Anthropic says Claude formalized Fermat's Last Theorem in 11 days with 13 million Lean lines

Fermat's Last Theorem was first proposed by Pierre de Fermat in 1637. Mathematician Andrew Wiles produced the first full mathematical proof in 1995, spanning 129 pages. Formalizing a proof means converting its mathematical reasoning into code that computers can check automatically without human assistance.

Anthropic says its internal research model completed the entire proof in 11 days of continuous, largely unsupervised work. The finished proof runs to 13 million lines of specialized code written in Lean, a programming language used by mathematicians. Along the way, Claude's agents reportedly proved roughly 30,300 separate theorems, ultimately using 29,500 of them in the final version. Human input was reportedly limited to occasional high-level guidance, rather than direct hands-on coding over the 11-day process.

At 13 million lines, the resulting proof is more than five times larger than Mathlib, the mathematical community's main proof library. Kevin Buzzard, a mathematician at Imperial College London, described the work as an extraordinary autoformalization achievement. 'This extraordinary autoformalization achievement…proves Fermat's Last Theorem with no assumptions other than the axioms of mathematics,' Buzzard said, according to TechRadar. 'Along the way we see autoformalization of algebra, harmonic analysis, geometry and number theory, and we learn that AI autoformalization artefacts are now robust enough to be built upon; the proof is multi-layered.'

Anthropic attempted the formalization several times before succeeding. Those earlier efforts contributed roughly 7% of the final proof's non-boilerplate lines, TechRadar reported.

The formalization follows a separate Anthropic result one month earlier involving the Riemann zeta function, a mathematical object at the center of the Riemann hypothesis. Rival lab OpenAI is also pursuing similar work, using its newest Astra model to solve several classic Erdős problems. That effort also reportedly narrowed several long-standing open questions in theoretical computer science.

Anthropic says the breakthrough came after it gave Claude access to an open-source software tool called Prove2Me, built by outside collaborators. The software helps AI agents pick the most useful next step during a long, multi-stage research workflow, while also cutting inference costs. Anthropic has also expanded free access and research credits for mathematicians working specifically on formalization projects, alongside dedicated larger grants.

Despite the record pace described by the company, an 11-day timeline still shows how labor-intensive full formalization remains, even with today's most capable systems, according to TechRadar.