Anthropic AI Formalizes Proof of Fermat's Last Theorem in Just 11 Days

An AI system from Anthropic has fully formalized the famous proof of Fermat's Last Theorem in under two weeks, into a computer-verifiable proof — a task that normally takes mathematicians years to complete.

Anthropic AI has achieved a remarkable milestone in mathematics: the company behind the chatbot Claude claims to have fully formalized the proof of Fermat's Last Theorem in just eleven days. That means the famous mathematical puzzle, unsolved for decades, has now been converted into a form that can be verified step by step by a computer. According to the renowned scientific journal Nature, this is a breakthrough that could fundamentally change the way mathematicians work with proofs.

What exactly is Fermat's Last Theorem?

Fermat's Last Theorem is one of the most famous problems in mathematics. The French lawyer and amateur mathematician Pierre de Fermat wrote in the margin of a book in 1637 that he had a proof for the theorem, but that the margin was too small to write it down. It wasn't until 1994 that the British mathematician Andrew Wiles succeeded in delivering a complete, accepted proof, after years of solitary work. However, that proof is so complex and extensive that formalizing it — rewriting it in a strictly logical language that computers can check — has long been regarded as one of the greatest challenges within the mathematical community.

Why the formalization is so remarkable

Formal verification is a process in which every step of a mathematical proof is rewritten in a programming language for proof systems, such as Lean, so that a computer can check whether there are any logical errors or gaps. For Wiles's proof, this project — known as the "Fermat Formalization" or similar initiatives — was estimated to require multiple years of work from teams of mathematicians and computer scientists. The fact that Anthropic's AI reportedly accomplished this within eleven days is therefore stunning. It shows that modern artificial intelligence is no longer just good at generating text or code, but is also becoming increasingly capable of deep, structured mathematical reasoning at an expert level. For more background on how AI systems have developed over the years to reach this kind of achievement, check out the history of artificial intelligence.

A new phase for AI in science

This result fits into a broader trend in which large language models and specialized AI systems are being deployed for complex scientific and mathematical tasks. Earlier, systems such as Google DeepMind's AlphaProof and AlphaGeometry already showed that AI is capable of solving olympiad-level math problems. With this formalization of Fermat's Last Theorem, Anthropic builds on that trajectory, but raises the bar even higher by tackling one of the most iconic and complex proofs in modern mathematics. For scientists, this potentially means an enormous acceleration of research: proofs that previously required years of manual, error-prone work can now possibly be verified — or even co-developed — with the help of AI within weeks. That opens the door to faster checking of existing mathematical knowledge, but also to tackling problems that remain unsolved. Curious about other concrete AI applications in science and technology? There is now a wide range of examples, from protein folding to climate modeling.

Critical notes

Still, some caution is warranted. Experts point out that formalizing a proof is different from independently coming up with a new mathematical insight: the AI was given Wiles's human proof as a starting point and had to "translate" it into a machine-verifiable form, with support from human mathematicians who checked the results. So this is not a proof that the AI "discovered" on its own, but it is an impressive demonstration of reasoning ability, consistency across a long chain of logical steps, and collaboration between human and machine. In addition, the rapid progress of AI systems, even in such technical domains, raises broader questions about oversight and accountability — something recently emphasized by international organizations such as the UN, with warnings about the risks of uncontrolled AI development.

Looking ahead: what does this mean for the future?

The formalization of Fermat's Last Theorem by Anthropic's AI system is a powerful signal that AI is set to play an increasingly serious role in fundamental scientific research. If this technology is refined further, formalizing and verifying complex mathematical proofs could become a routine task, allowing mathematicians to focus more on developing new ideas rather than meticulous checking work. For those who want to follow developments closely, our site offers continuous updates: check out more AI news for the latest developments, or dive deeper into the background via our knowledge base. One thing is certain: the line between human and machine mathematical creativity is blurring rapidly, and breakthroughs like this will appear in the news more and more often in the years to come.

Nature

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Source: Nature