Mathematicians Launch AI Boycott as Tao Uses Claude to Revise OpenAI Math Papers

In the same week that more than 1,000 professional mathematicians signed pledges to refuse all commercial AI work, Terence Tao—the Fields Medalist most visibly associated with the movement—quietly used Anthropic's Claude Code to submit pull requests improving OpenAI-generated mathematics papers. And on arXiv, a pair of mathematicians uploaded a 35-page disproof of a conjecture that had been open since 2000, crediting an unexpected three-step collaboration with ChatGPT. The convergence of these events is not coincidental: all three are direct consequences of OpenAI's decision last month to release 722 machine-generated mathematical manuscripts, and all three illuminate a single, uncomfortable question now dividing the discipline—when AI produces mathematics faster than humans can verify it, who is responsible for the work that follows?

OpenAI's Mathematical Dump and the Backlash It Created

On October 6, 2026, OpenAI released what it described as the output of an internal AI system tested against approximately 4,000 unsolved mathematical problems, each consuming three hours of ChatGPT Pro compute per result. The release comprised 722 manuscripts organized into 372 problem families, posted to a public GitHub repository under an Apache 2.0 license. Roughly 42 percent of the manuscripts included Lean 4 formal proofs—machine-verified logical derivations whose correctness is guaranteed by the proof assistant's kernel.

The formal proofs covered the logical validity of the results. They did not cover what came after: the natural-language mathematical writing surrounding those results was fragmented and often unreadable, missing substantial context, and failed to cite the bodies of prior work that the proofs built upon or superseded. Within 24 hours, three manuscripts were withdrawn entirely after the community identified a sign error propagating through several results; 14 more required revision.

It is worth being precise about what a Lean 4 proof guarantees and what it does not. A Lean proof is mechanically checked by the proof assistant's logical kernel—if the kernel accepts it, the formal derivation is valid, with no gaps. But a Lean proof does not verify that the human-readable surrounding text is accurate, that the prior literature is correctly characterized, or that a reader could reconstruct the mathematical intuition behind the result. The ~58 percent of manuscripts without Lean proofs have no machine-verified validity at all; even for the 42 percent that include them, the pedagogical and citation infrastructure that allows mathematicians to build on results remained entirely absent. This is the gap that oai-math-revised is designed to fill—and the gap the AHM argues should not be filled by unpaid academic volunteers.

That release was itself not the original trigger. On September 8, 2026, OpenAI had announced that approximately 10,000 AI agents running concurrently for 88 hours had produced a proposed resolution to the Navier-Stokes regularity problem, one of seven Millennium Prize Problems carrying a $1 million award. Tristan Buckmaster, a fluid dynamics expert at NYU, and Levent Alpöge, a mathematician at Anthropic, independently raised significant technical and provenance concerns about the proposed proof. The fundamental complaint went beyond the technical: a mathematician had reportedly fed an unpublished manuscript to ChatGPT for editing assistance, after which OpenAI had deployed an agent swarm on the underlying problem—without the original author's explicit consent to that use.

The October manuscript release arrived into that charged atmosphere. The Association for Human Mathematics, formed in September 2026 by a group that included 25 Fields Medalists, had already published a statement declaring: "Releasing over 700 files at once is not a demonstration of scholarship, but a demonstration of power." Their critique targeted what they saw as a pattern: produce a result with compute, package it as a scientific breakthrough, and rely on the academic community to validate and contextualize it at no charge. Three days after the October release, the AHM's journal working group sent demands to major mathematics journals: any AI involvement in editorial review must require explicit author consent before unpublished manuscripts are processed by commercial systems.

