Eleven days of machine time turned Wiles's 100 pages into 13 million lines of Lean
Anthropic says its Claude agents ran autonomously for 11 days to formalise Fermat's Last Theorem in 13 million lines of Lean, a result that rests on a finished human proof and 2 million lines of prior formalisation.
The Scientist · Science desk
What happened
- Anthropic says a group of AI agents worked for 11 days to produce a formalised proof of Fermat's Last Theorem, confirming that the human proof proposed in the 1990s is correct.
- The artefact runs to 13 million lines of Lean and covers roughly 29,500 intermediate theorems that were needed as stepping stones to the final result.
- That makes it over five times the current size of all previous work on Mathlib, and the largest Lean proof ever written.
- Kevin Buzzard of Imperial College London said, in a statement published by Anthropic, that the proof leaves no assumptions other than the axioms of mathematics.
- Buzzard had been running a five-year project to turn Wiles and Taylor's 100 pages into Lean code, an effort that Anthropic's announcement has now overtaken.
Why it matters
- What's now possible capability If Buzzard is right that autoformalisation artefacts are now sturdy enough to build on, a small team can start a formalisation from a working foundation instead of reconstructing the number theory underneath it.
- What it limits constraint The 11-day figure applies only to cases where a corrected human proof already exists to translate; formalising a problem that is still open is a different task entirely.
- What it costs cost The published account covers eleven days of continuous multi-agent inference but gives no compute or spend figure for it, leaving outsiders unable to budget a repeat.
- Who has to decide decision Reusing this code means trusting the checker rather than a reader: at 440 lines per intermediate theorem across 29,500 of them, line-by-line human review is not on the table.
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Divide 13 million lines of Lean by 11 days and the run emitted about 1.18 million lines a day, close to 14 lines every second, without a pause [15]. Set the same file against the 100 pages of Wiles and Taylor's argument and each page of human prose expands to roughly 130,000 lines of code [16]. The 29,500 intermediate results average about 440 lines each [17]. None of those ratios measures mathematical difficulty. They measure how much a natural-language proof leaves implicit, and how cheap writing out the implicit part has become.
What the 11 days does not include is the substrate. The clock starts with an argument that was already finished and already repaired: Andrew Wiles worked on the problem for seven years in secret, announced in 1993, and then spent about a year with Richard Taylor fixing a flaw found in the proof [11]. It also starts with Mathlib, the central repository, already holding 2 million lines of formalised mathematics available to build on [10]. The agents were translating toward a target known to be true, with a specification in hand.
The run broke on coordination, not mathematics: several times the agents lost track of the project's state and stopped collaborating effectively, and progress came after Anthropic began using Prove2Me, a tool designed for human mathematical collaboration, to help agents track their work and pick next tasks [14]. Human experts also stepped in occasionally with high-level instructions to keep the work on track [13]. At this scale the binding constraint on a swarm of formalisers looks like coordination rather than proving.
Correctness is a different matter, and the mechanism is doing the work: a formalised proof sits in code that a machine grinds through step by step, which is what exposes a broken link [6]. Kevin Buzzard of Imperial College London drew the wider inference in his statement, saying the work shows autoformalisation of algebra, harmonic analysis, geometry and number theory, that such artefacts are now robust enough to be built upon, and that automatic formalisation of the modern mathematical literature is a big step nearer [19]. His is the only outside assessment in New Scientist's account, and it reached the public through Anthropic's own announcement [8].
So the demonstrated capability is narrower than the elapsed time suggests and still worth taking seriously: converting a settled, corrected human proof into machine-checkable form is now a days-long compute job, given a library beneath it and handlers watching. Buzzard's claim that these artefacts can be built upon is testable in the ordinary way, and the test is specific: the next formalisation project either imports the 13 million lines or re-derives them.
What to watch
- Whether Mathlib maintainers absorb any of the 13 million lines, the practical test of Buzzard's claim that these artefacts can be built upon.
- An independent re-run of the Lean checker over the full artefact, and a figure for what that costs in time and compute.
