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

For some suggested approaches, see

[elid]

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

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.

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!