Mathematical discoveries from program search with large language models
Problem
LLM confabulations hinder scientific discovery, and the cap set problem in extremal combinatorics lacked constructions beyond the best-known ones.
Why it matters
Trustworthy LLM-driven discovery could accelerate progress on established open mathematical problems.
What the AI did
FunSearch pairs a pretrained LLM with a systematic evaluator to evolve programs, discovering new cap set constructions beyond the best-known ones.
Results
New constructions of large cap sets going beyond best-known ones, in both finite-dimensional and asymptotic cases.
Impact
Shows LLM-based search can make genuine new discoveries for established open problems in mathematics.
Record
| Venue | Nature |
|---|---|
| Published | 2023 |
| Work type | article |
| Authors | Bernardino Romera‐Paredes, Mohammadamin Barekatain, Alexander Novikov, Matej Balog, Manish Kumar, Emilien Dupont, Francisco J. R. Ruiz, Jordan S. Ellenberg et al. |
| Citations | 509 (OpenAlex, at import time) |
| References | 74 |
| Model or method | FunSearch (pretrained LLM paired with systematic evaluator; specific LLM not stated) |
| Organization | not stated in source |
| Primary source | https://doi.org/10.1038/s41586-023-06924-6 |
| Open access | hybrid |
| Keywords | large language models, FunSearch, cap set problem, program search, combinatorics |
Importance rating
significant — thousands to millions affected
Abstract states FunSearch surpasses best-known results on important problems and enables discoveries for established open problems, a genuinely new capability for trustworthy LLM-driven scientific discovery; no scale given.
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