About 40 top mathematicians gathered at OpenAI’s offices earlier this month to discuss the future of their profession, an off‑the‑record meeting that, by one account, reflected widespread anxiety about jobs and careers.
What the authors — writing with Kasra Rafi in The Guardian — conclude
The essay, written with Kasra Rafi and originally published in The Guardian, lays out a cautious counterargument to the pessimism. "We think the contrary view is more likely, at least in the short-term," the authors write. Their central claim: current AI models are capable of striking, PhD‑level achievements but remain short of replacing the deep, theory‑building work of experienced academic mathematicians.
OpenAI's mid‑May result: a disproof of the unit‑distance conjecture
In mid‑May, OpenAI announced that a frontier AI model disproved the unit‑distance conjecture, an approximately 80‑year‑old problem in discrete geometry. The authors treat this as an example of AI finding a novel application of known techniques: the counterexample drew on algebraic number theory and exploited a line of thought most mathematicians had not pursued because the conjecture had been motivated by an elegant construction that many assumed was essentially optimal.
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See what we buildAnthropic's July cryptanalysis papers and Claude's attempt at the Riemann hypothesis
Anthropic published two AI‑derived results in academic cryptanalysis in July. The company also published Claude’s attempt to prove the Riemann hypothesis, a problem described in the essay as "a century‑and‑a‑half‑old" question. The authors use these items to illustrate both the breadth of AI output in 2026 and the mixed character of that output: sometimes revealing counterexamples, sometimes applying existing ideas in novel contexts.
The Jacobian conjecture counterexample: search plus learned intuition
The counterexample to the Jacobian conjecture is singled out as the most notable of the first kind of AI success: discovery of counterexamples. According to the essay, once the counterexample had been found, checking it was "quick and straightforward"; the hard part was finding it among a large space of possibilities. The authors argue the AI appears to have combined intuition acquired via machine learning with extensive computational search to hit on the right example.
What current AI systems are good at — and not good at
The essay draws a clear distinction between two types of mathematical advance produced by AI in 2026. One class is counterexamples to existing conjectures; the other is novel applications of known techniques to problems where human attention had not converged on those techniques. The authors note that "these results are relatively low‑hanging fruit for AI; none of them required developing an extensive new theory."
They further argue that current models are "very strong at searching and recombining existing ideas" and possess advantages over individual humans — larger working memories, broader factual reach, and faster information processing — but remain weak at "building any deep and sustained new theory." In short, the models are creative in recombination but have not yet delivered the kind of conceptually new structures that drive much of mathematical progress.
What this means for academic mathematicians, AI developers (OpenAI and Anthropic), and cryptographers
- Academic mathematicians: Many expressed fear for jobs and careers at the recent OpenAI meeting. The authors suggest that, at least in the short term, those fears may be moderated by the continued need for theory‑building that current models do not appear to perform.
- AI developers — OpenAI and Anthropic: The companies' publications (OpenAI’s mid‑May disproof and the release of 10 new mathematical results "earlier this month," plus Anthropic’s July cryptanalysis and Claude’s Riemann attempt) serve as concrete evidence that emergent capabilities are occurring without those capabilities being explicitly designed or planned.
- Cryptographers: Anthropic’s two published AI‑derived cryptanalysis results in July demonstrate that cryptography is already a domain where AI can produce publishable, research‑level work, raising practical questions about the role of AI as an accelerant for research in security‑sensitive fields.
The authors close with cautious prediction: they are "confident that someday we will see AI models that are capable of the type of creativity required to do novel mathematics," but concede they cannot say whether that day is months, years or decades away — their "guess is sooner rather than later." For now, the record from mid‑2026 shows striking demonstrations of emergent capability alongside clear, stated limits in conceptual novelty.
