OpenAI Releases 722 AI-Generated Mathematics Manuscripts; Mathematicians Would Need Years to Read Them All

[[**OpenAI releases 722 AI-generated mathematics manuscripts, claiming to have solved more than 370 open problems, among them a weakened version of the Riemann Hypothesis that mathematicians say would "win a Fields Medal immediately," but many of the proofs contain errors or cannot be verified, and the mathematics community's reaction is sharply divided.**

**Key points**

**1. The core results are highly significant**

The proof of a weakened version of the Riemann Hypothesis (no zeros in the region where the real part is greater than 7/8) was described by a Rutgers University mathematician as worthy of "an immediate Fields Medal," and the planar coloring problem was narrowed down to 6 or 7 colors.

**2. The quality of the proofs is concerning**

The 722 manuscripts have not been peer-reviewed; 3 were withdrawn on the second day after release, and another 14 were patched. About 42% passed machine checking, but some machine-verified conclusions do not correspond to the original claims of the papers.

**3. The mathematics community's reaction is polarized**

A "Human Mathematics Association" of more than 800 people called for an end to cooperation with OpenAI, and more than 20 Fields Medalists jointly criticized AI for treating hard problems as exam questions; some scholars, however, said that "we've been climbing all our lives, and now we can fly."

**4. The academic ecosystem has been shaken**

**5. The research burden is shifted onto the academic community**

Figuring out all the manuscripts is expected to take years; OpenAI says it will continue releasing more, and mathematicians can only hurry to finish the research they have in hand "before OpenAI gets ahead of them." 2026-10-10 20:12 OpenAI dumped a "mountain of crap," and mathematicians are holding their noses and panning for gold in it Guokr Quick Overview

This article is from the WeChat public account: Guokr, author: Steed, editor: Steed

This summer, Wang Hong won the Fields Medal for the three-dimensional version of the Kakeya conjecture. Less than 3 months later, OpenAI said its AI had solved the four-dimensional version as well.

On October 7, the American company OpenAI released 722 mathematics manuscripts in one go on the code-hosting website GitHub.

They came from the same never-publicly-disclosed internal model and cover 17 branches of mathematics, including number theory, geometry, probability, and theoretical computer science. OpenAI said the model attempted about 4,000 open mathematics problems in total and ultimately produced results on 372 sets of problems. The computing power consumed by each result on average was roughly equivalent to 3 hours of thinking by the paid premium version of ChatGPT.

One of them was described by a mathematician as follows: if a human had done it, "it would win the Fields Medal immediately, no question." The Fields Medal is the highest honor in mathematics and is awarded only once every 4 years.

But no one has yet read all 722 manuscripts from beginning to end, not even OpenAI's own researchers.

The table of contents and abstracts alone run to about 40 pages, and it took a mathematician more than half an hour to flip through from start to finish. Over the following days, experts in various fields looked through the few papers in their own areas and brought back bad news one after another: some proofs were wrong, some were simply incomprehensible, and some had not even been machine-checked.

One mathematician described it as a giant pile of crap dumped at their doorstep.

Yet in this mountain of crap, there is very likely real gold.

OpenAI claims progress on the planar point-set coloring problem | Olena Shmahalo/Quanta Magazine

The most understandable of the manuscripts is the planar coloring problem.

Color every point on an infinite plane, pick any length as 1, and require that any two points exactly 1 apart have different colors. What is the minimum number of colors needed?

This problem was posed back in 1950, and for decades afterward people only knew that the answer lay between 4 and 7. In 2018, Aubrey de Grey, a British biologist who studies aging and an amateur mathematician, proved that at least 5 colors are needed.

This time, OpenAI's model claims that 5 is not enough either, leaving only 6 or 7 as the answer.

The mathematician Riemann and the manuscript in which he proposed his hypothesis | Jonathan Groß

The most weighty item concerns the Riemann Hypothesis.

Prime numbers, that is, numbers divisible only by 1 and themselves, appear to be scattered haphazardly along the number line, yet behind them lies something called the Riemann zeta function. This function has infinitely many zeros, that is, positions where the function value equals 0, and their arrangement determines the arrangement of the primes.

Mathematicians already know that, apart from a set of zeros whose positions have long been clear, all the rest fall within a strip—in mathematical language, their real parts lie between 0 and 1. In 1859, the German mathematician Riemann conjectured that they are in fact neatly arranged on the line running down the middle of the strip, with all real parts equal to 1/2.

More than 160 years later, no one has proved the Riemann Hypothesis, and no one has even managed a greatly weakened version. It would count as success merely to prove that some section on the right side of the strip contains no zeros at all—even just the narrow sliver between 0.99 and 1 has defied human proof.

This time, the manuscripts claim that there is not a single zero in the region where the real part is greater than 7/8.

The "immediate Fields Medal" remark by Alex Kontorovich, a mathematician at Rutgers University in the United States, refers to this item.

This is still far from the Riemann Hypothesis itself. The conjecture calls for 1/2, and Matt Baker of the Georgia Institute of Technology in the United States cautioned that a complete proof may require an entirely different approach.

Moreover, these results are for now only claims made in manuscripts. None of the 722 manuscripts has been peer-reviewed, and none bears a human author's name.

On the second day, OpenAI withdrew 3 papers | X screenshot

On the second day after release, OpenAI withdrew 3 papers. The problem lay in a single symbol in the first paper: where a minus sign should have been, a plus sign was written, so a crucial cancellation did not hold. The other two papers were built on the same construction and were withdrawn along with it. On the same day, 14 more papers were patched.

