Fermat’s Last Theorem prediction market spikes to 99% after Claude’s Lean proof. A Manifold market asking whether the world will have a formalized, machine-checked proof of Fermat’s Last Theorem by May 1, 2029 jumped to a 99% implied chance of “yes,” with 58% of the market’s all-time volume changing hands in a single day. The trigger is concrete: on September 4, 2026, Anthropic said its Claude model produced what it calls the first complete, computer-verified formalization of the theorem in the Lean 4 proof assistant.
The market at the center of the move
The contract in question lives on Manifold Markets and asks a narrow, testable question: “Will we have a formalized proof of Fermat’s Last Theorem by 2029-05-01?” A formalized proof is not the same thing as a proof. Andrew Wiles solved Fermat’s Last Theorem in the mid-1990s. The open question the market tracks is whether that argument can be encoded, line by line, into a language a computer can check for logical gaps, and whether that would happen before the May 2029 deadline.
For years, that was treated as a multi-year engineering slog rather than a coin flip. The market’s sudden repricing reflects new information, not new mathematics. If you are new to how these contracts translate crowd money into a percentage, our explainer on how prediction markets work covers the mechanics.
Current odds and what they imply
As of September 05, 2026, the market showed a 99% implied probability of “yes” on Manifold, with roughly 58% of the contract’s all-time volume traded inside the prior 24 hours. That volume share is the more telling number. It signals that the price move is being driven by fresh conviction and fresh capital, not by a thin book drifting on stale bets.
A 99% reading is close to the ceiling. In practice it means traders now treat the outcome as near-settled and are pricing the residual 1% for tail risks: a resolution dispute, a flaw surfacing in review, or an ambiguity in how the question’s author defines “formalized proof.” For a primer on reading these numbers, see our note on implied probability.
What is actually driving the move
On September 4, 2026, Anthropic published a research write-up titled “Formalizing Fermat’s Last Theorem,” stating that Claude produced an end-to-end, machine-checked formalization of the theorem in Lean 4. Multiple outlets, including SiliconANGLE and CryptoBriefing, reported the claim the same week. The full proof chain was posted to a public GitHub repository, anthropics/fermats-last-theorem, so third parties can inspect it.
The reported scale is the reason the story traveled. According to Anthropic’s account, the effort produced around 13 million lines of Lean code, proved roughly 30,300 theorems (about 29,500 of them used in the final proof), and consumed on the order of 6 billion output tokens. The company says the work ran over 11 days of wall-clock time, using several dozen agents working in parallel rather than one sustained process.
What Claude did, and what it did not do
The distinction matters for anyone reading the odds. Claude did not discover a new proof of Fermat’s Last Theorem. It translated an existing human proof into a form Lean’s kernel can mechanically verify. Anthropic says the model followed a simplified version of the argument drawn from the work of Henri Darmon, Fred Diamond, and Richard Taylor, and that the finished formalization was accepted by Lean using only its standard axioms.
The path was not clean. By Anthropic’s own account, an initial attempt failed, and roughly 7% of the non-boilerplate lines came from dead ends. Success required adding Prove2Me, an open collaborative platform for formalizing mathematics developed by Tianyi Peng and collaborators at Columbia University, to help the agents manage decisions across a long workflow. Kevin Buzzard of Imperial College London, who leads the largest human-run FLT formalization effort, is named as having reviewed the work.
The human project it leapfrogged
Context explains why traders reacted so fast. Since 2024, a multi-year academic effort led by Buzzard has been formalizing Fermat’s Last Theorem in Lean, using a modern “R equals T” modularity route designed with Richard Taylor rather than Wiles’s original 1990s argument. That project, described on the Lean community blog and the Imperial College FLT repository, is funded by an EPSRC grant running through September 2029.
The timing is the point. The human effort was scoped to finish around the same window the market was betting on. Anthropic’s announcement arrives ahead of that schedule with a separate, independently posted artifact. For traders, that collapsed the central uncertainty of the contract from “can this be done in time” to “does this specific claim hold up.”
How the milestones stack up
| Milestone | Approx. date | Status |
|---|---|---|
| Wiles proves Fermat’s Last Theorem (human, on paper) | 1994-1995 | Peer-reviewed, accepted |
| Lean formalization of FLT for regular primes | 2024-2025 | Published, partial (specific primes) |
| Imperial College FLT project (Buzzard, Taylor) | 2024-2029 | Ongoing, grant funded to Sept 2029 |
| Anthropic/Claude full Lean 4 formalization claim | 2026-09-04 | Publicly posted, under community review |
| Manifold market on formalized proof by 2029-05-01 | 2026-09-05 | 99% implied “yes” |
Why a tech and finance reader should care
Two threads converge here. The first is the AI capability story. Autoformalization, turning human mathematics into machine-checkable code, has been a research testbed for large language models. A completed, inspectable formalization of a theorem this deep is a data point about how far agentic systems have moved on long, structured, verifiable tasks. The second thread is what prediction markets do well: they price attention and conviction quickly, and a 58%-of-volume-in-a-day spike is a market functioning as an early sentiment gauge on a technical event.
This is not the first time a math or research milestone has whipped a crowd-funded contract. Our coverage of an AI-and-millennium-prize market on Manifold tracked a similar dynamic, where speculative research odds moved on headline events rather than settled outcomes.
What to watch next
The remaining uncertainty is social and procedural, not mathematical. Watch for independent verification that the posted Lean code faithfully corresponds to the Wiles-Taylor argument, and for the mathematics and Lean/Mathlib communities to weigh in on completeness and axiom use. Also watch the market’s own resolution criteria: whether the author counts a corporate research artifact, an academic release, or requires broader consensus will decide how cleanly a “yes” settles. A dispute on any of those points is what the residual 1% is pricing.
For readers comparing where these contracts trade and under what rules, see our Kalshi versus Polymarket comparison and Polymarket review. Manifold, where this contract sits, uses play-money mechanics that differ from both.
Frequently asked questions
Did an AI solve Fermat’s Last Theorem? No. Andrew Wiles solved it in the 1990s. Anthropic says Claude formalized an existing proof into Lean 4 so a computer can verify each step.
What does “formalized proof” mean here? It means the argument is encoded in a proof assistant’s language and checked by that system’s kernel, leaving no informal gaps for a human to fill in.
Why did the market move so fast? Anthropic’s September 4, 2026 announcement provided a concrete, publicly posted artifact ahead of the market’s 2029 deadline, which collapsed the main uncertainty in the contract.
Is the claim fully confirmed? The code is public and was reviewed by at least one named expert, but broad, independent community verification is still in progress as of September 05, 2026.
Can I trade this market for real money? Manifold primarily operates on play-money mechanics, which differ from regulated, cash-settled venues. Availability and rules vary by platform and jurisdiction.
The Bottom Line
Sources
- Anthropic — Formalizing Fermat’s Last Theorem
- SiliconANGLE — Anthropic uses Claude to formalize proof of Fermat’s Last Theorem
- CryptoBriefing — Claude helps complete first formalized proof of Fermat’s Last Theorem
- Lean community blog — The Fermat’s Last Theorem Project
- Imperial College London — FLT Lean formalization repository
- Manifold Markets — Will we have a formalized proof of Fermat’s Last Theorem by 2029-05-01?
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