The quiet shift
Mathematics has always resisted automation at its core: a proof is not a computation, it is an argument, and arguments were supposed to need a mind willing to be convinced. That assumption is now being tested from two directions at once — large language models that produce plausible proof sketches on demand, and formal proof assistants (Lean, Coq, Isabelle) that can check, and increasingly suggest, the steps a human would have had to find alone.
What actually changed
- Automated systems (AlphaProof, AlphaGeometry, and the growing ecosystem around Lean's Mathlib) now solve competition-level problems that were, a few years ago, evidence of genuine mathematical talent.
- The bottleneck in formalizing a result has shifted from "can a machine check this" to "can a human state this precisely enough for a machine to check" — arguably a harder and more interesting problem.
- Mathematicians increasingly treat these tools the way physicists treat simulation: not a source of truth, but a fast way to rule out wrong paths.
What this note is not claiming
This is not a story about machines "understanding" mathematics, nor about proof becoming obsolete. It is a note on practice: on what a working mathematician's day looks like differently now, and what remains stubbornly, interestingly human about the parts AI has not touched.
Open questions
- Does formal verification change which conjectures get attempted?
- Does it narrow mathematical taste toward what is easy to formalize?
References and footnotes
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