Riemann hypothesis is "is a conjecture that the Riemann zeta function has its zeros only at the negative even integers and complex numbers with real part ". The Riemann zeta function is conventionally represented as the sum:
Recently, I read in Peter Woit's blog that some researchers have published a paper that describes a Hamiltonian operator H that can be used to possibly solve this problem. This operator has the property that if the eigenfunctions obey a suitable boundary condition, then the associated eigenvalues correspond to the nontrivial zeros of the Riemann zeta function! The paper is also available as a preprint. In a sense, this paper says that one can set up a quantum system whose evolution "solves" Riemann hypothesis. To me this is a reasonable approach to the solution of the problem. And it reminds me of the work of Leonard Adlemam.