Human Mathematicians Get Overtaken by AI in Finding Counterexamples

OpenAI's new model Sol not only generated counterexamples to mathematical conjectures but also succeeded in automatically formalizing them into code in Lean, a formal verification language.

Key achievements are as follows:

• Generated a counterexample to Erdős's Unit Distance conjecture: ChatGPT proposed a counterexample to this conjecture, and it was subsequently fully formalized into Lean code via the Sol model.
• Massive code generation capability: Over the 3 weeks it worked on this project, Sol generated approximately 1.2 million lines of Lean code. This is nearly half the size of mathlib4 (about 2.3 million lines), Lean's mathematics library.
• Autoformalization of advanced mathematical theory: The generated code was used to prove complex theorems in Global Class Field Theory, a core area of number theory, suggesting that AI can handle highly abstract mathematical theories.

Currently, several AI startups including Logical Intelligence and Logos Research are developing Autoformalization tools that convert human mathematical language into formal verification languages like Lean, changing the paradigm of mathematical research.