Scattered thoughts on how doing math feels these days

A working mathematician describes AI’s rapid shift from a novelty to a tool that can perform substantial mathematical work in just months. Yet the personal productivity gain is estimated at about 50%, not because AI cannot solve tasks quickly, but because mathematics also involves choosing questions, forming ideas, organizing arguments, and understanding results. The familiar workflow may not survive: as with cheap batteries reshaping energy systems, powerful proof-generating AI could change what doing mathematics means. Human understanding still seems to constrain the pace, though keeping a person involved need not prevent major gains.

The main weakness is not simply awkward prose: AI often fails to create useful abstractions, producing tangled proofs with sprawling lemmas and unclear structure. Patient questioning can help simplify arguments, sometimes uncovering shorter proofs or stronger results. For now, people supply judgment, problem decomposition, and taste, but it is unclear whether these abilities will remain a lasting advantage. AI-assisted mathematics can be worthwhile if its human collaborators genuinely understand and stand behind the work; otherwise, they risk becoming mere reviewers of material they cannot defend. The case for valuing clear exposition should not be dismissed as humans shifting standards to stay relevant: mathematical writing deserved more attention even before AI. Still, the prospect that machines may explain or independently reproduce a result makes the purpose and lasting value of producing proofs feel less certain.