Daniel Litt says AI already solves major open math problems, PhDs must change
Mathematician Daniel Litt, who cross-posts his writing to a venue called Proofs and Prompts, published an essay on September 13, 2026 titled 'A beginning for mathematics,' arguing that AI progress in his field has moved faster than the profession has adapted to. He writes that three years ago AI systems could not reliably add two numbers, that about a year earlier internal models at OpenAI and DeepMind reached the equivalent of a gold-medal score on the International Mathematical Olympiad (IMO), and that such systems are now, in his account, autonomously resolving major open mathematical questions, though he does not name which ones. He expects the trend to continue for another year and says it makes a radical rethink of the mathematics profession unavoidable.
The essay follows a talk Litt gave a few weeks earlier called 'The End of Mathematics,' which he says he regrets naming that way. That talk laid out a gloomy scenario: even if AI becomes robustly superhuman at mathematics, badly adapted institutions could cause human mathematical understanding, and possibly mathematical progress itself, to stall. Litt says he expects this outcome to be avoided but calls it a plausible default if academic mathematics fails to adapt, and says he shares this worry with many of AI's detractors despite his own relative enthusiasm for using AI in his work.
His diagnosis is that the field has operationalized its goals almost entirely through proving theorems, but that this cannot be the real goal, since a machine (or, in his example, a monkey) could trivially prove theorems by mechanically applying deduction rules to the axioms of ZFC with no understanding at all. What mathematicians are actually trying to do, in his own words, is produce and understand high quality mathematics and produce high quality mathematicians. That distinction matters now because, he writes, it has become possible to produce a PhD thesis one hasn't even read: a piece of mathematical text no longer reliably signals anything about the understanding of the person who produced it.
Litt's central proposal is to reconceive the math PhD around a rigorous oral defense, in which a student must explain their topic to examiners' satisfaction, rather than around a thesis document; he argues the topic's provenance, AI-assisted or not, should be irrelevant to that defense. He also wants departments to interview graduate-school applicants the way they already interview faculty hires, to reward sustained seminar talks and discussion over written papers as evidence of understanding, and to reward mathematicians who build research programs that persuade the community a given question is worth pursuing, since he argues the community's collective interest in open conjectures is itself a function the profession has underrated.
On cost, Litt writes that existing AI systems can already produce relatively high quality mathematical results for a marginal cost of 'a few dollars,' and that anyone with a laptop and 'a few hundred dollars' can now generate what would have been an Annals paper a year earlier. He argues that if a basic open question can be resolved for the cost of a nice dinner, mathematicians should be delighted rather than alarmed, because such answers will raise further, harder questions; some of those will again be cheap to resolve, and others will renew confusion and give rise to new research communities. He expects an abundance of machine-produced mathematical papers whose value will depend on whether a community of human mathematicians actually engages with them.
Key facts
- Litt says AI systems could not reliably add two numbers three years ago, but that about a year earlier internal OpenAI and DeepMind models reached the equivalent of a gold-medal IMO score, and that such systems are now autonomously resolving major open mathematical questions, without naming which ones.
- The essay follows an earlier talk, 'The End of Mathematics,' in which Litt warned that even robustly superhuman AI could let poorly adapted institutions cause human mathematical understanding to stall; he expects that outcome to be avoided but calls it a plausible default without reform.
- He proposes awarding math PhDs primarily on a rigorous oral defense of understanding rather than a thesis text, since it is now possible to produce a PhD thesis one hasn't even read, and says the topic's provenance, AI-assisted or not, should not matter.
- He says existing AI can already produce relatively high quality math results for a marginal cost of 'a few dollars,' and that anyone with a laptop and 'a few hundred dollars' can now generate what would have been an Annals paper a year earlier.
- He wants departments to interview graduate applicants like faculty hires, reward seminar talks and discussion over papers as evidence of understanding, and reward mathematicians who build research programs that persuade others a question is worth pursuing.
Why it matters
Litt's timeline places pure mathematics, long treated as one of the last strongholds of specialized human expertise, moving from unreliable arithmetic three years ago to, in his telling, autonomous resolution of major open questions now. His point is not that this makes mathematicians unnecessary but that the profession's traditional way of certifying progress and expertise, a proved theorem or a completed thesis, breaks down once that kind of text can be produced by a model for a few dollars. He argues academic mathematics has to decide what it actually values, understanding rather than proof output, before it can redesign itself around that value.
Who it affects
The essay speaks to academic mathematicians and the institutions around them: PhD programs and their advisors, hiring and graduate admissions committees, journals and peer review, and the arXiv. Litt writes as a working mathematician who describes himself as relatively enthusiastic about using AI in his own research, and he credits comments from more than a dozen named colleagues in the essay's acknowledgments, including Ravi Vakil, Boaz Barak and Michael Groechenig.
How to use it
Litt's concrete proposal is to award the math PhD primarily on the strength of a rigorous oral defense, in which the student explains their topic until examiners are satisfied, rather than on a thesis whose provenance he says should not matter. He wants departments to interview graduate applicants the way they already interview faculty candidates, to reward seminar talks and sustained mathematical discussion over papers as evidence of understanding, and to reward mathematicians who build research programs that persuade the community a question is worth pursuing, rather than chasing whichever narrow tasks AI still underperforms on.
How solid is it
This is a personal essay, not a study: a mathematician's opinion piece, cross-posted to a venue called Proofs and Prompts. Its central empirical claims, the IMO gold-medal-equivalent score and the assertion that AI is 'autonomously resolving major open questions,' are stated without naming the specific models, competitions or problems involved. The dollar figures Litt cites, 'a few dollars,' 'a few hundred dollars' and 'the cost of a nice dinner,' read as his own loose approximations rather than measured costs.
Risks and caveats
None of the 'major open questions' the essay says AI is now resolving is named, so the claim driving the whole argument cannot be checked against a specific result. The reform proposal is prescriptive: no university, program or journal is identified as having adopted it. Litt also flags his own uncertainty about the cost comparison, noting that a colleague, Michael Groechenig, questioned whether a machine-produced proof and a human-produced proof are really comparable products at all.
“A student will be confused. They will knock on their professor's door. … And the model might give them a beautiful explanation, but we all know that's not enough; no one can understand mathematics for us. We have got to do the work.”
— Daniel Litt, "A beginning for mathematics"