Fermat's Last Theorem
A famous theorem in number theory stating that the equation x^n + y^n = z^n has no positive integer solutions when the integer n > 2. The conjecture was proposed by Fermat in 1637 and a complete proof was completed by Andrew Wiles in 1994.
Timeline (last 90 days)
Alex revealed that within one month he was stunned by AI capabilities for the third time; the first two were the formalization of Fermat's Last Theorem and progress on the Navier-Stokes equations.
When giving a talk in the Princeton mathematics department, Alex judged that AI was at least three years away from formalizing Fermat's Last Theorem, but two days after the talk (Friday) a 13-million-line, sorry-free Lean formal proof generated by Anthropic's AI system appeared.
Part of the value of solving mathematical conjectures comes from the new tools, methods, and subfields born during the process; for example, the proof of Fermat's Last Theorem spawned many advances in algebraic number theory, and the solution of the Poincaré conjecture advanced the fusion of Ricci flow and geometric analysis.
Several important theorems have been formalized in Lean, such as the four-color theorem and partial results of Fermat's Last Theorem
The final proof of Fermat's Last Theorem was completed within the scheme-theoretic framework of algebraic geometry.
Anthropic's Claude has completed the first formal proof of Fermat's Last Theorem.
To support the main proof, this work also proved more than 29,000 subsidiary theorems.
Fermat's Last Theorem states that for integers n > 2, the equation x^n + y^n = z^n has no positive integer solutions.
What Claude accomplished this time was the formalization and translation of Fermat's Last Theorem, not an original mathematical discovery.
Anthropic announced that its AI model Claude operated largely autonomously for 11 days and successfully formalized Fermat's Last Theorem in Lean.
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All Facts (20)
Fermat's Last Theorem was fully proved by Andrew Wiles in 1995.
70%UnverifiedFermat's Last Theorem was proposed by Fermat in 1637, proved by Andrew Wiles in 1995, and had puzzled the mathematical community for 358 years.
60%UnverifiedFermat's Last Theorem states that when the integer n is greater than 2, the equation x^n + y^n = z^n has no positive integer solutions.
60%UnverifiedThe Taniyama–Shimura conjecture, which was the core tool Andrew Wiles used to prove Fermat's Last Theorem, is a special case of the Langlands program.
60%UnverifiedPart of the value of solving mathematical conjectures comes from the new tools, methods, and subfields born during the process; for example, the proof of Fermat's Last Theorem spawned many advances in algebraic number theory, and the solution of the Poincaré conjecture advanced the fusion of Ricci flow and geometric analysis.
50%UnverifiedSeveral important theorems have been formalized in Lean, such as the four-color theorem and partial results of Fermat's Last Theorem
50%UnverifiedThe final proof of Fermat's Last Theorem was completed within the scheme-theoretic framework of algebraic geometry.
50%UnverifiedTo support the main proof, this work also proved more than 29,000 subsidiary theorems.
50%UnverifiedWhat Claude accomplished this time was the formalization and translation of Fermat's Last Theorem, not an original mathematical discovery.
50%UnverifiedFermat's Last Theorem states that for integers n > 2, the equation x^n + y^n = z^n has no positive integer solutions.
50%UnverifiedAndrew Wiles completed the proof of Fermat's Last Theorem in 1994; the proof was 129 pages long and combined elliptic curves, modular forms, and the Taniyama–Shimura conjecture.
50%UnverifiedPierre de Fermat wrote down the conjecture of Fermat's Last Theorem in 1637 in the margin of the book Arithmetica.
50%UnverifiedThe formalization of Fermat's Last Theorem relies heavily on modules in Mathlib such as elliptic curve theory and Galois representation theory.
50%UnverifiedWiles's paper proving Fermat's Last Theorem is 129 pages long.
50%UnverifiedFermat's Last Theorem eluded the mathematics community for 358 years.
50%Unverified怀尔斯1993年提交费马大定理证明后被发现存在关键漏洞，花费近一年时间才完成修补
50%UnverifiedAlex revealed that within one month he was stunned by AI capabilities for the third time; the first two were the formalization of Fermat's Last Theorem and progress on the Navier-Stokes equations.
50%UnverifiedWhen giving a talk in the Princeton mathematics department, Alex judged that AI was at least three years away from formalizing Fermat's Last Theorem, but two days after the talk (Friday) a 13-million-line, sorry-free Lean formal proof generated by Anthropic's AI system appeared.
50%UnverifiedAnthropic's Claude has completed the first formal proof of Fermat's Last Theorem.
50%UnverifiedAnthropic announced that its AI model Claude operated largely autonomously for 11 days and successfully formalized Fermat's Last Theorem in Lean.
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