OpenAI Publishes 722 AI-Generated Math Manuscripts, With Verification Still Uneven

Mathematicians largely back OpenAI’s quasi-Riemann proof as checking continues

A claimed AI-generated proof with consequences across mathematics is gaining support from human experts. Mathematicians studying OpenAI’s shorter quasi-Riemann hypothesis proof largely believe it is correct, Quanta Magazine reported on October 19. But their work is unfinished: they have not yet checked and understood every detail, and the full Riemann hypothesis remains unresolved.

The new assessment follows OpenAI’s October 6 release of mathematical results, including two versions of this proof. The significance is not simply that a model produced an argument. Experts now examining it say the model found an unexpected way to connect established ideas—using tools some mathematicians had believed were insufficient for the problem.

The Riemann hypothesis concerns the zeta function, a mathematical function closely tied to patterns in prime numbers. Its nontrivial zeros—the inputs, apart from a known set of simple cases, where the function equals zero—are known to occupy a vertical strip on the complex-number plane. That strip runs between real parts zero and one.

The full hypothesis says every nontrivial zero lies on the line at one-half. The quasi-Riemann hypothesis asks for less: a narrower strip containing all those zeros. Narrowing that region would still give mathematicians stronger information about how primes are distributed. OpenAI’s two papers claim different bounds, with different levels of verification.

Readability has shaped the review. New York University mathematician Maksym Radziwiłł told Quanta that both papers fall far below his field’s standards for clear exposition. Researchers have concentrated on the shorter version because it appears to use similar techniques and has similar consequences, while requiring far less material to work through.

That effort is producing more manageable explanations. Radziwiłł says he can sketch the argument in half a page. More detailed accounts by other mathematicians run seven to 13 pages, though those write-ups are circulating privately rather than published. Princeton’s Peter Sarnak has decided to repurpose a course this semester to study the proof.

Sarnak told Quanta he would not regard the result as a theorem until humans had checked and understood all the details. The shorter paper also received human editing before release. OpenAI did not identify the editor when asked, instead telling the magazine: “The paper is the result of work from everyone at OpenAI.”

The mathematical surprise lies in the combination. Sarnak had long advocated treating the zeta function as part of a larger family of functions, then proving statements about that family. But choosing the right family had remained a problem. According to the experts Quanta interviewed, OpenAI’s model identified one that had been overlooked.

That choice involved specialized mathematical objects called metaplectic forms. A formula Alexander Dunn and Radziwiłł proved in 2021 became a crucial ingredient, alongside other researchers’ work. Radziwiłł said researchers in this area had wrongly assumed their tools could not resolve quasi-Riemann and that techniques from another branch of number theory would be needed.

Radziwiłł expects the result to establish scores of consequences across number theory, geometry and theoretical computer science. That reach does not make it a clear route to the full Riemann hypothesis. Princeton mathematician Will Sawin told Quanta he suspects researchers will still feel just as far from that goal after absorbing the methods, while acknowledging uncertainty.

OpenAI Claims a Landmark Computer Science Proof After Researchers Rush Their Own Paper

A major computer science question now has an AI-generated proof claim—and human researchers have already changed their publishing plans under its shadow. OpenAI announced a proof of the Unique Games Conjecture on October 6, 2026, according to Quanta Magazine. The anticipated announcement had pushed three researchers to rush a related result into public view.

The conjecture concerns problems with many rules that must be satisfied at once. Think of coloring a network of points, with each connection imposing a rule about the colors at its ends. Even when a near-perfect solution exists, the conjecture says finding one that satisfies only a tiny fraction of the rules can remain hard. Lowering the standard does not necessarily make the task easy.

Its importance extends beyond that coloring puzzle. In 2008, computer scientist Prasad Raghavendra showed that, if the conjecture is true, one classic algorithm is the best strategy for every constraint satisfaction problem without a perfect solution. Researchers could not improve on it by exploiting a particular problem’s quirks. OpenAI’s announcement included 376 other mathematical results, including 40 other theoretical computer science proofs, Quanta reported.

On September 11, MIT professor Dor Minzer began receiving messages about a rumored OpenAI proof. He and graduate students Yumou Fei and Shuo Wang had not solved Unique Games. They had proved a related result, called the 4-to-1 games result, and were writing it up. Three days after the messages began, they posted a 95-page draft to avoid being overshadowed by OpenAI’s announcement.

Their result addresses a gap in Unique Games: cases where every rule can be satisfied. It is a weaker variant of Subhash Khot’s 2-to-1 games conjecture, allowing four possible colors across a connection rather than two. Yet it carries a long-sought consequence: even for networks that can be colored with three colors, allowing extra colors does not eliminate hard cases where finding a valid coloring remains difficult.

Speed came at the expense of explanation. Minzer told Quanta that, from section six onward, the draft contains definitions and intermediate proofs without connecting prose. The team plans a fuller revision. Their breakthrough had itself emerged from months of unsuccessful attempts: in April 2026, they finally combined lessons from five failures with a new error-correcting code, a method for detecting and fixing errors in transmitted messages.