In a guest essay on Terence Tao’s blog, mathematician Frank Calegari argues that AI-generated proofs should change what mathematics rewards. A result matters, he says, but so do understanding it, explaining it and deciding which questions are worth asking next.
His proposed changes reach beyond individual tool use:
- Hiring: Assess research vision and technical understanding through substantive conversations, not just publication lists.
- Journals: Demand clearer writing, attribution and ideas. Calegari criticizes the writing and attribution of a recent batch of AI-generated papers and says some are wrong.
- Training: Give students breadth and communication practice while preserving deep technical skills.
Calegari would credit someone who uses AI to obtain a proof if they understand it and develop worthwhile new directions. His optimism about what AI will enable is an argument about the future, not a measured outcome.
The 427-comment thread on Hacker News raises questions about what happens to craft and access.
What the thread adds
- Loxicon — A writer and developer values doing the work itself, not just the resulting output.
- gcanyon — Describes enjoying AI-assisted software creation while still writing fiction personally; a counterexample to a single view of craft.
- ethanlipson — Questions whether the skills Calegari emphasizes, including explaining and choosing directions, will remain beyond future AI systems.
- qnleigh — Argues that the benefits to mathematicians depend on whether they can access the models, rather than competing with their owners.
HN handles are pseudonymous, per-comment scores are unavailable, and ordering follows HN’s ranking; this is a slice of the discussion, not a consensus.