Wednesday, March 14, 2007

Another Millennium problem down?

After Grigori Perelman's proof of the Poincaré conjecture and Penny Smith's failed attempt at the Navier-Stokes equation comes another claim that a Millennium problem of the Clay Mathematics Institute has been solved. This time it's the Riemann hypothesis -- and it's a disproof.

Here is the arxiv submission by Tribikram Pati, a respected mathematician from Allahabad. I certainly can't evaluate the paper, but from what I have heard of the author, this must be at least a very serious attempt. According to the Clay Institute rules, even if Prof Pati's attempt is correct, it will need to be published in a peer-reviewed journal and then evaluated by the community over two years (so Perelman, too, needs to wait -- if he's interested at all.)

The Riemann hypothesis was also one of David Hilbert's problems for the twentieth century, and the only one to appear both on his list and on the Clay Institute's.


Anonymous said...


are there any links discussing the proposed solution in general terms. also is there a biography of professor pati online.


Anonymous said...

sort of (indian-type) biography of Prof. Pati is here:


Rahul said...

I'm sure the links will come up... I'm not a mathematician (let alone a number theorist) myself. The paper looked kind of straightforward though, not terribly long, one just has to work through it. If there are any errors I suspect they'll be extremely subtle. The link that vani provides suggests Prof Pati has been sitting on his results (no doubt, trying to convince himself it's bulletproof) for several months, if not longer.

issan said...

theres no $ 1 million award for disproof of RH
since the paper is small and many of the results are known it shud take less time for a flaw to come out if there is any.

Rahul said...

Issan -- that's not what the rules page says. It only casts doubt in the case where a counterexample may leave open a slightly modified form of the hypothesis -- but they're probably happy if it "effectively resolves the problem". Note that Prof Pati's disproof is a reductio ad absurdum, not a counterexample.

You are right that the paper looks like it should be easy to check. Let's wait and see.

Anonymous said...

yeah that is possible of course!
Some of my teachers must be having a look at the proof here at ISI so we hope to get some report very soon!