AI Just Solved a 350-Year-Old Math Problem By Writing the Longest Proof Ever
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Anthropic says its Claude AI 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.
Key facts
- He spent almost a year fixing it with a former student, Richard Taylor, nearly gave up, and finally published a corrected, 129-page proof in May 1995
- By the time it was done, Claude had proven more than 30,000 supporting theorems and burned through billions of tokens, running on a research model Anthropic says is roughly comparable to Claude Fable
- 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 taking a mathematician's word for it
- The real proof didn't show up until 1995, from British mathematician Andrew Wiles, and it came with a plot twist
Summary
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. 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. 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 taking a mathematician's word for it.