Low Dimensional Topology

July 2, 2008

Riemann hypothesis?

Filed under: Misc. — Jesse Johnson @ 12:05 pm

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?


  1. 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 | Reply

  2. 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 | Reply

  3. 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 | Reply

  4. 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 | Reply

  5. 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 | Reply

  6. 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.

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

  7. 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 | Reply

  8. 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 | Reply

  9. 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 | Reply

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