Mathematician Accepts Paper Written By AI She Cannot Refute

Dr. Sarah Chen, a topologist at the University of Chicago, approved a forty-seven-page mathematics paper submitted to the Journal of Differential Geometry on Tuesday without fully verifying its central proof, according to her peer review notes filed last week. The paper was generated by Claude 3.5 Sonnet, an AI model built by Anthropic, and addressed an open problem in symplectic geometry that has resisted human proof for twelve years. Chen spent four hours reading the argument, checking the lemmas, and cross-referencing the citations. She then spent another two hours determining that a complete verification of the main proof would require approximately eighty additional hours of work, more than the journal's assigned budget of six hours per submission.

"The proof is probably correct, and I cannot afford to be wrong about it," Chen wrote in her decision letter to the editorial board.

The proof is probably correct, and I cannot afford to be wrong about it.

The acceptance marks a pivot in how mathematics is validated at scale. The Journal of Differential Geometry receives approximately one thousand two hundred submissions per year, and the volunteer peer review system that sustains it relies on mathematicians donating labor that most universities no longer count toward promotion and tenure. A complete verification of a forty-seven-page proof in an unfamiliar subfield now takes longer than most reviewers can justify to their department chairs. The AI paper was accepted because the alternative, rejecting it based on incomplete review, would require Chen to claim expertise she did not possess.

The editorial board at the journal confirmed the decision in a statement saying that the field faces a choice between accepting papers that cannot be fully verified and rejecting papers that cannot be fully verified, and that the former position was preferable from a risk management perspective.

Chen is now a coauthor on three additional papers generated by the same model, all submitted to the same journal, all addressing problems that predate the existence of the model itself. She has accepted two without complete verification and desk-rejected one after skimming the introduction. A spokesperson for the Journal of Differential Geometry declined to characterize the situation as a crisis, noting instead that the journal has always operated under constraints that prevented complete certainty, and that the constraints have simply become explicit rather than hidden.

At press time, the AI model had submitted a paper claiming to have solved the Riemann Hypothesis using a method that relies on a lemma from the first accepted paper, which itself relies on a lemma whose proof Chen has not read. The editorial board is considering whether accepting the second paper would constitute a vote of confidence in the first one or a separate judgment entirely.