Thursday, June 10, 2004

Has the Riemann Hypothesis been Proven?

From this press report, it would appear that Louis de Branges, of Bieberbach Conjecture fame, is claiming a proof of the Riemann Hypothesis.

This, if true, would be the single greatest mathematical result of the decade, and maybe even of the last 100 years, depending on one's viewpoint; as such, I shall refuse to accept that the Riemann Hypothesis has fallen until de Branges' proof goes through the normal process of peer review several times.

The strangest thing about this purported proof is the rambling style of the "apology", which touches on, amongst many other things, de Branges' early life, his mathematical education and even his ancestral backround, including how he intends to use the million-dollar Clay prize to rehabilitate his ancestral seat; the real meat and potatoes are saved for a 124-page paper innocuously titled Riemann Zeta Functions. Now, it may be that the guy's always been an oddball, but there's just something about the way he's chosen to announce his results (why a press release, instead of via ArXiv?) that tells me that the old boy's gone completely nuts, a known occupational hazard of the mathematician's profession.

Even if Louis de Branges hasn't gone absolutely mad, I'm still betting that the euphoria which drove him to release his results in this manner will not bear up under examination, and some irreparable hole will be found in his work that will leave the Riemann Hypothesis where it's long been, as the single most famous unsolved problem in all of mathematics. Euphoria's a dangerous thing, and even we lesser talents know what it's like to feel absolutely convinced for a while that we've finally cracked some difficult problem, only for the illusion to fall apart under sober re-examination.

ADDENDUM: Looking around on Slashdot, I see that this is far from being the first time he's claimed to have a proof of the Riemann Hypothesis, and that he's apparently made grandiose claims for other problems as well. This looks very much to me like a guy hoping that lightning will strike twice; I'd put the odds of his being correct at no more than 250-to-1.