Frank Calegari proposes new hiring and publishing standards: assess all mathematics papers as though AI helped produce them
Frank Calegari proposes new hiring and publishing standards: assess all mathematics papers as though AI helped produce them
On 1 November, University of Chicago professor Frank Calegari proposed a plan to reshape the profession. He argues that professional recognition should depend on choosing problems, understanding proofs and developing research directions.
The proposal followed OpenAI’s release of hundreds of mathematics manuscripts on 6 October. Calegari describes a gap: obtaining a new proof can take less time than understanding its ideas and connections to the rest of mathematics. Previously, proving a difficult theorem was evidence of the author’s skill. If AI can produce the proof, a paper alone tells us little about how well its author understands the work. Calegari proposes assessing that understanding separately.
“Evaluate every paper as though it was produced with AI assistance.”
Authors should explain what makes a problem interesting, how it connects to the rest of mathematics and what further questions its solution opens up. Calegari would recognize the contribution of someone who chose a worthwhile problem, obtained the entire proof from AI, developed a thorough understanding of it and pursued new research directions. New ideas for proofs also deserve recognition, even if a machine can already reach the same conclusion.
Mathematicians seek recognition, jobs and grants; Calegari proposes using hiring and publication decisions to reward understanding and new research questions. He therefore recommends in-person interviews for admission to doctoral programs and for hiring postdoctoral researchers, who hold temporary research positions after completing their doctorates. Candidates should be able to discuss different areas of mathematics, explain their methods and describe where they want to take their research. Calegari places depth of knowledge above verbal fluency: the purpose of the conversation is to assess the candidate’s understanding.
He calls on journals to pay greater attention to ideas and clarity of explanation. If editorial boards retain their existing selection criteria, he considers temporarily forgoing journal publication so that each paper is judged on its content. Calegari himself serves on the editorial board of Essential Number Theory. The journal encourages clear exposition of other researchers’ results; such papers should help researchers in their work.
These expectations for candidates also change the purpose of training. Calegari describes the familiar path of a doctoral student: learn a technique by solving a variation on an existing problem, then apply it more broadly. He now proposes combining independent work on difficult mathematical problems with a broad view of mathematics. After a course, students should understand what the subject allows them to do in other areas and remember those connections even if they forget some technical details.
Students should learn to discuss mathematics with colleagues through seminars and conversations with one another. Calegari proposes organizing seminars around a broad question: where researchers are stuck, what approaches they have tried and where they might go next. Speakers can present their own new results at the end.