AlphaEvolve: an LLM-based coding agent, to find and verify combinatorial structures that improve results on the hardness of approximately solving certain optimization problems.

Recently, large language models (LLMs) have demonstrated surprising capabilities in competitive mathematics and competitive programming, demonstrating world-leading performance across both of these fields. However, their successes in mathematical discovery — proving novel theorems or uncovering new combinatorial structures — have been relatively few (with some notable exceptions [1, 2, 3]). Since mathematics and theoretical computer science demand absolute correctness[1], any AI-based method that makes mathematical discovery must either have a proof of correctness that can be confirmed computationally (without any human involvement), or have a domain-expert human in the loop to certify correctness.