Mathematical exploration and discovery at scale
2025/11/03 by Bogdan Georgiev, Georgiev, Bogdan, Javier Gómez-Serrano +6 · 13 voices · 13 citations
Computer Science · #Evolutionary Algorithms and Applications #Artificial Intelligence in Games #Mathematics, Computing, and Information Processing
paper · pdf · doi:10.48550/arxiv.2511.02864
Abstract
AlphaEvolve (Novikov et al., 2025) 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 paper we showcase AlphaEvolve as a tool for autonomously discovering novel mathematical constructions and advancing our understanding of long-standing open problems. To demonstrate its breadth, we considered a list of 67 problems spanning mathematical analysis, combinatorics, geometry, and number theory. The system rediscovered the best known solutions in most of the cases and discovered improved solutions in several. In some instances, AlphaEvolve is also able to generalize results for a finite number of input values into a formula valid for all input values. Furthermore, we are 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 and further mathematical insights. These results demonstrate that large language model-guided evolutionary search can autonomously discover mathematical 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 mathematicians and AI systems. We present AlphaEvolve as a powerful new tool for mathematical discovery, capable of exploring vast search spaces to solve complex optimization problems at scale, often with significantly reduced requirements on preparation and computation time.
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Discussions
- A new paper with Bogdan Georgiev, Javier Gomez-Serrano, and Adam Zsolt Wagner: "Mathematical exploration and discovery at scale" arxiv.org/abs/2511.02864. Further discussion is at terrytao.wordpress.c [bsky, 125 points, 0 comments]
- Mathematical exploration and discovery at scale – Terence Tao et al. [hn, 4 points, 1 comments]
- I *thought* it was weird that we hadn’t heard more from mathematicians using AlphaEvolve. It turns out they were just biding their time to drop an 80-page mega-paper describing its use on 67 different [bsky, 4 points, 2 comments]
- Mathematical Exploration and Discovery at Scale [hn, 4 points, 2 comments]
- "Building a pipeline of .. AI tools.. for the Kakeya problem, AlphaEvolve discovered an interesting general construction. When we fed this .. to Deep Think, it successfully derived a proof.. This proo [bsky, 3 points, 1 comments]
- must have missed this [bsky, 2 points, 0 comments]
- AlphaEvolve integrates large language models with evolutionary algorithms to autonomously generate, test, and refine mathematical constructions. It rediscovered known results, improved others, and poi [bsky, 2 points, 0 comments]
- Mathematical Exploration and Discovery at Scale [hn, 2 points, 0 comments]
- 谷歌DeepMind AlphaEvolve取得重大突破，由大语言模型驱动的进化智能体，获数学家陶哲轩认可并联合发论文 它通过进化算法在程序空间搜最优解，能将有限结果泛化为通用公式，在亲吻数问题、矩阵乘法等领域刷新成果 更与DeepThink、AlphaProof构建“发现-验证”闭环，彻底打通AI数学研究全流程，有兴趣伙伴看一下论文 arxiv.org/pdf/2511.02864 [bsky, 1 points, 0 comments]
- Mathematics and software engineering have more overlap than is often acknowledged. A new AI coding agent called AlphaEvolve produced new results on a range of mathematical problems. arxiv.org/abs/2511 [bsky, 0 points, 1 comments]
- I have worked out that the side length of the new best packing of 12 hexagons in a hexagon found by AlphaEvolve (arxiv.org/abs/2511.02864) is the positive root of 27s^10 - 108s^8 - 8118s^6 - 211591s^4 [bsky, 0 points, 0 comments]
- arxiv.org/abs/2511.02864 <<-- [bsky, 0 points, 0 comments]
- Mathematical exploration and discovery at scale arxiv.org/abs/2511.02864 [bsky, 0 points, 0 comments]
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