Mathematics has changed. Let's act like it

Frank Calegari argues that OpenAI’s release of more than 700 mathematical papers marks a watershed: AI can now make major contributions, but the papers’ poor writing, attribution failures and errors expose serious problems in how AI companies engage with mathematical norms. He rejects the fear that solving famous problems would finish mathematics. The classification of finite simple groups offers a cautionary parallel: its announcement redirected attention from group theory, though rich questions remained and the classification itself needed decades of revision. Fields should treat breakthroughs as openings for new inquiry, not declarations that their subject is complete.

Calegari sees AI as a chance to pursue broad, structurally ambitious questions that specialists may have lacked time or tools to formulate. He illustrates this with links between arithmetic and hyperbolic three-manifolds, and argues that understanding the deeper meaning of a result - such as the arithmetic behind ζ(3) - matters more than merely proving a conjecture. But he warns that researchers are already rushing out AI-assisted proofs, intensifying competition and rewarding speed over insight. A mathematician who selects a worthwhile problem, verifies and understands an AI-produced proof, and develops fruitful follow-up questions deserves substantial credit, even without inventing the proof’s key step. The profession should reward problem selection, exploration and explanation, and senior mathematicians should help create new research directions rather than race AI to answer existing questions.