OpenAI retracted three maths papers in one day – now the significance of the publication for encryption is disputed
When OpenAI released 722 AI-generated mathematics manuscripts in one go, it wasn't only mathematicians who reacted. Cryptographers are now divided: one leading researcher puts the probability at 15 percent that we could lose trust in the algorithms protecting messages and banking logins, while others point out that not a single one of the papers touches on cryptography. The debate over whether AI's advance in mathematics also threatens the foundation of the internet's security is underway — without anyone having documented a breakthrough.
What OpenAI Actually Published
On October 6, 2026, OpenAI posted the 722 manuscripts on GitHub, organized into 372 groups. The company described them as results from an internal model not yet available to external users, and said that many of the proofs exist in computer-checkable forms, with protocols for review and citation (58a0e7d8).
The release was far from flawless. According to Scientific American, OpenAI retracted three of the papers within one day, and the reason has not been given. Mathematicians are still working through the rest (038b1500).
The release came in the wake of the company's claimed solution to the Navier–Stokes problem, one of mathematics' most famous open questions. According to OpenAI's own stated figures, the proof was produced by an "agent swarm" of roughly 10,000 copies of the company's new, math-focused language model, which used about 88 hours of compute time and 130 billion tokens to construct a "blowup" (0d863c24). The claimed breakthrough triggered a dispute over source usage and an open letter from more than two dozen Fields Medal winners, warning that the industry's approach risked undermining mathematics as a discipline (58a0e7d8). Later, experts who reviewed the Navier–Stokes paper concluded, according to Scientific American, that the proof probably does not follow the so-called Spanish program by Córdoba and Martínez-Zoroa, as early reports suggested (0d863c24).
The Worry Side: 15 Percent and a Narrow Mathematical Base
A few days after the release, Matthew Green, a cryptographer at Johns Hopkins University, wrote in a social media post that he estimated a 15 percent probability that we could lose trust in existing public-key encryption algorithms — the systems behind encrypted messaging and secure logins (038b1500).
That is a high estimate for a field where losing trust would in practice mean much of the internet's security architecture would have to be rebuilt. Green's argument rests partly on history: an algorithm called the number field sieve made it far easier to break RSA when systems used 512-bit keys. Cryptographers' response was to make the keys longer, and today 2,048 bits is considered the minimum. The point is that progress in mathematics can force entire infrastructure to change — but also that the field has weathered such shocks before.
Govind Pimpale, of the think tank Foundation for American Innovation, points to another vulnerability: public-key encryption rests on relatively few mathematical problems, each studied by a relatively small research community. Machines can throw far greater force at the same problems and potentially find flaws or faster algorithms that let attackers compute from public keys to secret ones (038b1500).
The Pushback: "No Evidence Whatsoever"
The skeptical voices are no less prominent. Yehuda Lindell, a professor at Bar-Ilan University in Israel and head of cryptography at Coinbase, wrote on X that there is "no evidence whatsoever" of a breakthrough against the mathematical problems underlying these systems. And Dan Boneh, a professor of computer science at Stanford University, notes that not a single one of OpenAI's 722 papers deals with cryptography — something he describes as "a little striking" (038b1500).
That last point may be the most concrete in the whole story: the release that sparked the debate provides, in itself, no indication of progress against the core problems of cryptography. The split is therefore not about what OpenAI has proven, but about what one should read into the direction and pace of AI capability in general.
Why the Question Is Alive Anyway
Even though the 722 papers are silent on cryptography, there are other signals of rapid progress in AI-driven cryptanalysis. In a recent preprint, Florian Tramèr, a computer scientist at the Swiss federal institute ETH Zürich, and his colleagues — three of them at the AI company Anthropic — pitted leading AI models against 191 code-breaking challenges. "It is clear that the models' ability in cryptanalysis is growing extremely rapidly," Tramèr said, according to Scientific American (038b1500).
Anthropic has also reported — and this is the company's own statement, not independently verified — that the Claude model found a significantly improved attack on HAWK, a proposed digital signature scheme designed to withstand quantum computers (038b1500). HAWK is a future-proofing proposal, not a system in use today, and an improved attack on one candidate proposal is not the same as breaking established encryption. But together, the preprint and the HAWK attack form the backdrop for why the concern cannot be dismissed as pure speculation.
It is worth noting that all of these voices — Green's estimate, Lindell's statement, and the Tramèr preprint — reach us through secondary journalism, primarily Scientific American's October 15 analysis. None of the underlying documents are in this coverage, and the estimates are thus quotes within quotes.
The Backdrop: a Contested Release
The cryptography debate is taking place in an already heated climate. NYU professor Tristan Buckmaster told CNBC's "Squawk Box," according to Business Insider, that "entire research programs were wiped out Tuesday by their dump" (58a0e7d8). Buckmaster has also raised the question of whether unpublished work may have fed the model's results. These are one-sided claims: according to the coverage, OpenAI did not respond to questions from Business Insider but claims the model cannot have seen Buckmaster's data. The matter is unresolved, and it primarily concerns the mathematics community, not cryptography.
There is, moreover, no source in the coverage suggesting that encryption has been broken or is about to be. That part of the debate is about probability and direction, not facts on the ground.
Open Questions
Three things remain unresolved. First, the review of the 722 manuscripts is ongoing, and the quality of the majority of them has not been established. Second, the reason three papers were retracted within one day has not been made public. Third, the scientific question itself is open: Can AI accelerate cryptanalysis of the underlying mathematical problems — factoring large numbers, lattice problems, and the other foundations of public-key encryption — as it apparently has accelerated pure mathematics?
Pimpale's point about a small research community around few problems, and Tramèr's observation of rapid progress in cryptanalysis, point in one direction. Boneh's observation that none of the 722 papers concern cryptography, and Lindell's dismissal of all evidence, point in another. Until someone documents actual progress against these problems, the split — not the answer — is the news.