Physicists Giuseppe Mussardo and André LeClair published an article in which, using physical rather than mathematical methods, they demonstrated (mathematically!) that “while a violation of the Riemann Hypothesis (RH) is strictly speaking not impossible, it is nevertheless extremely improbable.”; that is, it is technically possible for the RH to be false, but it is extremely unlikely. SISSA – where Mussardo works – published a press release titled “The Riemann Conjecture Revealed by Physics.” The Riemann Hypothesis, or Riemann Conjecture, is a conjecture about the distribution of nontrivial zeros of the Riemann zeta function ζ(s). Its importance stems from its implications for the distribution of prime numbers. From the functional equation it follows that the Riemann zeta function ζ(s) has zeros, called trivial, in the even negative integers, s = −2, s = −4, s = −6, … The Riemann conjecture, on the other hand, concerns non-trivial zeros and states that “The real part of every non-trivial root is 1/2”. In other words, the non-trivial roots should all lie on the line described by the equation s = 1/2 + it (the so-called “critical line”) with t being a real number and ei being an imaginary unit. The Riemann hypothesis, first formulated in 1859 by Bernhard Riemann, is considered the most important open problem in mathematics. It is one of the twenty-three Hilbert problems and the seven Millennium problems, for the solution of each of which the Clay Mathematical Institute has offered a prize of one million dollars.
