{"slug": "spare-a-thought-for-the-mathematicians", "title": "Spare a thought for the mathematicians", "summary": "OpenAI posted 722 math papers written by an unreleased model, covering 372 results across 17 fields, eight days after the author bet that math was next. The papers claim proofs of the quasi-Riemann hypothesis, the Unique Games Conjecture (Subhash Khot, 2002), the irrationality of Catalan's constant, the Mahler conjecture (1939), and Hilbert's tenth problem over the rationals; 162 of the papers have their main result verified in Lean, and each result took about 3 hours of ChatGPT Pro thinking on average out of about 4,000 problems posed. Diego Córdoba, whose \"forcing\" approach the model used for a Navier-Stokes proof, told Scientific American, \"We're a little bit in shock.", "body_md": "Eight days after I [bet that math was next](https://www.ariwilson.com/writing/ai-capability-overview), OpenAI [posted 722 math papers](https://github.com/openai/math) written by an unreleased model, covering 372 results across 17 fields. I have mixed feelings.\n\nSome of what it claims, with the year each question goes back to:\n\n- [The quasi-Riemann hypothesis](https://github.com/openai/math/blob/main/preprints/The-Quasi-Riemann-Hypothesis-September-30-2026/paper.pdf) : the Riemann zeta function has no zeros with real part above 7/8. It’s a weaker cousin of the Riemann hypothesis (1859).\n- [The Unique Games Conjecture](https://github.com/openai/math/blob/main/preprints/The-Unique-Games-Theorem-September-23-2026/paper.pdf) (Subhash Khot, 2002), which means the classic approximation algorithms for problems like Max-Cut and Vertex Cover are already as good as they’ll ever get, unless P = NP.\n- [Catalan’s constant is irrational](https://github.com/openai/math/blob/main/preprints/Catalans-constant-is-irrational-September-24-2026/paper.pdf) : 1 - 1/9 + 1/25 - 1/49 + …, a number Eugène Catalan wrote about in 1865.\n- [The Mahler conjecture](https://github.com/openai/math/blob/main/preprints/The-symmetric-Mahler-conjecture-and-its-equality-cases-September-22-2026/paper.pdf) (1939), about the smallest volume product of a convex shape and its “polar” dual.\n- [Hilbert’s tenth problem over the rationals](https://github.com/openai/math/blob/main/preprints/Hilberts-tenth-problem-over-the-rational-numbers-September-24-2026/main.pdf) : no algorithm can tell whether any given polynomial equation has a rational solution. Hilbert asked about whole numbers in 1900, and that version was settled in 1970.\n\nThe first four come with a proof in [Lean](https://lean-lang.org/), a programming language where a computer checks every step, and 162 of the papers have their main result checked that way. Hilbert’s tenth isn’t checked yet. Each result took about 3 hours of ChatGPT Pro thinking on average, out of about 4,000 problems posed.\n\nIn that same post I called OpenAI’s Navier-Stokes proof a sign of acceleration. I didn’t write about the people. Diego Córdoba and Luis Martínez-Zoroa had developed “forcing”, the approach the model used, and Tristan Buckmaster and Levent Alpöge posted a blowup result for the related Euler equations the night before OpenAI’s announcement. “We’re a little bit in shock,” Córdoba [told Scientific American](https://www.scientificamerican.com/article/openai-claims-blockbuster-math-breakthrough-amid-swirl-of-controversy/).\n\nI haven’t thought deeply about pure math in a long time. I’ve spent about 18 years building software, and I’ve always been more of a fan of math that does something in the real world. But I remember the joy of coming up with a new conjecture, or a proof nobody showed me first. In January 2005 I [asked this blog for help](https://www.ariwilson.com/writing/can-anyone-help-me-prove-that-set-of) because it took me 3 hours to solve 3 problems in my first proof-heavy course. The model averaged 3 hours per open problem.\n\nI’ve been mostly positive about AI in software engineering, even with the short-term disruption, because of the [Jevons paradox](https://en.wikipedia.org/wiki/Jevons_paradox): when something gets cheaper, we use more of it, and cheaper code means a lot more software. Math might not work that way. A conjecture only gets proven once. If you’d spent 10 years on the Mahler conjecture, Tuesday took that problem away, and no amount of new demand gives it back.\n\nI hope math as a form of human expression and creativity at the frontier keeps going, even if it looks more like cyborg exploration: people choosing which questions are worth asking and what the answers mean, with a model grinding through the cases. Maybe Jevons applies after all, and cheaper proofs mean more questions worth asking. Someone also has to read and understand 722 papers.", "url": "https://wpnews.pro/news/spare-a-thought-for-the-mathematicians", "canonical_source": "https://www.ariwilson.com/writing/ai-math-proofs/", "published_at": "2026-10-07 00:00:00+00:00", "updated_at": "2026-10-07 10:48:16.127329+00:00", "lang": "en", "topics": ["artificial-intelligence", "ai-research", "large-language-models", "generative-ai"], "entities": ["OpenAI", "ChatGPT Pro", "Lean", "Subhash Khot", "Diego Córdoba", "Luis Martínez-Zoroa", "Tristan Buckmaster", "Levent Alpöge"], "also_reported_by": [], "alternates": {"html": "https://wpnews.pro/news/spare-a-thought-for-the-mathematicians", "markdown": "https://wpnews.pro/news/spare-a-thought-for-the-mathematicians.md", "text": "https://wpnews.pro/news/spare-a-thought-for-the-mathematicians.txt", "jsonld": "https://wpnews.pro/news/spare-a-thought-for-the-mathematicians.jsonld"}}