Mathematicians’ Leiden Declaration Challenges AI Math Claims

Over 150 mathematicians from institutions in ten countries published the Leiden Declaration on Artificial Intelligence and Mathematics on June 2, 2026, calling on governments to consult working mathematicians when forming policy on AI’s mathematical capabilities and asking them not to rely on company press releases or popular news coverage of results. The 11-page document, endorsed by the International Mathematical Union (IMU), names five concrete threats AI now poses to mathematical research, from unreliable proofs entering peer-reviewed journals to commercial incentives that make academic skepticism financially costly.

Thirteen days separate the declaration’s June 2 publication from OpenAI’s May 20 announcement that its internal model had autonomously cracked an 80-year-old conjecture in discrete geometry. The declaration’s drafting had been underway since September 2025.

A Declaration Eight Months in the Making

The idea emerged at a September 2025 conference at the Lorentz Center in Leiden, where about 60 researchers from ten countries, including mathematicians, computer scientists, philosophers, and historians, spent several days working through what rapid AI development meant for their discipline. Jim Portegies of Eindhoven University of Technology convened a working group of 16 from that cohort. Over the following eight months, in consultation with the wider mathematical community, they produced the text.

• 150+ signatories by June 7, 2026, with the declaration still open for new signatures
• 16 drafters drawn from 15 universities, including Oxford, Cambridge, ETH Zurich, Columbia, and Northwestern
• 60 participants at the founding September 2025 workshop
• Endorsed by the International Mathematical Union, the field’s principal international body

Among the signatories: Fields Medal recipient Peter Scholze of the Max Planck Institute. Ulrike Tillmann, the IMU’s vice president, argued in the accompanying statement that AI “raises questions that cannot be left unexamined.” The IMU’s formal endorsement letter called on the mathematical community to engage with the document’s recommendations. “The future of mathematical research must be guided by human judgment, fair and transparent practices, and the shared values of the global mathematical community,” Tillmann said. The document notes its solidarity with other research and creative professions confronting AI’s impact on attribution and consent, positioning the declaration alongside existing scientific ethics frameworks such as the San Francisco Declaration on Research Assessment.

Five Threats, One Discipline

The declaration identifies five distinct areas where AI threatens the foundations of mathematical practice.

• Unreliable results: Current AI can produce arguments that look like proofs but may contain errors that are hard to detect, putting the peer review system that underpins mathematics’ quality control under increasing pressure.
• Attribution failures: Models trained on published mathematical work frequently generate outputs without citing the human contributions they draw on. Many training datasets were assembled using data obtained in violation of copyright or the access terms under which academic papers were originally shared.
• Incentive distortion: AI use is becoming a metric in hiring and funding decisions, which advantages researchers with access to commercial AI infrastructure and disadvantages those who cannot or will not use tools controlled by companies whose values they don’t share.
• Bypass of peer review: Results announced through press releases and blog posts reach public attention before the mathematical community can evaluate them, letting companies capture the narrative before any accepted process of community evaluation has begun.
• Erosion of autonomy: As technology companies become more involved in funding and directing mathematical research, questions risk being chosen for their amenability to automated methods, with expert judgment about what matters being pushed aside.

The full declaration archived on Zenodo asks individual researchers to disclose AI use in their papers, journals to require that disclosure, institutions to invest in public computational infrastructure independent of private companies, and governments to consult practicing mathematicians rather than company communications when forming AI policy.

The Proof That Preceded the Pushback

OpenAI’s May 20 announcement was different from earlier claims in the space. The company’s internal reasoning model had tackled the planar unit distance problem, a question first posed by Hungarian mathematician Paul Erdős in 1946 that asks how many pairs of points placed in a flat plane can sit exactly one unit apart. For 80 years, mathematicians had broadly assumed that square-grid point arrangements were close to optimal. The model found an entirely new family of constructions, using algebraic number theory and the Golod-Shafarevich framework from class field theory, that beat the grid by a polynomial factor. Will Sawin, a Princeton mathematician, later refined the construction, showing the improvement amounts to at least n to the 1.014 unit-distance pairs for large point sets.

The result came with external scrutiny built in. External mathematicians had been given early access before the announcement; OpenAI published the full proof text, companion remarks, and an edited summary of the model’s reasoning on the same day. Fields Medal winner Tim Gowers called it “a milestone in AI mathematics” in a companion paper by the external review group. Among those who co-authored that paper: Thomas Bloom of the University of Manchester, who maintains the erdosproblems.com database and who, seven months earlier, had publicly called an earlier mathematical claim from the same company “a dramatic misrepresentation.” His endorsement this time was unambiguous.

