A 2026 Fields Medalist has made a surprising admission about AI. John Pardon says he has used AI to find “a few nontrivial proofs” for mathematical results he believed were true but hadn't fully established. AI has also caught subtle errors in his arguments. But there is a catch: it still struggles with some of his most serious research questions. His latest interview offers a glimpse into how one of the world's leading mathematicians actually works with AI.

A new report published by Quanta Magazine on 19 October 2026 describes significant progress in the independent examination of an AI-generated proof of the quasi-Riemann hypothesis. Leading number theorists, including Peter Sarnak, Maksym Radziwiłł, and Alexander Dunn, have been closely studying the argument. According to the report, experts increasingly believe that the proof is correct, although a complete mathematical assessment is still underway. The classical Riemann hypothesis, one of mathematics' most famous unsolved problems, asserts that every nontrivial zero of the Riemann zeta function lies on the critical line Re(s) = 1/2. The AI-generated argument addresses a weaker but still significant result, claiming that every nontrivial zero satisfies 1/12 < Re(s) < 11/12. If established, this would narrow the region in which nontrivial zeros can occur, bringing mathematicians closer to the prediction of the original hypothesis. After studying the 49-page manuscript, Radziwiłł reportedly found that he could summarize its essential argument in approximately half a page. Sarnak has also redirected a university course toward examining the proof, reflecting the growing mathematical interest in the result. Nevertheless, important questions remain. The 49-page argument has not yet been formally verified in Lean. A separate AI-generated argument claims the stronger bound 1/8 < Re(s) < 7/8 and is accompanied by a Lean formalization, although researchers are currently concentrating on understanding the shorter proof. The full Riemann hypothesis remains unsolved, and the mathematical community has not yet reached a final consensus on these AI-generated results. Even so, the ongoing independent examination marks a noteworthy development in the emerging relationship between artificial intelligence and advanced mathematical research.

Terence Tao has published a detailed mathematical exposition of an AI-generated argument addressing the longstanding Landau–Siegel zero problem, one of the important unsolved problems in analytic number theory. Unlike the recently reported investigation of an AI-generated argument concerning the quasi-Riemann hypothesis, this development focuses on a shorter, nine-page argument that claims to rule out exceptional real zeros of Dirichlet L-functions. Tao examines a simplified formulation developed by mathematician Ben Green, showing how the argument brings together ideas from algebraic number theory, polynomial interpolation, and the geometry of numbers. The Landau–Siegel zero problem concerns the possible existence of exceptional real zeros of Dirichlet L-functions extremely close to s = 1. For decades, the possibility of such zeros has complicated important estimates concerning the distribution of prime numbers, particularly primes in arithmetic progressions. A related reconstruction by mathematician William Banks establishes the explicit bound (1 − β) log q ≥ 0.003, where β is a real zero of a primitive real Dirichlet L-function with conductor q ≥ 3. This inequality gives a quantitative restriction on how closely such a zero can approach 1 as the conductor increases. It does not, by itself, establish the complete nonexistence of Landau–Siegel zeros in every conventional sense of the term. The AI-generated argument has now prompted substantial mathematical reconstructions by three researchers. William Banks submitted a detailed proof with explicit numerical constants on 11 October, Bryce Kerr followed with a simplified argument on 15 October, and Ben Green presented an alternative formulation using polynomial methods, revised on 18 October. Tao's exposition, published on 19 October, connects these developments and explains the mathematical mechanism underlying the argument. He also acknowledges using the SAIR Open Math model to help understand the preprints. The significance of this development lies not only in the mathematical claim but also in the independent scrutiny it has attracted. Several established mathematicians have examined, reconstructed, and simplified an argument originating from AI, making its essential ideas more accessible to the wider mathematical community.