# Mathematical exploration and discovery at scale

arXiv: https://arxiv.org/abs/2511.02864 · HTML: https://mlsanity.com/paper/2511.02864/

## Key facts

- Cited by 77 papers in the map (data through 14 Oct 2026).
- Placed in Educational agents and math problem solving, one of 16 directions in LLM agents and tool use.
- First posted on arXiv 3 Nov 2025.

## Placed in

- LLM agents and tool use / [Educational agents and math problem solving](https://mlsanity.com/agents/educational-agents-and-math-problem-solving/)

## Built on by (most cited first, 30 of 77)

- [Beyond Benchmarks: MathArena as an Evaluation Platform for Mathematics with LLMs](https://mlsanity.com/paper/2605.00674/) (2026)
- [ThetaEvolve: Test-time Learning on Open Problems](https://mlsanity.com/paper/2511.23473/) (2025)
- [EvoX: Meta-Evolution for Automated Discovery](https://mlsanity.com/paper/2602.23413/) (2026)
- [A Survey of Agentic Reasoning for Large Language Models: Towards Recursively Self-Improving and Collective Agents](https://mlsanity.com/paper/2601.12538/) (2026)
- [Building Production-Ready Probes For Gemini](https://mlsanity.com/paper/2601.11516/) (2026)
- [Towards Autonomous Mathematics Research](https://mlsanity.com/paper/2602.10177/) (2026)
- [MLEvolve: A Self-Evolving Framework for Automated Machine Learning Algorithm Discovery](https://mlsanity.com/paper/2606.06473/) (2026)
- [DeltaEvolve: Accelerating Scientific Discovery through Momentum-Driven Evolution](https://mlsanity.com/paper/2602.02919/) (2026)
- [Advancing Mathematics Research with AI-Driven Formal Proof Search](https://mlsanity.com/paper/2605.22763/) (2026)
- [Structured Scaling of AI Discovery Across Diverse Scientific Domains](https://mlsanity.com/paper/2604.19341/) (2026)
- [Dream-RSI: Recursive Self-Improvement through Evolving Worlds](https://mlsanity.com/paper/2609.14858/) (2026)
- [AgenticSciML: Collaborative Multi-Agent Systems for Emergent Discovery in Scientific Machine Learning](https://mlsanity.com/paper/2511.07262/) (2025)
- [GigaEvo: An Open Source Optimization Framework Powered By LLMs And Evolution Algorithms](https://mlsanity.com/paper/2511.17592/) (2025)
- [Simple Baselines are Competitive with Code Evolution](https://mlsanity.com/paper/2602.16805/) (2026)
- [Reinforced Generation of Combinatorial Structures: Ramsey Numbers](https://mlsanity.com/paper/2603.09172/) (2026)
- [Measuring Progress in Reasoning Toward Mathematical Discovery with Automatic Verification](https://mlsanity.com/paper/2603.15617/) (2026)
- [ATHENA: Agentic Team for Hierarchical Evolutionary Numerical Algorithms](https://mlsanity.com/paper/2512.03476/) (2025)
- [ArchAgent: Agentic AI-driven Computer Architecture Discovery](https://mlsanity.com/paper/2602.22425/) (2026)
- [LEVI: Stronger Search Architectures Can Substitute for Larger LLMs in Evolutionary Search](https://mlsanity.com/paper/2605.09764/) (2026)
- [GRAFT-ATHENA: Self-Improving Agentic Teams for Autonomous Discovery and Evolutionary Numerical Algorithms](https://mlsanity.com/paper/2605.11117/) (2026)
- [Large Language Model Agent for User-friendly Chemical Process Simulations](https://mlsanity.com/paper/2601.11650/) (2026)
- [LiveMathematicianBench: A Live Benchmark for Research-Level Mathematical Reasoning with Proof Sketches](https://mlsanity.com/paper/2604.01754/) (2026)
- [Computer Architecture's AlphaZero Moment: Automated Discovery in an Encircled World](https://mlsanity.com/paper/2604.03312/) (2026)
- [Discovering Multiagent Learning Algorithms with Large Language Models](https://mlsanity.com/paper/2602.16928/) (2026)
- [The Agentic Researcher: A Practical Guide to AI-Assisted Research in Mathematics and Machine Learning](https://mlsanity.com/paper/2603.15914/) (2026)
- [Flow-based Extremal Mathematical Structure Discovery](https://mlsanity.com/paper/2601.18005/) (2026)
- [ConvexBench: Can LLMs Recognize Convex Functions?](https://mlsanity.com/paper/2602.01075/) (2026)
- [CausalEvolve: Towards Open-Ended Discovery with Causal Scratchpad](https://mlsanity.com/paper/2603.14575/) (2026)
- [What Do Evolutionary Coding Agents Evolve?](https://mlsanity.com/paper/2605.20086/) (2026)
- [LLMs, Reasoning and Plagiarism](https://mlsanity.com/paper/2601.02380/) (2025)

## Abstract (arXiv)

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.