The November 3, 2025 paper provide an overview of the **AlphaEvolve** system, an AI-powered evolutionary approach for mathematical exploration and discovery, often involving large language models (LLMs) to generate and mutate programs that act as search heuristics for finding extremal mathematical objects. The first source is a **GitHub repository** from Google DeepMind that serves as a **collection of 67 mathematical problems** used to test AlphaEvolve, noting that the code for the system itself is not included. The second, more extensive source is an **academic paper** detailing AlphaEvolve's methodology, contrasting it with its predecessor FunSearch, and showcasing its application to solving a **wide array of complex, open mathematical problems** across combinatorics, geometry, analysis, and number theory, frequently achieving or improving upon state-of-the-art bounds. This system demonstrates proficiency in both a standard search mode for fixed problem sizes and a "generalizer mode" for developing programs that solve problems for arbitrary inputs.

Sources:

https://arxiv.org/pdf/2511.02864

https://github.com/google-deepmind/alphaevolve_repository_of_problems