As AI Cracks Open Problems, a Mathematician Rethinks What the PhD Is For

Daniel Litt argues that AI’s leap from failing at basic arithmetic to autonomously resolving open mathematical problems in just a few years forces an institutional reckoning that academia is too slow to meet on its own terms. His core premise is deliberately modest: even if you doubt that machines will soon be superhuman across all of mathematics, it is already true that the production of mathematical text is decoupling from actual mathematical understanding. That break matters because the profession has quietly relied on a single signal—the proved theorem, the published paper, the thesis—to certify both genuine progress and individual expertise. When a laptop and a few hundred dollars can generate what would have counted as a top-journal result a year ago, that signal collapses.

Litt is careful to separate the goal of mathematics from its bureaucratic proxy. Proving theorems is not the point; a brute-force enumerator grinding through the axioms of ZFC could do that, and even a hypothetical machine that wrote elegant, well-chosen proofs would still not generate human understanding of them. He warns against two tempting mistakes: trying to freeze the current shape of institutions (peer review, arXiv gatekeeping, the journal system) rather than the values beneath them, and chasing whatever narrow skills—theory-building, exposition, question-asking—models happen to be weak at this quarter, since capabilities improve far faster than universities adapt.

His constructive proposal targets the most urgent question: what students should now do, given that a PhD thesis can be produced without its author even reading it. He would redefine the doctorate as becoming a world expert on a deep topic and being able to transmit that understanding, with the degree awarded chiefly through a rigorous oral defense in which the candidate explains the subject rather than on the written text itself. The framing is optimistic—Litt sees an explosion of interesting mathematics ahead and argues human mathematicians will be needed more than ever—but only if the profession consciously chooses to preserve the community, seminars, and conversations that produce real comprehension.