I've been working (together with Javier Gomez-Serrano) with a group at Google Deepmind to explore potential mathematical applications of their tool "AlphaEvolve", a successor of their earlier tool "Funsearch" that was publicly announced today: https://deepmind.google/discover/blog/alphaevolve-a-gemini-powered-coding-agent-for-designing-advanced-algorithms/ . Very roughly speaking, this is a tool that can attempt to extremize functions F(x) with x ranging over a high dimensional parameter space Omega, that can outperform more traditional optimization algorithms when the parameter space is very high dimensional and the function F (and its extremizers) have non-obvious structural features.

Some of the preliminary problems we have tried this on, including problems involving harmonic analysis inequalities, additive combinatorics, and packing, were already mentioned in the announcement; we are now gradually moving on to more challenging problems where the parameter space has a sparser set of good solutions. The work is still ongoing, but I hope to be able to report more upon it when we are closer to completion (probably a few months from now).