The developer used AI to prove Conway's hypothesis

Developer Dan Abramov presented a formal proof of the 50-year-old Conway's conjecture about surreal numbers, using the capabilities of generative models to work with the Lean programming language. The process took about a month of continuous work with AI tools for generating and verifying mathematical statements.

Conway's conjecture, concerning the clarification of properties of surreal numbers, had remained unsolved for half a century. In the course of the work, the author used LLM to write code in Lean, which formalizes mathematical objects and logical transitions. The final result is a set of scripts that compile in the Lean environment, confirming the correctness of the derived statements within the given axiomatics.

Despite the successful compilation of the code, the proof is currently awaiting independent verification by the professional mathematical community. The use of AI allowed for the automation of routine stages of formalization, which usually require significant time costs when manually entering data into a proof system.

This case demonstrates the potential for integrating LLM into the field of formal verification of mathematical theorems. Previously, such tasks required in-depth knowledge of Lean syntax and years of practice, but the application of AI lowers the entry threshold for formalizing complex mathematical constructs. Further development of Lean-based tools can accelerate the verification of hypotheses that were previously considered too labor-intensive for manual processing.