Claude formalized Fermat's Last Theorem in 11 days against a human project funded through 2029
Anthropic's own account has dozens of agents writing 13 million machine-checked lines in 11 days, about 7% of them dead ends, and only after a Columbia team built the shared to-do list that stopped them duplicating work.
The Investor · Invest desk
What happened
- Anthropic says its Claude AI produced the first fully computer-checked proof of Fermat's Last Theorem in 11 days, largely on its own, in what it calls the longest math proof ever built.
- Kevin Buzzard of Imperial College London reviewed the output and confirmed it holds up using nothing but math's most basic logical rules.
- Buzzard has been running a human-led project to do the same translation into Lean since 2024, with an 86-page outline and funding locked in through 2029, and it is not close to finished.
Why it matters
- What it limits constraint The eleven days were graded by a proof assistant at every step, so the result bounds how far this ports: work with no machine verdict on correctness gets no equivalent curve from this evidence.
- What it costs cost Consumption was disclosed in tokens and not dollars, so anyone converting the run into headcount savings is supplying the one number the disclosure withheld, and paying for the guess if it is wrong.
- What doesn't add up contradiction The publisher's framing credits AI with solving the theorem while its own text credits Wiles, which moves the finding from discovery to verification throughput and changes what a buyer is buying.
- Who has to decide decision Grant-funded formalization programmes now face a schedule question, and the person best placed to press it is the mathematician who vouched for the machine's output.
Next story · Science · 2d ago
Thomas Bloom stops marking Erdős problems open or solved as AI-written proofs multiplyConfirmed2 publishers
Thirteen million lines in eleven days works out to about 1.18 million lines a day, close to 49,000 an hour, sustained, with Lean rather than a person checking each one [2][3][16]. Divide those lines by the more than 30,000 supporting theorems Anthropic says the agents proved and the average result runs about 433 lines [15][18], which gives the shape of the job: thousands of small results stacked, rather than one long argument. Checking is the expensive half of mathematics, since finding a single broken link inside a hundred pages of dense argument can cost other mathematicians years [14], and a 1908 German prize for a valid proof of this same theorem drew 621 wrong submissions in its first year [13].
The disclosure's clearest number is also its least flattering. Roughly 7% of the lines in the finished proof are false starts from the early phase, when the agents kept losing track of what they had already proven and stopped collaborating [8], which is about 910,000 lines of dead work carried into the artifact [17]. Coordination broke down first, and Prove2Me fixed it: a tool from Tianyi Peng's Columbia team that handed every agent the same live to-do list, reorganized files so Lean could check them faster, and kept plain-English notes so one agent could reuse another's result [9][1]. The eleven days therefore sit on top of a human-built shared-state layer; the scarce input in this run was that coordination layer itself, not raw model access.
Which is where the capital-allocation reading gets thin. Anthropic's post is dated September 4, 2026 and puts completion in the previous month [10]; it quantifies consumption as billions of tokens and no dollars, on a research model it says is roughly comparable to the Claude Fable 5.1 version it later shipped [15]. The account does not say what share of Kevin Buzzard's 86-page outline the proof covers, nor whether it drew on the Imperial project's existing Lean library [12][5]. Buzzard's funding is committed through 2029 [5], and eleven days is about 0.6% of that window [20], a striking ratio measured in time, not dollars.
My read, with the counter-thesis beside it: the transferable capability is throughput on work where a checker returns a verdict at every step, and a verifier like Lean is the rarer asset here, not the agent. The counter is that Prove2Me is a to-do list and a file organizer rather than a new model [9], so if that scaffolding ports cheaply, any domain with a compiler or a test suite inherits the same curve. A third path runs through the review itself: Buzzard is the one named mathematician who has confirmed the proof reduces to math's most basic logical rules [4], and Wiles's 1993 announcement survived three lectures before a reviewer found the hole in it [6].
Note also the gap between the framing and the event. Decrypt's headline calls this a 350-year-old problem solved by AI [11] while its own text counts 358 years from Fermat's 1637 margin note [7] and credits Wiles with the proof, corrected with Richard Taylor and published across 129 pages in May 1995 [6]; what Claude did was translate that argument into a language a machine can check [2]. For scale on that translation, the formal version carries roughly 100,000 lines per published page of Wiles [19]. Until someone publishes the token bill, eleven days is a quote with the price torn off.
