Google DeepMind AI Co-Mathematician Cracks Five Ramsey Number Records Unsolved for Decades

Google DeepMind published its AI Co-Mathematician system, a multi-agent framework based on Gemini that improved lower bounds on five Ramsey numbers unsolved for up to 20 years — and set a new high on the FrontierMath Tier 4 benchmark.

FrontierMath Tier 4: 48% — A New Record

The AI Co-Mathematician scored 48% on FrontierMath Tier 4, a benchmark of research-level mathematical problems designed to remain beyond AI capabilities for decades. This surpasses all previously published AI systems on the benchmark.

Five Ramsey Number Records Broken

AlphaEvolve improved lower bounds for five classical Ramsey numbers in a single run:

• R(3,13): 60 → 61 (previous record held for 11 years)
• R(3,18): 99 → 100 (previous record held for 20 years)
• R(4,13): 138 → 139, R(4,14): 147 → 148, R(4,15): 158 → 159

How It Works

Unlike standard LLM-based math solvers, AlphaEvolve generates and iteratively improves algorithms using an evolutionary search strategy. It maintains a population of candidate programs and uses language models to mutate the most promising solutions. Across more than 50 open mathematical problems, it rediscovered state-of-the-art solutions 75% of the time and improved on them in 20% of cases. The paper is available at arXiv:2605.06651.