Claude Advances 167-Year-Old Math Problem: 31 Million Tokens, 60 Agents, and a Leap from 41.6% to 67.2%

Anthropic's Claude model has shifted a 167-year-old mathematical problem off the dead center, achieving a significant breakthrough. The problem, posed in 1859, is rooted in analytic number theory and involves the nature of prime numbers. Claude's performance on this problem jumped from 41.6% to 67.2% after applying a novel training regime. The model consumed 31 million tokens, which is equivalent to roughly 25.6 million words, and during the process, it generated 650 GB of data. To tackle the problem, Claude used 60 specialized agents, each analyzing around 2400 papers, including 54 relevant papers from arXiv, to ensure its reasoning was sound. The use of reinforcement learning and verification through Lean, a proof assistant, were crucial. Anthropic attributes the success to this combination of large-scale computation and formal verification, marking a new milestone in AI-assisted mathematical discovery.