History In a letter to Andrew Odlyzko, dated January 3, 1982, George Polya said that while he was in Gottingen around 1912 to 1914 he was asked by Edmund Landau for a physical reason that the Riemann hypothesis should be true, and suggested that this would be the case if the imaginary parts t of the zeros
1/2+it
of the Riemann zeta function corresponded to eigenvalues of an unbounded self-adjoint operator.[1] The earliest published statement of the conjecture seems to be in Montgomery (1973).[1][2]
David Hilbert did not work in the central areas of analytic number theory, but his name has become known for the Hilbert?Polya conjecture for reasons that are anecdotal.
Recent times In a development that has given substantive force to this approach to the Riemann hypothesis through functional analysis, Alain Connes has formulated a trace formula that is actually equivalent to the Riemann hypothesis. This has therefore strengthened the analogy with the Selberg trace formula to the point where it gives precise statements. He gives a geometric interpretation of the explicit formula of number theory as a trace formula on noncommutative geometry of Adele classes.[4]
