by the solution. This is done by supplying motivation for the argument in a chronological order which also gives an account of how the solution was obtained.

Hilarious stuff. He apologizes to the people who will now feel the need to go over his proof with a fine toother comb, looking for mistakes...and also explains (three pages in) why he's chosen to start his proof with a history of the golden age of mathematics, stretching back to Newton. Basically, he's saying "oh hey, thanks for joining me. I was just explaining ALL OF MATHEMATICS for those playing at home. Bear with me, this one's worth it, and I promise you can get back to your euclidian algorithms and Ving diagrams in short time."

Ever read "The Life and Opinions of Tristram Shandy?" It's an amazing book from the 18th century, which attempts to tell a simple narrative but due to the extremely schizophrenic style of the narrator, it keeps breaking down into tangential pockets of narrative self awareness. Basically, the author wrote from the perception of a disturbed dandy who couldn't keep his mind on the task at hand, an author who keeps apologizing to his readers for the inconvenience of his own poor editing.

This mathematical proof reminds me a lot of this book...the text of the proof doesn't act as though the proof isn't something interesting or ground breaking, nor does it make a big deal of this. It just ambles on in all directions until the Riemann hypothesis is well and truly proven, but with no real hurry to illustrate the proof until the outlines have been inked. Not that I know for sure that Riemann is proven or isn't...my brain was full when I got to differentials. But if it is, this paper will stand out not only as a great work of mathematics, but a great work of WRITING about mathematics.

I'm going to read it again. Maybe I'll understand it this time!

Re:If there's one thing I know

[Ckwop]

De branges is a bit of a crank on the Riemann hypothesis. No-one believes his approach(s) will work. This is well documented in the book "Riemann's Zeros". When some of the leading mathematians were asked about his approach they said it was "full of errors" and "unlikely to work". The only reason he is given the light of day is because he managed to prove to the Bieberbach conjecture. That was a difficult problem, hats off to him for getting it aswell, but it's no Riemann hypothesis!

Rest assured, we'll all be dead and burried when it actually gets solved.

Simon

Overview of proof?

[alex_tibbles]

Could someone capable in the apropriate math(s) please explain how the proof works?