New Delhi: On Tuesday, OpenAI shared a massive library of mathematics facts that it says it generated with an “extremely cutting-edge” model it developed internally. The company has uploaded 722 manuscripts to GitHub in 372 result families. They are taken from tests carried out on the model when it was pitted against approximately 4000 unsolved problems, like in number theory and computer science.
In a post on X, OpenAI stated that it has taken advice from and relied on the recommendations of the independent Advisory Group on Mathematics and Artificial Intelligence from the Institute for Advanced Study, influencing the way in which the results have been made public.
The headline claims
The most eye-catching is the result on the Riemann zeta function. In the release, the model was shown to be effective in proving that the zeta function and related L-functions have no zeros within the region where the real part of s is greater than 7/8. One of the most known unsolved mathematical problems, the Riemann Riemann Hypothesis, says that there are no zeros above the 1/2 critical line. Until now, the widest known zero-free regions have contracted upwards along the imaginary axis.Until now, the largest known zero-free regions have shrunk further up the imaginary axis. A strip where every band has the same width would be another type of answer.
We’re releasing a broad range of new mathematical results produced by an internal frontier model.
We’ve been consulting with the independent Advisory Group on Mathematics and Artificial Intelligence at the Institute for Advanced Study, and we have drawn on their advice and public recommendations to inform how we release these results.
https://t.co/7N6TPlft1P
— OpenAI (@OpenAI) October 6, 2026
Other notable features are: lowering the exponent of the matrix multiplication from 2 to 9/4, and a nearly n log n algorithm for integer multiplication. Many of the manuscripts are formally written with Lean, a tool to enable machine checking of the proofs as well as checking by human readers.
Early reaction
The zeta result is extraordinary, according to Rutgers mathematician Alex Kontorovich. “If done by a human it would be a Fields Medal guaranteed, no questions asked,” he said about his X, formerly known as Twitter, posting. He said he was expecting a thickening of the existing area, at least, and “insane” was his description of the zero-free strip.
When possible, we want to give people a choice—and be clear about what watermarking can and can’t do.
A text watermark helps answer one question: “Was this likely generated by an OpenAI model?”
It works by embedding an invisible statistical signal in text as it’s generated. A detector can look for this signal, and it doesn’t add visible marks or special characters. It doesn’t say who originally wrote the text or who owns it. It doesn’t identify a person, organization, account, conversation, or prompt.
In our testing, watermarking hasn’t affected how capable or fast our models are, or how their responses read.
— OpenAI (@OpenAI) October 5, 2026
Do you feel like the world is about to enter a new era of discovery?It feels like the world is … entering a new era of discovery, according to an OpenAI CEO, Sam Altman. A few commentators went further. AI commentator Dan McAteer said it is as though “a nuclear bomb hit” mathematicians and that OpenAI is downplaying the importance of the announcement. Reasoning models were comparatively new, and had grown from performing simple arithmetic tasks to solving problems which had taken decades for the human race to master.
Verification still ahead
The results are preliminary, not yet peer-reviewed, and now are waiting to be closely studied by the mathematical community. Lean formalizations should help do that for the manuscripts containing them, as a formal proof that can be compiled would eliminate most of the uncertainty about logical mistakes. It won’t answer every question, however. Reviewers will still have to establish whether formal statements are consistent with what is being claimed and whether the manuscripts not written in formal language hold up.
Practical issues also arise with regard to the release scale. The effort required by specialists in many subfields to read and check 722 manuscripts will be significant and time consuming and it is not yet clear how fast the community can distinguish between the major advances and the minor ones or distinguish from errors.
If it remains unchanged, for the time being the zeta result would be one of the biggest advances in the problem in decades. The next few weeks will tell us what’s left where it landed after being scrupulously scrutinized.
