Mathematical Exploration

Fascinating preprint by some reasonably credible mathematicians 🤓 (Terence Tao, Javier Gómez-Serrano) working with Google DeepMind's Bogdan Georgiev and Adam Zsolt Wagner: MATHEMATICAL EXPLORATION AND DISCOVERY AT SCALE.

They used Alpha-Evolve, which uses an LLM to perform a type of "evolutionary computation" by mutating and modifying populations of programs that perform tasks to optimize an objective (or fitness) function. What they found was that Alpha-Evolve is not a superstar on single instances but "can be readily scaled up to study large classes of problems at a time, without requiring extensive expert supervision for each new problem. This demonstrates that evolutionary computational approaches can systematically explore the space of mathematical objects in ways that complement traditional techniques, thus helping answer questions about the relationship between computational search and mathematical existence proofs." Hence the title: discovery at scale.

It has been fun to watch Tao experiment with AI over time. Enjoy!

Vlad Tenev, Tudor Achim, Vivek Natarajan