What Exactly Was Anthropic’s AI Breakthrough in Hard Math?
Claude translated an already proven theorem into a detailed computer-related derivation, which is much more difficult than, say, translating it into CantoneseThere has been a lot of buzz in the last few days that Anthropic’s chatbot Claude is making big breakthroughs in math. The most recent claim concerns Fermat’s Last Theorem.
A bit of background…
The Theorem1 says that it’s impossible to find three whole numbers that — when each is raised to the same power greater than two — add up exactly to one another.2
In 1994, Oxford math prof Andrew Wiles3 solved the Theorem,4 a problem that had stood unsolved for over 350 years.
Wiles’ initial work had a flaw, which he corrected. When other mathematicians verified his revised proof, it was found to be true and Wiles was thus awarded the Abel Prize5, the mathematics equivalent of the Nobel Prize.
Wiles’s proof of Fermat’s Last Theorem was so culturally monumental that it inspired a musical. Fermat’s Last Tango, available on YouTube,6 is great fun — and hilarious if you’re a nerd.7
For his effort, he was knighted by Queen Elizabeth II in 1999 for “For Services to Sciences.”8 Incidentally, in proving Fermat’s Last Theorem, he did not use a computer.9
So what did Claude do?
Now there is much celebration over an AI confirmation of Fermat’s Last Theorem10:
“… an artificial intelligence system from Anthropic has taken this famously difficult proof and turned it into something a computer can verify from start to finish — in just 11 days.”
We are thus celebrating because AI can now verify a theorem previously verified by humans. But Anthropic’s large language model Claude translated the theorem into a detailed computer-related derivation. Doing so is exponentially more difficult than translating Fermat’s last theorem into Cantonese.
Claude’s accomplishment is impressive. Since 2024, Imperial College London mathematician Kevin Buzzard has led a human-driven effort to formalize Fermat’s Last Theorem.
Has Claude solved another problem? It gets tricky
A more intriguing claim is that Claude has solved a portion of the Navier–Stokes problem.11 If true, this is a biggie. A complete and valid solution to this Clay Mathematics Institute’s Millennium Prize Problem, one of seven problems, would qualify for a $1 million prize. However, some experts dispute whether Claude’s result actually meets that standard.12
Others question whether or not human input guided Claude to the solution. The Verge13 reports that one day before the announcement, NYU mathematics professor Tristan Buckmaster and Anthropic researcher Levent Alpöge published findings on a related problem. In an accompanying statement, Buckmaster said he contacted OpenAI after learning that the company was aware of their progress.
He then discovered that OpenAI had produced a Navier–Stokes proof using an approach that he and Alpöge had been exploring with OpenAI’s Codex and Anthropic’s Claude. Buckmaster questioned whether their Codex sessions, which contained project drafts, could have contributed to OpenAI’s result.
We need to wade through all the hype to get to the truth. Right now, the jury’s still weighing the evidence.
[1] Fermat’s last theorem says there are no solutions to xn+yn = zn where x, y and z are positive integers and n is an integer greater than 2.
[2] Wiles was ineligible for the Fields Medal because recipients must be under 40, and he was 41 at the time.
[3] The Abel Prize, “Sir Andrew J. Wiles—The Abel Prize laureate 2016.” https://abelprize.no/abel-prize-laureates/2016.
[4] E. W. Weisstein, “Fermat’s Last Theorem,” MathWorld—A Wolfram Web Resource. https://mathworld.wolfram.com/FermatsLastTheorem.html.
[5] There is no Nobel Prize in math. The Abel Prize is an equivalent.
[6] A. Mazur, “Fermat’s Last Tango (2001),” YouTube, Oct. 6, 2016. https://www.youtube.com/watch?v=RNqQPcMYcG8.
[7] Robert J. Marks, “FERMAT’S LAST TANGO: LIVELY MUSICAL FOR NERDS”
Mind Matters News, April 9, 2021. https://mindmatters.ai/2021/04/fermats-last-tango-lively-musical-for-nerds/
[8] Central Chancery of the Orders of Knighthood, “The Most Excellent Order of the British Empire,” The London Gazette, no. 55710, suppl. 1, p. 34, Dec. 31, 1999. https://www.thegazette.co.uk/London/issue/55710/supplement/34/data.pdf.
[9] S. Singh and J. Lynch, dirs., “Fermat’s Last Theorem,” Horizon, BBC, Jan. 14, 1996. https://vimeo.com/978635806.
[10] T. Puiu, “An AI formalized and verified Fermat’s Last Theorem in 11 days, a task expected to take years,” ZME Science, Sep. 8, 2026. https://www.zmescience.com/science/news-science/fermats-last-theorem-formalized/.
[11] D. Castelvecchi, “OpenAI claims huge maths breakthrough on a famed ‘Millennium Problem’,” Nature, Sep. 8, 2026, https://www.nature.com/articles/d41586-026-02842-5ishe
[12] J. Howlett, “AI may have just solved a million-dollar math problem. The field will never be the same,” Scientific American, Sep. 8, 2026. https://www.scientificamerican.com/article/ai-may-have-just-solved-a-million-dollar-math-problem-the-field-will-never-be-the-same/
[13] E. Roth, “Drama swirls around OpenAI’s legendary mathematical milestone,” The Verge, Sep. 8, 2026. [Online]. Available: https://www.theverge.com/ai-artificial-intelligence/991710/openai-navier-stokes-solution
