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Cosmos & Physics · Week of September 17, 2026

AI's Math Breakthroughs Face Credit, Verification, and Over-Reading

Last week, the story was OpenAI's claim that its agents had cracked the Navier-Stokes existence and smoothness problem, one of the Clay Mathematics Institute's seven Millennium Prize Problems. This week, the story is everything that claim has dragged into the light: an NYU mathematician alleging his unpublished work was used, a formalization pipeline being mistaken for peer review, and a 75-page arXiv paper on Lorentzian polynomials co-authored by two high school students.

Start with the contradiction most readers will feel before they can name it. OpenAI says its unreleased model solved a problem that stumped mathematicians for nearly 90 years, in 88 hours, using roughly 10,000 agents. That sounds like a clean victory. It is not.

The timing is the first problem. On September 8, OpenAI announced its Navier-Stokes result. One day earlier, Tristan Buckmaster at NYU had posted a proof on Mastodon showing that a simplified version of the equations can break down. He and Levent Alpöge, a researcher at Anthropic, had worked on it for almost a year, using publicly available models from both OpenAI and Anthropic.

Buckmaster says OpenAI asked him to collaborate after hearing about his progress. He also says one of the company's scientists warned he might 'ruin his career' if he refused.

Buckmaster says OpenAI asked him to collaborate after hearing about his progress. He also says one of the company's scientists warned he might "ruin his career" if he refused. OpenAI denies that any of its researchers or agents saw the pair's work before publication.

The company concedes something narrower but still unsettling: de-identified data drawn from product use may have improved its models. Buckmaster and Alpöge had used OpenAI's Codex assistant while assembling their proofs. OpenAI can train on those sessions unless users opt out.

That is not a smoking gun. It is a structural problem. If a company's models learn from the sessions of the researchers it later races, "independent replication" becomes a phrase without a clear referent.

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The verification question is the second over-read. OpenAI released verification materials converting the proof into a computer-checkable format. That is real and valuable. But as the Korean outlet SBS reported, a computer checks whether the logic of the entered content holds. It does not check whether the original mathematical content was accurately translated into computer-readable form. The 166-page paper still needs independent review by mathematicians.

Terence Tao, who is arguably the world's greatest living mathematician, put the cultural cost plainly. "Now there's no speed limit, and suddenly things are breaking down," he told New Scientist. His metaphor for the flood of results was blunter: companies are "dumping carcasses of raw meat onto our communal village table" and leaving the field to cook and eat.

That is not Luddism. It is an observation about absorption. Mathematics has always had competition, but the difficulty of the work acted as a natural brake. AI removes the brake. Tao fears new findings will land faster than the field can assimilate them into textbooks, into teaching, into the shared understanding that makes a result usable.

Now look at the high-school story, because it is where the over-reading becomes most visible. Two students at Oak Park High School in California, Aayush Bathija and Prince Rohatgi, published a 75-page paper on arXiv titled "Bounded Ratios for Lorentzian Polynomials." They worked under a UCLA postdoctoral researcher, Daniel Soskin, and used Claude Opus 5 and GPT-5.6 Sol.

The framing that spread online was that they solved a problem June Huh, a Fields Medalist, never cracked. That framing is wrong in a specific, instructive way. Huh and collaborators had characterized which ratios have upper bounds for quadratic Lorentzian polynomials and found optimal bounds for the three-variable case. The students extended the conclusions to arbitrary degrees, showing that whether a coefficient ratio has a uniform upper bound can be determined by a set of discrete convexity conditions.

That is a genuine contribution. It is not "solving" Huh's problem in the sense the headlines implied. It is advancing a research program he helped establish. The distinction matters because it is exactly the kind of over-read the field keeps making: treating a step as a summit.

The direction of the over-read is predictable. Formalizability is being treated as truth. A proof that compiles is treated as a proof that is correct. An agent swarm that finds a path is treated as having understood the path. A high-school paper that extends a result is treated as having solved the problem the result came from.

There is a counterargument worth taking seriously. As one commenter put it, mathematics is a "completely in-compute and perfectly verifiable domain." It is what AI is best at. We should not extrapolate from math to the messy real world. That is fair.

But the counterargument cuts the other way too. If math is the domain where verification is cleanest, and we still cannot establish attribution, cannot confirm independent derivation, and cannot distinguish a formalized proof from a reviewed one, then the problem is not that AI is bad at math. The problem is that the social and institutional infrastructure around mathematical truth has not kept pace with the tools producing it.

Ramez Naam made a related point about recursive self-improvement. We conflate RSI with a fast takeoff to superintelligence. They are not the same. RSI means a model can improve on itself. It does not mean it can do so more at each iteration. Diminishing returns are the more likely outcome, governed by power laws and log-scale effects.

That is a useful corrective, but it does not resolve the credit problem. Buckmaster said he did not care about the $1 million or winning the race. "I love math, and I just wanted to be part of the story," he said. Instead, he became a bystander in what he called "petty games" between OpenAI and Anthropic.

The Clay Mathematics Institute's president, Martin Bridson, said the evaluation process is "deliberately unhurried" and will be "absolutely rigorous." That is the right posture. It is also a reminder that the prize, if it is awarded, may go to no one for years.

What matters now is not whether AI can do mathematics. It clearly can. What matters is whether the field can build norms for crediting, verifying, and absorbing AI-assisted work before the next 88-hour result lands. The alternative is a mathematics that produces more proofs than it can understand, attributed to systems that cannot explain where the ideas came from.

Sources

Researched from 10 sources. Primary source: wattsupwiththat.com

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