It appears that someone has just posted a 40 page preprint that claims to prove the Riemann hypothesis. I don’t know anything about the author or the research program that this came out of, so I can’t judge how likely it is to be correct. Does anyone else know?

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Long experience with arxiv preprints makes me confident the answer is “not correct”, no matter how credible the source or research program.

Comment by Walt — July 2, 2008 @ 12:34 pm |

I don’t like your attitude either. Perelman’s proof of Poincaré conjecture is a preprint of the arxiv. Of course this is not making me confident of the correctness of this proof, but it probably deserves some attention.

Comment by Maurizio — July 2, 2008 @ 2:23 pm |

Perelman’s proof was not titled “A proof of the Poincare conjecture”. So minus a few points for being so flashy.

Comment by Index Guy — July 2, 2008 @ 2:41 pm |

For what it’s worth, the author was apparently a student of Louis de Branges who himself claims to have proven the Riemann Hypothesis in 2004.

Comment by Rohit — July 2, 2008 @ 6:31 pm |

Maurizio: Why? Most announced proofs of famous results on arxiv are later retracted. Perelman is the only exception that I know of. I think it’s fine that they put up the preprints, assuming they’ve made a good faith effort to find any mistakes, but the more press the result gets, the more humiliating when they have to retract it. Someone announced a solution to the Navier-Stokes problem on arxiv that get sufficient press that it appeared in the newspaper. Someone later found a mistake — I can’t imagine that level of humiliation that person must have felt.

Comment by Walt — July 2, 2008 @ 7:41 pm |

Walt: i agree with you that a lot of press attention is not a good thing, i was just saying that a tentative proof should not be totally ignored by the scientific community just because it is a preprint on the arxiv. These proofs should get some more checking before being publicized, as you say they have a high probability of being wrong, and it can be humiliating for the publisher.

Regards!

Comment by Maurizio — July 3, 2008 @ 8:01 am |

It appears that Terry Tao has found a flaw in the proof, which he discusses in a comment on his blog.

Comment by Jesse Johnson — July 3, 2008 @ 2:26 pm |

Alain Connes found a better flaw.

Btw, send me an email, Jesse. You know me from college (I saw Willow and Zach and figured I should reconnect with you, too). I’ll send you my non-pseudonomous address in return.

Comment by feldspar — July 3, 2008 @ 3:12 pm |

What, nobody cares about the recent combinatorial 14 page proof of the Poincare conjecture? For shame! http://arxiv.org/abs/0807.0577

Comment by yoyoyo — July 5, 2008 @ 6:58 am |