Google researchers Ansh Nagda, Prabhakar Raghavan, and Abhradeep Guha Thakurta have published a paper (arXiv:2603.09172) demonstrating that AlphaEvolve, Google DeepMind's LLM-based code mutation agent, can make verifiable advances in pure mathematics. The system improved lower bounds for five classical Ramsey numbers: 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, and R(4,15) from 158 to 159. Ramsey numbers quantify the minimum size of a complete graph required to guarantee certain monochromatic subgraph structures — a problem area where progress has historically been measured in years or decades of effort by mathematicians and computer scientists.
Traditionally, each improvement to a Ramsey lower bound requires a hand-crafted search algorithm built specifically for that target. AlphaEvolve replaces this: it uses an LLM to generate and <a href="/news/2026-03-14-autoresearch-fork-evolutionary-database-claude-codex">mutate search algorithm code</a>, evaluating each candidate against automated verifiers, acting as a single meta-algorithm adaptable across cases. The system also recovered all Ramsey lower bounds known to be exact and matched best-known bounds across many other cases — including ones where prior literature does not document the underlying algorithms used at all.
Raghavan, Google's Chief Technologist, has spent his career in algorithms and complexity theory, which makes him a natural fit for a paper centered on automating combinatorial search. His co-author Thakurta is a Google DeepMind research scientist known for deploying differential privacy at production scale. Google DeepMind first unveiled AlphaEvolve in May 2025 as a Gemini-powered evolutionary coding agent; its documented applications before this paper include optimizing data center scheduling, improving TPU circuit design, and accelerating LLM training. The Ramsey numbers paper, submitted March 10, 2026, is the first time the system has produced results in peer-reviewable pure mathematics.