Can AI Symbolically Derive the Zeta Operator? Early Signs Are Encouraging.

[Mqhele-dot]

Hi all,

Over the past few months, I've worked with AI tools like PySR and quantum eigenvalue solvers to pursue something long considered unreachable: deriving a self-adjoint operator whose spectrum aligns with the non-trivial zeros of the Riemann zeta function — a concept central to the Hilbert–Pólya conjecture.

Using symbolic regression, the AI discovered the following operator:

H = -d²/dx² + x² + sin(7x)

This operator, when numerically evaluated, yields eigenvalues that align closely with the imaginary parts of the first 50 non-trivial zeros of the zeta function — with less than 5% deviation in several regimes.

GitHub repo with full source and data:
https://github.com/Mqhele-dot/zeta-operator

Challenge to the Community:
Can this operator be derived analytically from known zeta structures?

Is the spectral alignment mathematically meaningful or coincidental?

Can AI-assisted methods like PySR accelerate discovery in unresolved conjectures?

Would love your insights, challenges, or criticisms. Even if this doesn't yet form a formal proof, it's an example of symbolic-AI meeting deep math problems head-on.

Looking forward to feedback!