Human mathematicians are being outcounterexampled

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. Unit distance 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. 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…