Checking that a major mathematical proof is correct can take years. Formalization—converting the mathematical reasoning into a form computer proof assistants like Lean can verify—can help. Last month, Claude completed the first formalized proof of Fermat’s Last Theorem, one of the most famous theorems of all time. This was a project experts thought would take many years. It is the largest Lean proof ever written. Fermat’s Last Theorem was first proven in 1995 by Sir Andrew Wiles, more than 350 years after it was conjectured. Our proof, which totals over 13 million lines of code, provides machine verification. More importantly, it proves over 29,000 other theorems that the proof requires, across many areas of math which had never before been formalized. We see this as a major step in the long process of firming up the core of mathematical knowledge, building on work from three centuries of mathematicians and hundreds of contributors to Lean and Mathlib. We are optimistic that AI-assisted verification of mathematical proofs will help reduce the burden of refereeing mathematics in an era where more proofs are being produced than ever before. You can read about the process on our Science Blog: anthropic.com/research/forma… And see the complete proof on GitHub: github.com/anthropics/fermat…

There’s been a lot of speculation about where we stand on open-weights models. We’ve outlined our views in full here: anthropic.com/news/position-…

Since June 12, we’ve been working closely with the US government to restore access to Claude Mythos 5 and Fable 5. Today, the government notified us that Mythos 5, our strongest cybersecurity model, can be redeployed to a set of US organizations that operate and defend critical infrastructure. We’re restoring access for these organizations quickly, and we’re continuing to work with the government to expand access to Mythos 5 and make Fable 5 available for general use again.

We've raised $65 billion in Series H funding at a $965 billion post-money valuation, led by @AltimeterCap, Dragoneer, @Greenoaks, and @sequoia. This investment will help us advance our research and expand our capacity to meet growing demand for Claude.