# Generative Modeling for Mathematical Discovery

arXiv: https://arxiv.org/abs/2503.11061 · HTML: https://mlsanity.com/paper/2503.11061/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Builds on 1 of its 13 references that are in the map.
- First posted on arXiv 14 Mar 2025.

## Builds on (most cited first, 1 of 1)

- [PatternBoost: Constructions in Mathematics with a Little Help from AI](https://mlsanity.com/paper/2411.00566/) (2024)

## Built on by (most cited first, 10 of 10)

- [A Survey of Agentic Reasoning for Large Language Models: Towards Recursively Self-Improving and Collective Agents](https://mlsanity.com/paper/2601.12538/) (2026)
- [MiGrATe: Mixed-Policy GRPO for Adaptation at Test-Time](https://mlsanity.com/paper/2508.08641/) (2025)
- [Mendel G"odel Machine: Recursive Self-Improving Coding Agents via Comparative Evolution](https://mlsanity.com/paper/2608.07645/) (2026)
- [Symbolic Regression with Multimodal Large Language Models and Kolmogorov Arnold Networks](https://mlsanity.com/paper/2505.07956/) (2025)
- [Using Reasoning Models to Generate Search Heuristics that Solve Open Instances of Combinatorial Design Problems](https://mlsanity.com/paper/2505.23881/) (2025)
- [An AI enhanced approach to the tree unimodality conjecture](https://mlsanity.com/paper/2510.18826/) (2025)
- [Human agency in initial human-AI proof formalization workflows](https://mlsanity.com/paper/2606.04273/) (2026)
- [Project Auto-World: Towards Automated Benchmarking of Neural Relational Reasoners](https://mlsanity.com/paper/2606.24965/) (2026)
- [Mathematical Discovery in the Wild: AI-Guided Proofs in Banach Space Theory](https://mlsanity.com/paper/2607.17388/) (2026)
- [Infrared Subtraction with Artificial Intelligence](https://mlsanity.com/paper/2609.36007/) (2026)

## Abstract (arXiv)

We present a new implementation of the LLM-driven genetic algorithm it funsearch, whose aim is to generate examples of interest to mathematicians and which has already had some success in problems in extremal combinatorics. Our implementation is designed to be useful in practice for working mathematicians; it does not require expertise in machine learning or access to high-performance computing resources. Applying it funsearch to a new problem involves modifying a small segment of Python code and selecting a large language model (LLM) from one of many third-party providers. We benchmarked our implementation on three different problems, obtaining metrics that may inform applications of it funsearch to new problems. Our results demonstrate that it funsearch successfully learns in a variety of combinatorial and number-theoretic settings, and in some contexts learns principles that generalize beyond the problem originally trained on.