Lean

Interesting update: a few days ago, Nathanson presented a talk at the New York Number Theory Seminar explaining how Aristotle solved some of his problems.

To my mind, what seems most important here is not so much the results themselves, nor even the particular methods used in the proof. What really matters is the workflow: the closed loop from autonomous discovery of the right constructions, to formal verification of the proof in Lean, to informalised exposition back into a manuscript that mathematicians can read, understand, rewrite, and improve. It suggests a framework in which formal proof is not merely a static final certificate, but an active part of mathematical research: a medium through which ideas are found, organised, tested, explained and made available for human judgment. That dynamic loop is the real story for me. The natural next question is how far it can be pushed.

Max Tegmark says the way through the AI black box may be to deploy its outputs instead. A cat can learn, but it cannot export what it learned. A human scientist can. As intelligence rises, more knowledge may become externalized into code and proofs. Deploy what the mind can verify, not the mind itself.