NederlandsA thousand Claude agents reproduce a formal proof of Fermat's Last Theorem
In 28.7 hours, a thousand AI agents running an early version of Claude Fable 5.2 turned the proof of Fermat's Last Theorem into code that a computer can check. According to Anthropic, it was faster and more efficient than in September, with more prepared work as a starting point.
After the launch of Claude Fable 5.2 and Mythos 5.2, Anthropic described how a thousand AI agents running an early version of Fable 5.2 rebuilt a formal proof of Fermat's Last Theorem. According to the company, this took 28.7 hours, without a researcher steering the content of the work.
Fermat's Last Theorem says that there are no positive whole numbers a, b and c for which a to the power n plus b to the power n equals c to the power n, when n is greater than 2. Pierre de Fermat wrote it in the margin of a book around 1637. It was not until 1995 that Andrew Wiles came up with a proof of 129 pages.
So this is not a new proof. The agents translated the existing proof into Lean, a programming language in which a computer can check every step of a mathematical proof. A formal proof like this leaves no room for a forgotten intermediate step.
Faster than in September
Anthropic already made such a formal version in September. Dozens of agents worked on it then, using an internal research model similar to Claude Fable 5.1, together with the mathematics platform Prove2Me and occasional hints from researcher Tianyi Peng. That took eleven days and produced thirteen million lines of Lean code. Mathematician Kevin Buzzard reviewed that proof.
According to Anthropic, this time the agents wrote a third as much text as in September, and the proof is one-seventh the length. The starting point was different, though: the agents were given sixty statements to prove (the theorem itself and 59 intermediate steps), the related definitions, a one-sentence description of the classical route and 47 supporting results that had already been proved in September. They got no hints about the approach or how to divide the work.
How a thousand agents worked together
One lead agent divided the work among 999 helpers. Each agent worked in its own sealed-off computer without internet access. They shared their code through version control and a shared database, in which the lead agent created five lists: announcements, who is working on what, notes, open tasks and finished work.
The hardest part was split into 2,418 tasks, up to ten levels deep. Around the eighteenth hour, activity came to a standstill. The researchers restarted the run from the last save and gave the agents twelve extra hours. In the end, 54 of the 60 statements were proved; the rest turned out to be no longer needed or were dropped.
The final result has been checked by Lean's official checker. A comparison with the intended theorem or a review by an independent mathematician, as with the September version, has not yet been reported for this new version.
What does this mean for the road to the singularity?
This experiment shows that a large team of AI agents can organise itself and work together on one difficult mathematical job for more than a day, with a shared database as its workspace. What took eleven days and human guidance in September now succeeded in just over a day. The step forward lies in the teamwork and in working out existing mathematics without errors, with prepared work as a starting point. If this also works for mathematics that nobody has proved yet, AI could play a real part in finding new knowledge.
What is the technological singularity? Read the explanation →
