AI Agent AlphaEvolve Advances Ramsey Number Research with Nine Improved Lower Bounds
A new preprint on arXiv highlights improved computational lower limits for nine traditional Ramsey numbers in combinatorial math. Researchers used AlphaEvolve, a code mutation tool powered by a large language model, to make notable progress: they updated R(3,13) from 60 to 61, R(3,18) from 99 to 100, R(4,13) from 138 to 139, R(4,14) from 147 to 148, R(4,15) from 158 to 159, R(4,16) from 170 to 174, R(4,18) from 205 to 209, R(4,19) from 213 to 219, and R(4,20) from 234 to 237. Additionally, AlphaEvolve found lower bounds for all exact Ramsey numbers and matched leading lower bounds in other scenarios. The paper is archived as arXiv:2603.09172v5 and illustrates how large language models can advance mathematical research through automated coding.
Key facts
- AlphaEvolve is an LLM-based code mutation agent used for mathematical research
- Nine classical Ramsey numbers received improved lower bounds
- R(4,16) increased from 170 to 174
- R(4,19) increased from 213 to 219
- R(4,20) increased from 234 to 237
- The system recovered lower bounds for all known exact Ramsey numbers
- The research paper is arXiv:2603.09172v5
- Virtually all known Ramsey lower bounds are computationally derived
Entities
Institutions
- arXiv