Human mathematicians are being outcounterexampled
TLDR
AI models have disproven three major mathematical conjectures in recent weeks: ChatGPT refuted Erdős' Unit Distance conjecture, OpenAI's Sol found a counterexample to Grothendieck's 60-year-old question about group schemes, and Claude found a counterexample to the century-old Jacobian Conjecture. The achievements range from 1.2 million lines of Lean code for the Erdős proof down to 1,076 lines for the Grothendieck counterexample, with formalization times measured in days or weeks. Mathematicians are now considering AI tools essential for research, with some institutions offering free access to PhD students and faculty, fundamentally shifting how mathematical discovery and verification happen.
Why it matters
AI tools are now starting to solve theorems and write proofs in Lean, which is speeding up the research process for mathematicians by providing verified solutions to mathematical problems.
