Human mathematicians are being outcounterexampled (xenaproject.wordpress.com)

In a groundbreaking development for the AI and mathematics communities, recent weeks have seen significant breakthroughs in the use of AI to generate and formalize mathematical counterexamples. ChatGPT first disproved Erdős’ Unit Distance conjecture, demonstrating its capability to connect a longstanding mathematical problem to a profound theorem in number theory. Following this, Logical Intelligence’s AI was able to autoformalize this ChatGPT-generated proof in Lean, paving the way for rapid, real-time formalization of complex mathematical arguments. Notably, the AI generated over 1.2 million lines of Lean code in just three weeks, outpacing the collective effort that went into Lean’s extensive mathematics library over nine years. The significance of these events cannot be overstated: AI tools are not only finding counterexamples to well-established mathematical conjectures but are also contributing to formalized proofs, thereby challenging traditional notions of human expertise in mathematics. Notably, the recent counterexample to the Jacobian Conjecture, discovered using AI during a prominent workshop, highlights the potential for AI to lead to breakthroughs in long-standing mathematical queries. This rapid progress suggests a paradigm shift in mathematical research, where AI-generated code, while still requiring human oversight, becomes a crucial asset for discovery and verification in the field.