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Claimed Proof of Riemann Hypothesis
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.
http://secamlocal.ex.ac.uk/people/staff/mrwatkin/zeta/RHproofs.htm
Part of the reason these problems are so tough because to solve them, you have to understand what the problem is first. I studied the Riemann hypothesis in college for a good week and I'm still not sure where you might begin solving it. Like the Navier-Stokes equations (another big problem with a big prize) solving it will probably require the invention of some new mathematics. Its not simply a matter of dividing by 3 and carrying the 2. I don't know about you but I haven't the slightest idea about how to go about inventing new math. That's the realm of Newton and Einstein, and few others.
New math is the only way to go about solving some of these problems.
Even those who arrange and design shrubberies are under considerable economic stress at this period in history.
Indeed. Among some mathematicians it is a pleasant diversion to take bets on which of the major unsolved (or unprovable) problems has the most solutions appear on the arXiv this week.
Not really, the kind of person who would solve a problem of this nature is probably going to be the Andrew Wiles reclusive genius type - a lot like the Russian gent whose name escapes me who solved the Poincare Conjecture. Thus he's not necessarily going to be too keen to teach/lecture/supervise and so would possibly not be too attractive to prospective employers.
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.
I would hardly consider Perelman's preprints to be "junk that couldn't pass peer review"
This guys advisor, according to the Math Genealogy Project, is Louis deBranges. DeBranges also claimed to have proven this a few years back, but his proof was not accepted (for reasons unknown to me). The $1M might still be safe.
it has huge effects on prime number distribution
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.
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.
That's true, but most of them are obvious drivel. I have looked through this one, and it is clearly a real attempt by a genuine mathematician who understands the relevant background. I'd still bet on it being wrong, but not stupidly wrong.
Here's another easy-to-grasp one: public key encryption (think: credit card purchases online) is dependent upon the use of large primes. Large primes are currently not the easiest/fastest to find - what if you knew better where to look for them?
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in portuguese, 50135.50738 (nice breasts).
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.
"The ability to delude yourself may be an important survival tool" - Jane Wagner -
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.
"The ability to delude yourself may be an important survival tool" - Jane Wagner -