Statistics and Optimization Make Up 20% of arXiv Theorems but Under 1% of OpenAI's 722 Math Papers

Statistics, machine learning theory, optimization and numerical analysis account for about 20% of theorems on arXiv but less than 1% of the results OpenAI published this month, according to a count by Daniel Paleka in his newsletter dated Oct. 16.

OpenAI posted 722 manuscripts on Tuesday, Oct. 6, The Next Web reported. They sit in a public GitHub repository, grouped into 372 families of results. The model that produced them has not been released.

What Paleka counted

Paleka wrote that "OpenAI has published very few results on statistics, ML theory, optimization, and numerical analysis." He compared the release with the share of those fields among arXiv theorems.

The gap shrinks but stays larger than chance would produce, by his test, when he limits the baseline to arXiv papers that solve open problems. He says that undercuts the idea that these fields simply lack open problems.

1. arXiv theorems (about)20 %
2. OpenAI release (under)1 %

Source: Daniel Paleka's Newsletter, Oct. 16, 2026; OpenAI figure is an upper bound ('less than 1%')

The only result he finds professionally interesting is a Max-Cut hardness bound of 0.878, assuming P is not equal to NP. He notes it follows from a Unique Games Conjecture result proven in the same batch.

Paleka's post opens by asking whether labs hold back the math most useful to their own work. He presents that as one possible explanation and does not answer the question directly. A commenter, Soroush Pour, made the same point, according to the post's page.

What OpenAI released

Item	Figure
Manuscripts	722
Families of related results	372
Problems given to the model	about 4,000
Average compute per result	about 3 hours of ChatGPT Pro thinking

Many proofs come with formal versions in Lean, a language a computer can check. Not all do. OpenAI said some results without formal versions could have issues and that it will fix them quickly, The Next Web reported. OpenAI also published ten summaries of the model's reasoning.

Two results did not follow the standard procedure. A human edited the write-up of a zero-free region for the Riemann zeta function, and a proof of the Hodge conjecture for CM abelian varieties is also in the set. Nearly every paper came from a single prompt to a single agent, according to OpenAI's comments to Scientific American, as relayed by The Next Web.

The advisory group's guidelines

The Advisory Group on Mathematics and Artificial Intelligence, hosted at the Institute for Advanced Study, published guidelines on Sept. 29. They asked labs to stop testing hard problems on private models and to publish the prompts, time and compute behind each result.

The group warned that "proprietary internal models" risk "creating a two-tier system where labs outrun the rest of the field." On the night of the release it said its advice did not endorse the results or how OpenAI obtained them.

OpenAI published problem counts, average compute and reasoning summaries. The Next Web did not report that it published the prompts.

Reactions from mathematicians

Dan Roberts, OpenAI's research lead, told The New York Times that testing internal models helps build better tools and that the proofs were a byproduct, The Next Web reported.

Tristan Buckmaster, a New York University mathematician who worked on the Navier-Stokes problem, doubted OpenAI had checked so many results at once. "I don't think they've done their sort of due diligence at all," he said. The Terminal covered his dispute with OpenAI last month. Andrew Sutherland, an MIT mathematician, told Scientific American that single-agent claims should be treated as unverified until others can run the model and reproduce them. Open-weight releases such as DeepSeek's V4.1-Flash-1017 can be rerun by anyone, and this model cannot.

OpenAI has not said why the fields Paleka names are so thin in the set. It said it will fund workshops, conferences and programmes on AI-produced results.