What to watch
- A disclosed dollar or token cost for the 11-day run, which would turn a speed comparison into a cost comparison against a funded human programme.
- Whether mathematicians other than Buzzard verify the 13 million lines, and whether any defect turns up in the formal statement rather than the steps.
- An equivalent multi-agent run in a domain with no Lean-style checker, which is the test of whether the scaffolding or the verifier was doing the work.
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Clarity's read
What the record supports and how the coverage leans. The claims behind it follow.
Reality
- Evidence60
- Adoption
- Not scored
- Hype gap+30
- Incentives70
- Confidence58
Claim ledger
Ranked by verification strength, evidence, and original report placement.
- [1]
Tianyi Peng, who builds AI formalization tools with a team at Columbia, ran the experiment; dozens of Claude agents worked in parallel writing definitions and proving small results, with almost no human input beyond occasional nudges such as which theorem to prioritize.
- [2]
Anthropic says its Claude AI produced the first fully computer-checked (formalized) proof of Fermat's Last Theorem in 11 days, largely on its own.
- [3]
The proof runs to 13 million lines of code that a computer can check line by line, described as the longest math proof ever built.
- [4]
Kevin Buzzard, the Imperial College London mathematician leading the human formalization project, reviewed Claude's proof and confirmed it holds up using nothing but math's most basic logical rules.
- [5]
Buzzard began a project in 2024 to translate Wiles's proof into Lean; the project's outline runs 86 pages, its funding is locked in through 2029, and it is not close to finished.
- [6]
Andrew Wiles announced his solution across three lectures in June 1993, a reviewer later found a hole in it, and he published a corrected 129-page proof in May 1995 after nearly a year of work with former student Richard Taylor.
- [7]
Fermat scribbled the claim into the margin of a math book in 1637, and mathematicians spent the next 358 years trying to reconstruct a proof.
- [8]
Early in the run the agents kept losing track of what they had already proven and stopped collaborating, and those false starts still make up about 7% of the lines in the final proof.
- [9]
Prove2Me, built by Peng's team, gave every agent the same live to-do list of which smaller proofs still needed doing, organized files so Lean could check everything faster, and kept plain-English notes on each result so agents could reuse each other's work.
- [10]
Anthropic's post announcing the result is dated September 4, 2026 and says that last month Claude completed the first formalized proof of Fermat's Last Theorem.
- [11]
The decrypt.co headline reads: AI Just Solved a 350-Year-Old Math Problem By Writing the Longest Proof Ever.
- [12]
The account does not state what share of the Imperial project's 86-page outline the Claude proof covers, nor whether it reused that project's existing Lean library, and gives no dollar cost for the run.
- [13]
A 1908 German prize, worth roughly $1 million to $2 million in today's money, offered for the first valid proof of the theorem, drew 621 wrong submissions in its first year alone.
- [14]
Checking that a major mathematical proof is correct can take years, and finding one broken link buried in a hundred pages of dense argument can take other mathematicians years of their lives.
- [15]
Claude proved 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 5.1, the version it later released.
- [16]
13 million lines over 11 days is about 1.18 million lines per day, or close to 49,000 lines per hour.
- [17]
About 910,000 lines of the finished 13 million line proof are false-start work.
- [18]
Across more than 30,000 supporting theorems, the proof averages about 433 lines per theorem.
- [19]
The formal proof carries roughly 100,000 lines per page of Wiles's 129-page published proof.
- [20]
The 11-day run is about 0.6% of the roughly five-year window from the Imperial project's 2024 start to its funding commitment through 2029.
Sources
2 independent publishers whose own reporting we read for this story.
- decrypt.coAI Just Solved a 350-Year-Old Math Problem By Writing the Longest Proof Ever
1 article · September 5, 2026
- techtimes.comFermat's Last Theorem Machine-Checked: Claude Completes in 11 Days What Took Years to Plan
1 article · September 5, 2026