AlphaEvolve is a generic evolutionary coding agent that combines the generative capabilities of LLMs with automated evaluation in an iterative evolutionary framework that proposes, tests, and refines algorithmic solutions to challenging scientific and practical problems. In this talk I will present AlphaEvolve, discussing its implications as a tool for autonomously discovering novel mathematical constructions and algorithms, advancing our understanding of long-standing open problems. Moreover, AlphaEvolve is also able to generalize results for a finite number of input values into a formula valid for all input values, and in some instances we were able to combine this methodology with Deep Think and AlphaProof in a broader framework where the additional proof-assistants and reasoning systems provide automated proof generation. These results demonstrate that large language model-guided evolutionary search can autonomously discover constructions that complement human intuition, at times matching or even improving the best known results, highlighting the potential for significant new ways of interaction between scientists and AI systems. We present AlphaEvolve as a powerful new tool for discovery, capable of exploring vast search spaces of algorithms to solve complex optimization problems at scale, often with significantly reduced requirements on preparation and computation time.
