Claude Opus 4.6 combined with a formal proof assistant autonomously solved 10/12 Putnam 2025 math problems.
March 24, 2026
Original Paper
Putnam 2025 Problems in Rocq using Opus 4.6 and Rocq-MCP
arXiv · 2603.20405
The Takeaway
It demonstrates a successful 'compile-first, interactive-fallback' strategy where LLM agents use formal verification (Rocq) to achieve near-expert performance on high-level mathematical reasoning tasks. This moves math benchmarks from probabilistic generation to verified autonomous proof construction.
From the abstract
We report on an experiment in which Claude Opus~4.6, equipped with a suite of Model Context Protocol (MCP) tools for the Rocq proof assistant, autonomously proved 10 of 12 problems from the 2025 Putnam Mathematical Competition. The MCP tools, designed with Claude by analyzing logs from a prior experiment on miniF2F-Rocq, encode a "compile-first, interactive-fallback" strategy. Running on an isolated VM with no internet access, the agent deployed 141 subagents over 17.7 hours of active compute (5