Physicists Attack Math’s $1,000,000 Question

Proving the Riemann hypothesis remains arguably the most important unsolved problem in pure mathematics—one whose solution would fetch a $1 million Millennium Prize from the Clay Mathematics Institute. Conversely, as the number theorist Enrico Bombieri, Professor Emeritus in the School of Mathematics, wrote in his description of the problem, “the failure of the Riemann hypothesis would create havoc in the distribution of prime numbers.”

. . . Physicists have been searching since 1999 for a quantum system whose energy levels correspond to the zeros of the zeta function. In a paper published on March 30 in Physical Review Letters, Carl Bender, Member (1969–70) in the School of Natural Sciences, Dorje Brody, and Markus Müller proposed just such a candidate system.

. . . Experts say that the new proposal is interesting, but that it’s far from certain whether the authors’ arguments about their unconventional quantum system can be made rigorous. “I would need more time to give a relevant opinion about the significance of their findings as a strategy towards the Riemann hypothesis,” said Paul Bourgade, Member (2013–14) in the School of Mathematics. In particular, Bourgade said, he would like to explore in more detail how the proposed quantum system compares with one previously proposed by Berry and Keating that has not yielded a concrete proof.