More of the manuscripts had problems that came down to being unable to understand them.

Brendan Hassett of Brown University in the United States opened the problem he knew best, skimmed it once, and found it incomprehensible. He said that if a human had written it, he would not have spent any more time on it, but there were still 721 papers to go.

Mihalis Dafermos of Princeton University in the United States, who studies the mathematics of black holes, looked at several papers in his field and could not pinpoint anything specifically wrong. They were written too vaguely, falling short of the standard of a proof—so vague that they could not even be called wrong.

Lean is an interactive theorem prover that uses code to write mathematical proofs and can automatically check their logical rigor by machine | viz-x/DEV Community

Proofs that cannot be understood could, in principle, still be handed to a machine.

Mathematics has a convenience that other disciplines lack: proofs can be translated into a language that programs such as Lean can read, and a computer can check them line by line. As of October 10, about 42% of the results had passed this kind of machine check. OpenAI also acknowledged in its explanatory document that the rest may have problems, and the 3 withdrawn papers were among them.

Machine checking also has blind spots. A program can only guarantee that the statement it was given has been proved; whether that statement is the same as the original problem in the paper still requires someone to read the code and verify it. Johan Commelin, who is responsible for the Lean mathematical library, suspects that some formalized versions actually prove weaker propositions.

Among the mathematicians who have been going through the manuscripts these past few days, some have already found that the statement verified by machine and the conclusion claimed in the paper do not always appear to match.

As a result, which paper is gold and which is rubbish can only be determined by having people read them one by one.

This job has fallen on the entire mathematics community.

Ursula Martin of the University of Oxford in the United Kingdom said that OpenAI has thrown a messy first draft at the academic community and then expects others to clean it up for it.

Fields Medalist Terence Tao publicly opposed and boycotted OpenAI's paper bombardment | David Esquivel/UCLA

In the past, explaining a proof clearly was the business of the person who produced it.

Fields Medalist Terence Tao has described the conventions of the mathematics community: after a long-standing problem is solved, the prover gives talks everywhere, peers organize seminars to work through it together, new collaborations and new questions emerge, young people are drawn into the field, the proof is simplified step by step, and finally it is written into textbooks.

Now that problems are being solved by AI in batches, and the people submitting the results cannot explain them clearly themselves, this chain of reactions almost no longer happens. Researchers have also begun to hide promising directions for fear of being scooped. Tao compared this to open-pit mining, stripping unresolved problems away patch by patch.

Some simply refuse to take on this work. On the second day after release, a group of more than 800 mathematicians called the Association for Human Mathematics issued a statement calling on peers to stop cooperating with OpenAI. The statement said that releasing more than 700 documents at once is a show of strength, not scholarship.

This was not the only group to speak out in criticism. In September, more than 20 Fields Medalists jointly issued a declaration criticizing AI companies for treating difficult mathematical problems as exam questions for testing models.

Young people have already suffered first. Doctoral dissertations, funding applications, and job materials often hinge on a single unsolved problem. After the manuscripts were released, some mathematicians said that a group of friends and colleagues around them had their funding applications invalidated overnight. Others worry that if the next generation no longer tackles hard problems, in a few decades these areas of mathematics may no longer be understood by anyone.

OpenAI has no intention of stopping | X user @ℏεsam

The mathematics community has not reached a consensus. Daniel Litt of the University of Toronto in Canada believes this is good for mathematics, and he relayed the feeling of a collaborator: "I feel like I've been climbing my whole life, and now I can fly." Others felt relief upon seeing problems they had studied being solved.

Whether excited or angry, everyone faces the same pile of manuscripts. Mathematicians generally estimate that it will take several years to make sense of these 722 papers.

OpenAI has no intention of stopping. It says it will continue to use mathematical problems to test its internal models, and word is already circulating in mathematics circles about the next batch of manuscripts.

Scott Armstrong, a mathematician at the French National Centre for Scientific Research (CNRS), considers himself among the most optimistic people about AI. Asked about his plans going forward, he said that the most important thing right now is to finish the research at hand, "before OpenAI beats us to it."

References

[2] OpenAI. openai/math (manuscript repository, including explanatory documents and update records). GitHub. https://github.com/openai/math

[3] Robert Hart. 'Pure insanity': Mathematicians will need years to make sense of OpenAI's latest drop. The Verge, 2026-10-09. https://www.theverge.com/ai-artificial-intelligence/1008726/openai-mathematics-solutions-chaos

[4] Peter Hall, Joseph Howlett. The most exciting claims from OpenAI's heap of new proofs. Scientific American, 2026-10. https://www.scientificamerican.com/article/the-most-exciting-claims-from-openais-heap-of-new-proofs/

[6] Cracks appear in OpenAI's wall of proofs. Quanta Magazine, 2026-10-09. https://www.quantamagazine.org/updates/transformation/

[9] A Severe Misalignment of AI in Mathematics (joint declaration by Fields Medalists). 2026-09-11. https://mathandai.org/

[10] Association for Human Mathematics. Statement on OpenAI's October 6 release of mathematical documents. 2026-10-07. https://www.ahmath.org/statementsAI industry signal channel: Frontier technology. This content comes from the internet and the original link; the views represent only the author and do not represent the position of Huxiu. If there is a copyright issue, please contact hezuo@huxiu.com, and we will verify and handle it promptly. Everyone who is changing and wants to change the world is on the Huxiu APP [ ]