- Whether the next autoformalisation target is a theorem with no finished human proof to aim at.
Clarity's read
What the record supports and how the coverage leans. The claims behind it follow.
Reality
- Evidence58
- Adoption32
- Hype gap+18
- Incentives70
- Confidence64
Claim ledger
Ranked by verification strength, evidence, and original report placement.
- [1]
Anthropic has created a formalised proof of Fermat's Last Theorem; a group of AI agents completed the task in 11 days, confirming that the human-found proof proposed in the 1990s is correct.
- [2]
Anthropic said in a blog post that its Claude model worked continuously and autonomously for 11 days to write the proof, with numerous separate AI agents involved and different tasks, such as smaller chunks of the theorem, assigned to each.
- [3]
Anthropic's formalisation runs to 13 million lines of Lean and covers roughly 29,500 intermediate theorems that were necessary stepping stones to the overall work.
- [4]
Kevin Buzzard at Imperial College London was, until Anthropic's announcement, working on a five-year project to turn Wiles and Taylor's 100 pages of proof into Lean code; Anthropic's announcement has now overtaken that effort.
- [5]
Buzzard said at a conference he held in London earlier this year that when his project began he was confident of success, but recent advances in AI had convinced him the project would be complete much faster than he had previously believed possible.
- [6]
Formalising theorems puts them into computer code, allowing machines to methodically work through the logic and expose any flaws; a single erroneous step in a long chain of argument can collapse a whole proof.
- [7]
New Scientist's account of the result gives no figure for the compute used or the cost of the 11-day run, and describes the agents only as "numerous".
- [8]
The only external assessment of the formalisation reported by New Scientist is Buzzard's, and it came in a statement published by Anthropic.
- [9]
The formalisation is over five times the current size of all previous work on Mathlib, which also makes it the largest Lean proof ever written.
- [10]
There are already 2 million lines of formalised mathematics stored in a central repository called Mathlib.
- [11]
Wiles worked on the problem for seven years in secret before announcing his breakthrough in 1993; a flaw was later found in his proof, and it took him and collaborator Richard Taylor around a year to fix.
- [12]
Buzzard said in a statement published by Anthropic that the company's proof leaves "no assumptions other than the axioms of mathematics".
- [13]
Anthropic says human experts occasionally issued high-level instructions to keep the work on track.
- [14]
Anthropic says the agents several times lost track of the project's state and stopped collaborating effectively, and that success came after it began using Prove2Me, a tool designed for human mathematical collaboration, which helped different agents track their work and decide on next tasks.
- [15]
The run produced about 1.18 million lines of Lean per day, or roughly 14 lines per second of continuous operation.
- [16]
The formalisation averages about 130,000 lines of Lean for each page of the 100-page human proof.
- [17]
Each of the roughly 29,500 intermediate theorems averages about 440 lines of Lean.
- [18]
Fermat's Last Theorem states that there are no whole numbers a, b and c satisfying a^n + b^n = c^n where n is a whole number greater than 2; it was proven in 1995 by Andrew Wiles.
- [19]
Buzzard said: "Along the way we see autoformalisation of algebra, harmonic analysis, geometry and number theory, and we learn that AI autoformalisation artefacts are now robust enough to be built upon; the proof is multi-layered", and that if automatic formalisation of FLT is possible now, "then we have taken a big step towards automatic formalisation of the modern mathematical literature".
Sources
2 independent publishers whose own reporting we read for this story.
- nature.comAnthropic AI ‘formalizes’ proof of Fermat’s last theorem in just 11 days
1 article · September 6, 2026
- newscientist.comFermat’s last theorem formalised by AI agents in just 11 days
1 article · September 5, 2026
Topics and entities
Topics
- Autonomous agent orchestration
- Proof formalisation
- AI for Mathematics
Entities
- mathlib
- Claude
- Fermat's Last Theorem
- Alex Kontorovich
- Maryna Viazovska
- Prove2Me
- Kevin Buzzard
- Lean
- Imperial College London
- Anthropic