AI Tools Outcounterexample Human Mathematicians on Major Conjectures
Human mathematicians are being outcounterexampled
I witnessed AI systems like ChatGPT and Sol rapidly disprove long-standing mathematical conjectures, including those by Erdős and Grothendieck. These tools not only generated counterexamples but also autoformalized complex proofs in Lean, often surpassing human verification speeds. The speed of this AI-driven formalization suggests a future where large-scale mathematical developments are inevitable, challenging traditional trust in human technical details.
"It is now 9 years since I had a mid-life crisis, realised I no longer trusted many human mathematicians when it comes to technical details, discovered Lean, and started to argue that interactive theorem provers should play an important role in the future of mathematics."
HN discussion
- AI models excel at finding counterexamples because they lack aesthetic commitment to conjectures and feel no embarrassment about producing 'ugly' results.
- Formally verified counterexamples are uniquely valuable as they can instantly convert years of speculative mathematical effort into a definite answer.
- Modern Large Language Models are trained on diverse datasets simultaneously with a singular next-token prediction objective, rather than being trained individually for specific tasks.
- The mathematical community lacks a formal tradition for publishing 'negative results' or documenting unfruitful attempts, despite their importance for scientific progress.