# Spare a thought for the mathematicians

> Source: <https://www.ariwilson.com/writing/ai-math-proofs/>
> Published: 2026-10-07 00:00:00+00:00

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.

Some of what it claims, with the year each question goes back to:

- [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).
- [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.
- [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.
- [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.
- [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.

The 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.

In 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/).

I 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.

I’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.

I 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.