The approach was also unexpected for mathematical reasons. The unit distance problem sits in discrete geometry; the model found its solution in algebraic number theory, drawing on Golod-Shafarevich theory and infinite class field towers, tools specialists had simply never applied to this problem. Arul Shankar, a number theorist who reviewed the result, wrote that it demonstrates “current AI models go beyond just helpers to human mathematicians,” adding that they appear “capable of having original ingenious ideas.” Google DeepMind published parallel results the following day, solving nine additional Erdős problems using formal Lean proof verification through its AlphaProof Nexus system.

OpenAI’s Earlier Stumble

In October 2025, Kevin Weil, then the company’s vice president for scientific research, posted on X that “GPT-5 found solutions to 10 (!) previously unsolved Erdős problems and made progress on 11 others.” Bloom, who maintains the database the post referenced, responded that this was “a dramatic misrepresentation.” The problems weren’t unsolved in any meaningful mathematical sense; they were listed as “open” on his site only because he personally hadn’t encountered published solutions. GPT-5 had surfaced existing references in the literature, not produced new mathematical results. Yann LeCun mocked the claim publicly; DeepMind’s CEO Demis Hassabis called it “embarrassing.” Weil deleted the post. He left the company in April 2026.

The problem the episode illustrated goes beyond one deleted post. AI companies announce results on product schedules; peer review runs on academic ones. A mathematics journal’s review process can take months; a press release takes an afternoon. When the mathematical community’s eventual assessment is that a claim was wrong or overstated, the correction rarely reaches the same audience the original announcement did.

The conference that gave rise to the Leiden Declaration met in September 2025. Weil’s post went up the following month.

Proofs That Enter the Literature Without an Exit

Mathematical research almost never stands alone. A proof in a journal gets cited, then built on, then built on again; an error that enters without detection can propagate across a whole branch of work over years.

Current automated techniques can produce plausible but unreliable (or even incorrect) arguments which are difficult to distinguish from correct mathematical proofs. This is a serious problem: research in mathematics (and in mathematical disciplines like theoretical Computer Science) almost always builds on previous research, so it is essential for researchers to know that the results in the literature are correct.

Leslie Ann Goldberg, head of computer science at the University of Oxford and a declaration signatory, wrote that in a statement accompanying the publication. The declaration adds a second layer: when AI results travel through press releases rather than journals, the community loses its main mechanism for catching errors before they spread. A proof in a peer-reviewed journal can be challenged, corrected, or retracted; none of those mechanisms apply cleanly to a result that has circulated in news coverage, where by the time any correction arrives, the mistaken version has already shaped what other researchers think is settled.

The declaration targets unexamined AI use specifically. It asks journals to require clear disclosure of when and how AI tools contributed to a result, so readers can assess the provenance of a proof before building on it.

The Funding Trap

The declaration names the funding environment directly. “We recognize that industry has offered lucrative jobs, monetary rewards, computing resources, and intellectually stimulating opportunities that some mathematicians have found attractive,” the document reads. “This has taken place in an era of underfunding of higher education and precarious academic employment.”

The declaration is describing a structural pressure. When the same industry making mathematical breakthrough claims also controls the research positions and computing infrastructure that many academics depend on, the cost of public dissent rises. Policymakers, the document states, should “consult with experts, including mathematicians, in forming policy decisions rather than relying on press releases or popular reporting of mathematical results.”

Rodrigo Ochigame, a Leiden University anthropologist of AI who contributed to drafting the declaration, told Scientific American that “mathematicians who never intended to contribute to AI development are having their work used for this purpose without their consent,” describing the situation as deeply concerning. The declaration’s own language is pointed: it describes training datasets built by “systematically exploiting licenses and access arrangements that were not made with artificial intelligence in mind, or indeed by simply violating copyright protections.” The document asks the technology industry to seek consent before using published mathematical work in AI training and to provide compensation when that consent is granted.

Beyond mathematics, the document raises concerns about AI’s involvement in military programs and mass surveillance, its environmental costs, and its role in undermining democratic processes. The declaration is still open for new signatures at leidendeclaration.ai; by June 7 it had passed 150 signatories, and the count continues to rise.