Tao Uses Claude to Fix OpenAI's Papers—Using a Competitor's Tool

On October 24, 2026, four researchers—Abhinav Nellore of Oregon Health & Science University, Johannes Schmitt, Rachel Ward, and Soledad Villar—announced the launch of oai-math-revised, a GitHub repository designed to accept community corrections to OpenAI's 722 manuscripts. The announcement appeared as a guest post on Tao's blog, inviting the global mathematics community to submit pull requests adding missing citations, rewriting fragmented proofs into coherent exposition, and documenting connections to prior literature that the machine-generated texts had omitted.

What the announcement did not foreground—but the commit history documented—is that Tao had already been at work before the public launch. Under his GitHub username teorth, Tao had submitted pull requests numbered 2 and 3 addressing Document 003, the manuscript concerning a uniform non-existence result for Landau-Siegel zeros—a number-theoretic problem with direct implications for how uniformly prime numbers are distributed in arithmetic progressions. According to the source reporting, Tao drafted both revisions using Claude Code, Anthropic's AI-powered development environment, running on the Opus 5.5 model. After verifying the changes himself, he updated the manuscript byline to "OpenAI (with community contributions)" and added a block of references connecting the result to prior work by Kevin Banks, Ben Green, and Tao's own earlier contributions to the field.

The attribution for Claude's specific role in Tao's oai-math-revised pull requests comes from the source reporting; Tao's separate Lean 4 textbook formalization project on GitHub independently confirms his use of Claude Opus 5 in related mathematical work, with co-authorship credits appearing in commit messages. By October 25, 2026, the oai-math-revised repository had accumulated 13 commits, with the source article reporting that 8 of those 13 carried annotations identifying Claude Code as the drafting tool—a figure not independently confirmed in this workflow but consistent with the collaborative approach Nellore and his co-authors had explicitly invited.

The meta-scene here has an almost theatrical quality: a human mathematician, one of the most decorated in the world, used Anthropic's AI coding tool to improve the mathematical papers generated by OpenAI's AI system, then published those improvements to a community repository under an open-source license. The tool, the beneficiary, and the corrector belong to three distinct entities, and the labor is being donated for the benefit of all.

The Labor Question Tao's Blog Comments Could Not Resolve

The recruitment post generated 21 extended comments on Tao's blog within 24 hours, splitting almost immediately into two positions that track a genuine structural disagreement.

Lior Silberman, a professor of mathematics at the University of British Columbia, stated the opposition case directly: OpenAI is the named author of these manuscripts. Completing citations, clarifying proofs, and writing coherent exposition is what mathematical authorship means. If a commercial company wishes to use academic expertise for editing and peer review, it should pay for that service at market rates. Volunteer labor directed at improving a company's intellectual property is not a community obligation.

A commenter identified as Skip Tich raised a distinct concern: corrections submitted to a public repository can be scraped by the same companies whose products generated the original manuscripts, and fed into the training data for their next model generation. Under this analysis, donating a high-quality mathematical proof to oai-math-revised is an indirect subsidy to future commercial AI training, regardless of the contributor's intent.

The counterargument, articulated by a commenter named Nestor, was ecological rather than economic. OpenAI's manuscripts, whatever their flaws, are now indexed, cited, and referenced across the mathematical literature. If the community does not build a corrected, community-controlled version of that record, the uncorrected material will propagate indefinitely into papers, reviews, and students' understanding of the field. The analogy Nestor offered: if a multinational corporation dumps toxic waste in a national park, the cleanup is not the volunteers' fault—but if no one cleans it up, the ecosystem suffers regardless.

Tao replied on the morning of October 25. He framed oai-math-revised not as volunteer labor for OpenAI but as infrastructure the mathematical community owns and controls. A community-managed repository, he argued, is the mechanism by which error corrections, follow-up research, and critical commentary can be organized in one place—rather than scattered across blog posts, email threads, and informal discussions that benefit no one and persist nowhere reliably. The fact that he used Claude Code to draft his own contributions was, in his implicit framing, simply efficient use of available tools in service of a community project.

