Last July Xian-Jin Li claimed to have a proof of the Riemann hypothesis that turned out to be flawed.
Arturo Calderon just left a comment on one of my earlier posts on this topic pointing out a new paper by Julio Alcantara-Bode that claims to prove the Riemann hypothesis. The arXiv manuscript was submitted just two days ago.
The Riemann hypothesis is a very important open problem. If it is correct, a large number of other results follow. The result would be important to theoretical math and to practical cryptography. The Riemann hypothesis is one of the seven problems for which the Clay Institute has offered a $1,000,000 prize.
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Danny 02.05.09 at 23:34
My (limited and possibly incorrect) understanding of the Riemann hypothesis is that we’re pretty sure it is true–there have been very many zeros found, and they all have real component 1/2. Can you elaborate on what the practical implications of a proof would be?
John 02.06.09 at 15:15
I’m not a number theorist or a cryptographer, so you may want to take my answer with a grain of salt. I believe if RH were proven true, that would prove the existence of factoring algorithms that could have consequences to cryptography. Most people are pretty use RH is true, as you say. But if people knew for certain that RH were true, that might give them more confidence to try to make some of these algorithms practical. And it’s possible that a proof of the RH might itself suggest new algorithms.
RP 02.07.09 at 09:54
Julio’s proof was already withdrawn due to a crucial error.
Juan Vidal L. 02.13.09 at 09:55
La prueba del inigualable Phd Julio Alcantara es correcta.
UNI 2002-2 – IMCA lo máxino
Sam Gilbert 03.03.09 at 04:49
Re: Riemann hypothesis
Perhaps your readers would be interested in:
http://www.mmdnewswire.com/famous-math-problem-4626.html
http://www.riemannzetafunction.com
http://www.amazon.com/Riemann-Hypothesis-Roots-Zeta-Function/dp/143921638X/ref=sr_11_1?ie=UTF8&qid=1232825792&sr=11-1