Riemann Rave

The most intriguing physical anecdote in du Sautoy's The Music of the Primes is the one about Keating's talk, entitled "Random matrix theory and some zeta-function moments", at the Vienna meeting in 1998.

Many mathematicians were dubious that the physicists could tell them anything beyond their observations on the statistics of Riemann zeroes and quantum chaos on surfaces. Yet another fine bottle of wine had been put forward, which Keating collected in Vienna after his talk. Nina Snaith and Keating had found a formula for generating the numbers known as zeta moments. The sequence begins 1,2,42,24024. The last number had only just been found by mathematicians, and yet it fell out of the physicists' formula when they looked at it just before Keating's talk. Links to the papers by Keating and Snaith, and also to Snaith's thesis, are available on Watkin's page.

Later, Keating went to the library in Goettingen to look up Riemann's original notes on both the zeta zeroes and hydrodynamics. He made the two requests to the librarian, but was handed only one pile of papers. Riemann had been working on both problems at the same time.

More recently, Carl and Michael have been making solid progress on understanding quantum black holes in M Theory. It would be really very interesting if the quantum chaos of such black holes had something to do with the Riemann zeroes. Oh, wait. It already does, because one uses 3x3 Hermitean matrices in a matrix theory setting.