Claimed Proof of Riemann Hypothesis 345
An anonymous reader writes "Xian-Jin Li claims to have proven the Riemann hypothesis in this preprint on the arXiv." We've mentioned recent advances in the search for a proof but if true, I'm told this is important stuff. Me, I use math to write dirty words on my calculator.
Previous proofs (Score:5, Interesting)
Tough problems (Score:4, Interesting)
New math is the only way to go about solving some of these problems.
Re:not so fast (Score:2, Interesting)
Re:Apology for the Re (Score:2, Interesting)
I doubt too many Maths faculties in the world have people working full-time on the Riemann Hypotheses.
Of course I echo your sentiments that his proof is almost certainly flawed though.
Re:So what? (Score:1, Interesting)
I would hardly consider Perelman's preprints to be "junk that couldn't pass peer review"
His Advisor Also Claimed Proof (Score:2, Interesting)
Re:Congratulations! (Score:3, Interesting)
Prime numbers are distributed in pretty much the same way as they were before the proof.
The proof is mathematics for the sake of mathematics. The Riemann Hypothesis has been accepted as true true for over a hundred years, so practical applications that derive from it already exist.
The REAL importance is Primes (Score:5, Interesting)
Section two of the wiki article (http://en.wikipedia.org/wiki/Riemann_hypothesis) is the great importance here. If indeed there is a proof of Riemann's Hypothesis, then there is a similar proof of the Generalized Riemann Hypothesis, which is in turn a big step in finding the exact distribution of prime numbers.
Finding the distribution of prime numbers has epic consequences, like breaking most encryption, for starters.
Re:not so fast (Score:3, Interesting)
Re:Tried to RTFA (Score:3, Interesting)
Re:Dirty Words (Score:3, Interesting)
Re:Reimann hypothesis (Score:2, Interesting)
If you let g0(x)=1/x, then the integral at the bottom of page 38 blows up to Inf.
I don't see a way to fix that, Theorem 8.6 is pretty important to this proof, and probably false. Those bits represent Li's major contribution to the problem, the rest of it is restating previous results.
Disproof (Score:2, Interesting)
Ah well, not quite right. But let g0(x)=x works, because there's no integrability condition. Thm 8.6 then falls apart because h0 is no longer in L^2(C), or V(h) is not an operator, take your pick.