The value of “no” in why Hilbert can’t help you solve or prove RH.

Short answer: you can’t. But the setup gets close enough that it takes real work to find the exact reason it can’t — and that reason turns out to be more interesting than the failed attempt itself. The Paper The setup The Riemann Hypothesis says every non-trivial zero of the zeta function sits on a specific vertical line in the complex plane. Nobody has proven it, but there’s a beautiful conjectural shortcut called the Hilbert–Pólya program: if you could find some self-adjoint operator — the kind of thing that shows up constantly in quantum mechanics, always with real eigenvalues — whose eigenvalues happened to be exactly the zeta zeros, the Hypothesis would fall out for free. Self-adjoint operators can’t have complex eigenvalues, so if the zeros are a spectrum, they’re automatically on the line. The catch, for over a century, has been finding the operator. Nobody has one. But the conjecture is specific enough that you can go looking, and people have. This project is one of those…