AI systems can now reach extraordinary scores on difficult mathematics benchmarks, but a correct answer is only one part of mathematical progress. The deeper challenge is preserving explanation, attribution, verification, and the human process that turns a result into reusable knowledge.
Fermat’s Last Theorem has moved from a handwritten conjecture to a massive Lean formalization checked by a computer kernel. This beginner-friendly guide explains proof assistants, Wiles’s strategy, AI collaboration, and the limits of machine verification.
Tarski’s high school algebra problem asks whether every true integer identity follows from 11 basic axioms. Using SAT solving and Lean verification, a new result shows the smallest countermodels have size 12 and there are exactly 8,957,952 of them up to isomorphism.