Mathematician Claims Proof of Riemann Hypothesis 561
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."
Hilbert Turns in his Grave? (Score:5, Interesting)
"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:Proof of theory (Score:1, Interesting)
Impact on crypto? (Score:4, Interesting)
What are the consequences for cryptography? (Score:4, Interesting)
Does this affect prime based public key schemes at all? How does it affect them?
de Branges' reputation with other mathematicians (Score:4, Interesting)
A Proof .... Maybe (Score:4, Interesting)
quick google search (Score:3, Interesting)
Riemann hypothesis proof is useless (Score:2, Interesting)
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
Re:Hilbert Turns in his Grave? (Score:5, Interesting)
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:The Reimann Hypothesis (Score:2, Interesting)
For some suggested approaches, see (Score:5, Interesting)
Re:Apology (Score:5, Interesting)
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 (Score:5, Interesting)
Maybe (Score:3, Interesting)
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? (Score:1, Interesting)
Good Book about the Hypothesis (Score:3, Interesting)
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.
Re:Hilbert Turns in his Grave? (Score:3, Interesting)
The significance may be more in the mathematical machinery required to prove it than in the result itself.
Track record (Score:2, Interesting)
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 (Score:5, Interesting)
My favorite selection:
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 (Score:5, Interesting)
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
Re:Hilbert Turns in his Grave? (Score:2, Interesting)
Overview of proof? (Score:3, Interesting)
Re:Hilbert Turns in his Grave? (Score:1, Interesting)