Can AI assist in Mathematics and Computer Science research?

We share our experience using LLMs to obtain new results in mathematics and computer science. We begin with an illustrative example from load-balancing in planet-scale cloud systems, outlining the abilities and limitations of LLMs. Next, we describe our experience with AlphaEvolve, an evolutionary language model from Google DeepMind, to establish new results in the approximability of the Traveling Salesman Problem (TSP), and MAX-CUT problem. We also derive new bounds for several Ramsey numbers. Our methodology entails evolving fleets of Python programs that generate proof chunks to yield these results, and to accelerate proof verification by up to 10,000x. We suggest that our results on inapproximability and Ramsey theory could not have been discovered by hand, and conclude with reflections on the state and promise of AI in mathematics and CS research.

Speaker: Prabhakar Raghavan, Google

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