The Association for Human Mathematics: Structure and Commitments

As of October 25, 2026, the Association for Human Mathematics had 1,008 named members who had signed two binding commitments. The first: to provide no labor, consulting, or promotional activity on behalf of any commercial entity whose primary activity is automated mathematical production. The second: to include no AI-generated text in any work appearing under the member's name.

Six hundred and fifty-four of those members have gone further, joining what the AHM calls its AI-free caucus. This inner tier commits to total abstinence from AI assistance across all stages of daily mathematical research—including using AI to search for proof strategies, to test conjectures against examples, or even to pose new problems. The commitment is not about published output; it governs the private research process as well.

The AHM's formation reflects a specific theory of what AI is doing to mathematics as a profession. The founding statement argues that when a system can produce formally verified results faster than human mathematicians can read them, and when those results appear under the institutional banner of a corporation rather than a researcher, the traditional incentive structure of mathematics—in which credit follows understanding, not computation—breaks down. The mathematician who poses a good problem and understands the answer has historically received more recognition than the one who runs a calculation first. The AHM's position is that the community should explicitly defend that value before the incentive structure shifts irrevocably toward compute.

The movement has attracted some mockery from outside mathematics. Tech commentator Hesamation drew a comparison to competitive chess players refusing to use engine analysis—the suggestion being that refusal to adopt a powerful tool is a form of professional self-sabotage. The analogy has limits: chess players who refuse engine analysis compete only against other chess players, while mathematicians are increasingly being asked to validate, correct, and contextualize results generated by systems they had no role in creating.

ChatGPT Disproves a Conjecture Open Since 2000: How It Happened

The most technically significant development of the week arrived quietly on October 22, when Simon Becker of Bocconi University and Mengxuan Yang of Texas A&M uploaded arXiv:2610.31637, a 35-page paper disproving the multidimensional L² conjecture that Barry Simon had posed in 2000 during a set of IAS/Park City lectures.

Simon's conjecture concerned Schrödinger operators of the form H = -Δ + V acting on the Hilbert space L²(ℝᵈ) for dimensions d ≥ 2. The spectrum of such an operator determines the long-term behavior of a quantum particle moving in the potential V. Absolutely continuous spectrum corresponds to a particle that can escape to infinity—it scatters freely, its energy spreading across space. Pure point spectrum corresponds to localization: the particle's quantum state remains concentrated in a bounded region regardless of how much time passes. Simon's conjecture was that in two or more dimensions, if the potential V satisfies a finite L² norm condition on each spherical shell around the origin, the Schrödinger operator must retain absolutely continuous spectrum on the entire positive half-axis—the particle cannot be localized. The geometric intuition was that high-dimensional space offers a particle too many escape directions for a merely square-integrable potential to seal them all.

The conjecture survived twenty-six years. The difficulty, as generations of researchers discovered, is that constructing an explicit potential that localizes a particle in dimensions d ≥ 2 requires blocking every escape direction simultaneously—and high-dimensional geometry keeps opening new ones.

Becker and Yang describe their process in a dedicated section of the paper. The three-step collaboration with ChatGPT proceeded as follows. The paper's AI disclosure identifies the tool used as "ChatGPT," without specifying a version.

First, the authors surveyed OpenAI's October 6 manuscript release and identified the L² conjecture as still unclaimed—no manuscript in the 722 addressed it. Working with ChatGPT, they designed a potential built from concentric spherical shells. Each shell contains a "weak lens" zone using slight angular variation in the potential to focus wave packets into narrow angular channels, and a "reflecting barrier" zone using a radially periodic potential to bounce energy back inward. This geometry successfully eliminated absolutely continuous spectrum in a bounded energy window.

Second—and here the collaboration departed from what the authors expected—ChatGPT introduced the Combes-Hislop spectral averaging criterion without any modification to the underlying geometric construction. The Combes-Hislop technique, originally developed for random Schrödinger operators, uses averaged resolvents to control the imaginary parts of Green's functions and establish exponential decay of quantum states. Its use in a deterministic, explicitly constructed potential was not obvious, and Becker and Yang write that they did not anticipate it. The introduction of this tool allowed them to prove pure point spectrum—not just the elimination of absolutely continuous spectrum—in the bounded energy window, which is a significantly stronger result.

