Anthropic AI reportedly finds proof for percolation theory’s “holy grail

An Anthropic AI system reportedly found a proof for a longstanding problem in percolation theory, which studies how substances move through porous materials such as coffee grounds. The problem was considered a “holy grail,” and the reported result came days after a Fields medalist predicted progress on it.

The system did not generate a finished solution on demand. Anthropic researchers gave high-level direction, then AI agents searched mathematical material for a result that humans could verify. The approach points toward AI searching huge mathematical spaces rather than replacing human validation. The reported effort used 950 agents, 210 million tokens, and 21 hours.