According to Anthropic, the AI group of agents, centered on Claude, built the 11 in days, and passed the test by cluster and independent kernel in addition to the Lean kernel.
Convert the proposition of natural numbers into Lean's type and logic.
Anthropic has positioned the finished outcome as the first complete computer-tested proof of Fermer's final theorem.11They worked mainly autonomously over the course of the day, replacing human evidence with a form Lean could judge.
The object of the proof is the proposition that for natural numbers n and positive natural numbers a, b and c above 3, the sum of a n and b n is not equal to c's n. Lean's proof support system examines by algorithm each phase described in type and logic rules rather than ambiguous words.
The theoretical graph connects the work of dozens of agents.
Dozens of Claude agents participated in building upper-level theorems using the definition of necessary concepts, proof of intermediate theorems, and proven theorems.In the early trials, the agent lost the state of the entire project, so the jointly formalized base prove 2me was responsible for sharing the work state.
prove2me retained the theorem as a non-circuit graph and showed the agent the unresolved theorem and the available dependencies. The configuration to divide the theorem and the certificate into separate files and manage the link reduced the compilation load, enabling the search and reuse of proven results that were explained in the natural language of each theorem.
About 1300 million lines have formalized the proof path of Wiles.
The finished result reached about 1300 million lines of Lean code, and the final proof pathway used an intermediate theorem of about 2 million 9500 cases. The mathematical structure of the proof follows discussion by Frey, Serre, Ribet, Wiles, and Taylor-Wiles.
Mathematical input from humans was limited to occasional high-level advice that directed the subject to be treated as a priority. Each agent established a lower theorem and passed its output to the next theorem on the dependent chart, so that individual evidence was connected to the final proposition.
Lean and test results in two different paths.
In building from scratch by Lean 4.33.1, all 6 million 475 modules of the outcome were constructed. The final theorem dependent on the principle was displayed as propext, Classical.choice, and Quot.sound's 3, and specified syntax such as sorry was removed from the outcome module.
The comparator compared the confirmed statements and constants in the statements with the test tasks described by Mathlib alone, and confirmed that they were the same statements and did not use any authorized principle. Additionally, the independent Lean kernel nanoda of Rust accepted declarations of 105 million 2234 from the same environment without error, and added a different test path from the Lean standard kernel.
Joint formalization in progress is another complete outcome.
Another open-source project run by Imperial College London is a multi-author project that is still underway to formalize Fermer’s final theorem Lean.This is not the completion of the project itself, but an independent research result of the AI group of agents connecting a different demonstration pathway to the end.
Mechanical testing ensures that the formalized proposition is guided by the specified principle and definition, while the name of the intermediate theorem is not automatically determined to match the mathematical meaning assumed by humans, so the result is considered an authoritative description of the Lean theorem rather than the name.