AI Just Solved a 350-Year-Old Math Problem By Writing the Longest Proof Ever

• Claude generated a 13‑million‑line proof of Fermat’s Last Theorem in 11 days.
• The proof can be verified automatically without any human oversight.
• Anthropic’s claim raises new questions for crypto‑focused AI safety and verification.

Anthropic announced that its AI system Claude spent 11 days producing a computer‑checkable proof of Fermant’s Last Theorem that spans 13 million lines of code. The achievement marks the longest formal proof ever generated by an artificial intelligence and demonstrates a level of self‑verification that does not rely on human trust. For the crypto community, where trustless verification is a core principle, the result suggests a new benchmark for automated proof systems. It also invites a deeper look at how such a proof is constructed, what kinds of participants can interact with it, and what concrete steps are needed to move from a research demonstration to practical deployment.

Why the size of the proof matters

The 13 million‑line proof dwarfs any prior formal verification effort. Traditional mathematical proofs are written for human readers, even when they are long. Claude’s output is designed for a computer to read and confirm each logical step. The sheer volume shows that AI can handle exhaustive case analysis that would be impractical for a human team. In crypto, similar exhaustive checks are used for smart contract audits and zero‑knowledge proof generation. Claude’s method mirrors those processes, but on a scale that far exceeds current blockchain verification tools. The size itself is a signal that the underlying formal system can express a vast number of intermediate lemmas, each of which is checked by a deterministic algorithm, thereby eliminating the need for any interpretive judgment by a person.

How Claude achieved the result

According to Anthropic, Claude worked continuously for 11 days. During that period the system translated the theorem into a formal language, then explored every logical branch needed to close the proof. The translation step involves encoding the mathematical statements into a language that a proof assistant can manipulate, such as a typed lambda calculus or a higher‑order logic framework. Once encoded, Claude employed automated theorem‑proving tactics that systematically apply inference rules, generate sub‑goals, and backtrack when a path leads to a contradiction. The resulting code can be fed into a verifier that checks each line for consistency. No human mathematician intervened to validate the steps. This “no‑human‑trust” approach aligns with the way decentralized networks validate transactions without a central authority, because the verification algorithm is public, deterministic, and runs the same on any compliant node.

Implications for crypto verification

Crypto protocols depend on mathematics that can be proven correct by machines. Zero‑knowledge proofs, for example, require a trusted setup that is later verified by a verifier algorithm. Claude’s ability to generate a massive, self‑checking proof suggests that similar AI tools could automate the creation of cryptographic primitives. If an AI can produce a proof that a smart contract follows its specification, developers could reduce audit costs and speed up deployment. The same underlying technology could be repurposed to generate the arithmetic circuits that underlie many privacy‑preserving protocols, potentially lowering the barrier to entry for new projects. However, the crypto sector will need to assess whether the AI’s internal logic is transparent enough for regulators and users, because trustless systems still require an open audit trail that can be inspected by any participant.

What the crypto community is likely to ask

First, practitioners will want to see the verification logs. The claim that “no human trust required” hinges on the verifier’s correctness, and the logs provide a concrete record of each inference step, the axioms applied, and the intermediate results produced. Second, developers will ask whether Claude’s approach can be adapted to domain‑specific languages used in blockchain platforms, such as those that compile to WebAssembly or specialized virtual machines. Third, investors will watch for any shift in funding toward AI‑driven verification startups, because the market may view the technology as a competitive advantage for firms that can certify code at scale. The proof’s length may also prompt concerns about computational resources needed to run similar checks on a public network, leading to discussions about how to balance thoroughness with efficiency.

What happens next

Anthropic has not released the full code publicly. If the proof becomes open source, researchers can test the verifier and compare it with existing proof assistants, examining how the AI’s heuristics differ from human‑crafted strategies. A public audit could confirm the claim and encourage broader adoption across industries that rely on formal methods. If the code remains closed, skepticism may limit the impact on crypto projects that demand full transparency, because participants would be unable to independently verify the underlying logic. Either way, the episode puts AI‑generated verification at the forefront of discussions about trustless systems, and it signals that the next wave of scrutiny will focus on the reproducibility of the verification process, the accessibility of the tooling, and the ways in which the community can integrate such capabilities into existing blockchain infrastructures.

Source: Decrypt.