AI Just Solved a 350-Year-Old Math Problem By Writing the Longest Proof Ever

In brief

• Anthropic says its Claude AI produced the first fully computer-checked proof of Fermat's Last Theorem in 11 days, largely on its own, writing what's now the longest math proof ever built.
• A human-led project doing this exact same job has been running at Imperial College London since 2024 and isn't close to finished. Claude beat it to the finish line.
• Kevin Buzzard, the mathematician leading that human project, reviewed Claude's proof and confirmed it holds up using nothing but math's most basic logical rules.

Anthropic says its Claude AI just wrote the longest math proof ever made, and used it to formally prove Fermat's Last Theorem, a problem that stumped mathematicians for 358 years.

Claude did it in 11 days, mostly on its own, producing 13 million lines of code that a computer can check line by line, instead of just taking a mathematician's word for it.

Fermat’s last theorem says you can't take three positive whole numbers, raise each one to a power higher than 2, and have the first two add up to the third. He scribbled that claim into the margin of a math book in 1637, adding that he had a "truly marvelous proof" that the margin was just too small to fit.

Then he died. Mathematicians spent the next 358 years trying to reconstruct whatever he thought he had.