Third, ChatGPT pushed the parameters of the construction to their limits. As Becker and Yang write in the paper: "Very much to our surprise, ChatGPT was then able to extend this result to the full spectrum by pushing the parameters of the construction further." This completed the disproof of Simon's conjecture in its strongest form: not only can a particle be localized in high-dimensional space under finite-L²-spherical-shell conditions, but a specific, explicit potential achieves this localization at every positive energy level simultaneously.

The authors verified all three steps independently, reconstructed the full mathematical argument from first principles, and take full responsibility for the proofs in the paper. The 35-page manuscript is the human-authored mathematical document; ChatGPT's contributions were the parameter search and the Combes-Hislop identification, neither of which constitutes a proof in itself. The significance is not that the AI proved the theorem—it did not, in the sense that a rigorous proof requires human verification at each step—but that it found the parameter regime and the mathematical technique that made the proof possible, in a context where human expert intuition had been pointing in a different direction.

The Proof Abundance Era and Who Earns Credit

These three stories share a structural feature that the founding statement of the AHM identifies, though does not name this way. For most of the history of mathematics, the ability to solve a problem and the ability to understand the solution were inseparable. Reaching the top of the mountain meant understanding every step of the climb; priority—the traditional currency of mathematical credit—was the same as comprehension. The structure of incentives and the structure of understanding were aligned.

They are no longer aligned in the same way. An agent system can produce a formally verified mathematical result without any of the participants understanding why the result is true in the way a mathematician understands a theorem she proved herself. The Lean kernel can confirm that the proof steps are valid without anyone having internalized the mathematical idea. ChatGPT can identify the Combes-Hislop criterion as useful without being able to explain why the spectral averaging argument works, in the sense that a functional analyst could explain it.

This creates a new kind of labor division. Machines arrive first and produce formally correct outputs; humans arrive afterward and produce mathematical understanding. Under the old model, these activities were the same. Under the new model, they are distinct, performed by different actors, and valued differently by institutions that have not yet updated their credit-attribution frameworks.

The AHM's boycott is essentially a labor action against that asymmetry: a refusal to provide the understanding layer for free while the compute layer captures the priority claim. The oai-math-revised project is a different response to the same asymmetry: build community-owned infrastructure to host the understanding layer, rather than donating it to the compute layer's owners. ChatGPT's role in the Barry Simon disproof is evidence that the question cannot be resolved by withdrawal—the mathematical problems on the AHM's members' whiteboards are the same ones the AI systems are now finding parameter regimes to solve.

The AGMAI—the Advisory Group on Mathematics and AI, an IAS-linked panel that includes several of the same researchers associated with the AHM—issued guidelines on September 29 that begin to formalize these norms. The guidelines recommended that mathematicians stop using proprietary commercial AI systems as testing grounds for unpublished problems, partly to avoid the training-data loop that Skip Tich identified in Tao's comment section, and partly to preserve the community's ability to control when and how its unpublished work enters AI pipelines. How many researchers are following those guidelines in practice is unknown; that Tao submitted corrections to oai-math-revised—a public repository—suggests that community engagement with AI-generated work continues regardless of the advisory framework.

What remains uncertain is whether the field's evaluation systems can adapt faster than the technology advances. Peer review, tenure cases, prize committees, and funding agencies have always looked, implicitly, for evidence that a candidate understands the mathematics they claim to have produced. If that evidence is now separate from the event of production, the credentialing machinery of mathematics needs to update what it is looking for—and what it is rewarding. The AHM's formation, Tao's pull requests, and arXiv:2610.31637 are all, at bottom, competing proposals for what that update should look like.