Human mathematicians are being outcounterexampled
A mathematician discusses the recent trend of AI models generating mathematical proofs, specifically noting ChatGPT's role in disproving a long-standing conjecture. The author highlights the importance of formalizing these AI-generated proofs using tools like Lean to ensure mathematical rigor.
Why it matters
This marks a shift in how mathematical research is conducted, suggesting that AI-human collaboration is becoming essential for complex formal proofs.
It’s been an interesting few weeks for counterexamples. This post is basically my perspective of what has been going on in the world of formalization, AI tools and, in particular, counterexamples.
Two months ago today (20th May 2026), ChatGPT disproved Erdős’ Unit Distance conjecture in discrete geometry. This is now old news but I had to start somewhere. The announcement was accompanied with testimonies by human mathematicians, many of whom I knew and a few of whom I trusted, saying that they believed the argument (they had been given early access to it and had checked it). The basic structure of the proof is that a profound theorem in number theory due to Golod and Shafarevich from the 1960s could be used to construct a counterexample to the conjecture.
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