Mathematicians Push Back as AI Firms Reshape Their Field

Sixteen mathematicians from fifteen universities published the Leiden Declaration on Artificial Intelligence and Mathematics on June 2, demanding AI companies disclose their methods before claiming another solved proof. The document went live in 2026, endorsed by the International Mathematical Union, and it does not ask anyone to stop using AI.

It asks something narrower and harder to dismiss: that the companies building these tools say plainly how they work, what they were trained on, and where that data goes afterward. Karthik Ganapathy, the Stefan E. Warschawski Postdoctoral Fellow in UC San Diego’s Department of Mathematics and one of the declaration’s authors, frames the danger as one of leverage, not intelligence. Tech companies now have money and reach that individual mathematicians simply do not.

Sixteen Mathematicians Draw a Line at Leiden

The declaration traces back to a workshop called “Mechanization and Mathematical Research,” held at Leiden University’s Lorentz Center in September 2025. Terence Tao, the UCLA mathematician and Fields Medalist, announced the finished document on the social platform Mathstodon, calling it “long-awaited” and noting that it stemmed directly from that gathering.

The text carries the endorsement of the International Mathematical Union and the signatures of sixteen researchers from fifteen universities, including Fields Medal recipient Peter Scholze, topologist Ulrike Tillmann, logician Kevin Buzzard and computer scientist Scott Aaronson. Rodrigo Ochigame and David Holmes, the Leiden University researchers who helped draft the text, described a long negotiation among people who do not always agree. “We worked on the declaration for several months, bringing together different points of view in search of shared principles,” they said, according to Leiden University’s own announcement.

The full text remains open for mathematicians to add their names, and the list has kept growing since launch.

The Episode That Made the Warning Concrete

The declaration’s worries about corporate opacity are not abstract. In late 2024, the nonprofit Epoch AI built FrontierMath, a benchmark of unpublished, expert-level problems meant to measure how far AI models had actually come. Contributing mathematicians got paid modestly for their work, and were not clearly told who was funding the project or who would see the results.

OpenAI had quietly funded FrontierMath’s creation and held early access to its problems and solutions. Epoch AI only acknowledged that funding in a later version of its paper, after outside researchers noticed it was missing from the original. Weeks later, OpenAI announced its o3 model had aced a huge share of those same problems, without mentioning its own financial tie to the test it had just topped.

• $300 to $1,000 paid to each mathematician who contributed a FrontierMath problem, with the funding source undisclosed at the time
• November 7, 2024: the first FrontierMath paper posted with no mention of OpenAI’s funding role
• 25%: OpenAI’s o3 score on FrontierMath problems, up from roughly 2% for earlier models

The episode is a preview of the exact scenario the declaration’s authors describe. The mathematicians who wrote FrontierMath’s questions were early-career researchers doing exactly the kind of work universities rarely reward well, a gap that shows up elsewhere too. Recent survey data found that nearly every college senior now uses AI daily, yet only 28% were ever taught how, leaving the next generation of researchers no better equipped to negotiate with the companies building these tools than the contributors were.

The Power Imbalance Behind the Declaration

Ganapathy describes mathematics as a deliberative field, where research directions emerge from years of thought passed between generations of specialists within tight subcommunities. He calls that process the hallmark of basic research itself.

That slower culture now sits next to an industry that moves on a different clock. Ganapathy told UC San Diego Today that growing corporate involvement creates “a stark imbalance of power between these companies and the mathematical community,” a gap he says directly challenges the discipline’s autonomy.

Underfunded universities and precarious academic jobs make corporate labs attractive, Ganapathy said, describing an industry that has “successfully offered intellectually stimulating opportunities” many researchers find hard to turn down. His deeper worry is what that migration does to the questions mathematicians choose to chase in the first place, with research risking prioritization for its “amenability to automated mathematics rather than their deeper intrinsic value.”

The declaration asks for transparency on three specific fronts:

• Methodology – how AI systems actually arrive at the solutions credited to them
• Training data – which published and unpublished mathematical work trained the models
• Data reuse – how that training data and its outputs get used afterward

Ganapathy also points to a separate incentive working against candor: technology firms face constant pressure to outpace competitors, which he says pushes some toward overstating what their products can do and announcing breakthroughs through press releases before independent review. A similar dynamic has already played out in other knowledge industries. Google’s redesigned search results have entrenched its AI lead as publisher traffic sinks, leaving publishers with little say over a platform that now filters their work for readers. Mathematicians are trying to set terms before a comparable dynamic locks in around their own field.

Is AI Replacing Mathematicians Yet?

The clearest answer comes from the mathematician who uses the technology more than almost anyone in the field. Terence Tao, a Leiden Declaration signatory himself, described current models as tireless assistants, useful for scanning known methods, running long routine calculations and connecting a problem to the right literature, not as sources of deep original mathematical ideas.

Tao has called AI “ready for primetime” in mathematics and theoretical physics, and used it in a project on equational theories meant to test whether mathematics could be done experimentally at scale. The project did not produce a flash of machine insight. It showed that a new kind of mathematical process could still turn up genuinely new results.

In March 2026, Tao suggested AI could eventually let mathematicians split their work into specialized roles, but only if proof checking and review keep pace with automated output. Without that, he warned, weak machine-generated claims would simply pile up faster than anyone could check them. Tao posted the finished declaration himself the same day it launched, a detail that undercuts any read of the document as anti-technology.

A Second Leiden Warning, Eleven Years Apart

This is not the first time a document bearing the Leiden name has warned that a new technology risks distorting how science gets judged. In 2015, a team led by Diana Hicks and Paul Wouters, director of the Centre for Science and Technology Studies at Leiden University, published ten principles for judging research by numbers in the journal Nature.

Both documents share the same underlying diagnosis: left alone, a powerful new way of measuring or producing knowledge will crowd out the expert judgment that built the field in the first place. The full text of the earlier document is still posted at leidenmanifesto.org, over a decade after it first ran.

The List Keeps Growing

The declaration carries no legal weight. It cannot stop OpenAI, Google DeepMind or any other company from announcing the next solved problem before mathematicians have reviewed it themselves.

What it offers instead is a public marker, signed by people with enough standing that AI companies cannot easily wave it off: Scholze, Tao, Tillmann, Buzzard, Aaronson and eleven others across fifteen universities, with the list still open. Ganapathy frames the goal in modest terms, as baselines for scientific integrity that mathematicians broadly already agree on, meant to keep research guided by intellectual significance rather than market pressure.

Whether the declaration changes anything now depends on companies the mathematicians who wrote it do not control.

Frequently Asked Questions

Is the Leiden Declaration legally binding on AI companies?

No. It carries no regulatory or legal force of its own. Its authors are counting on professional norms, reputational pressure and the standing of signatories like Scholze and Tao to push AI companies toward more disclosure than they currently offer.

Did OpenAI break any rules by funding the FrontierMath benchmark?

No law was broken. The criticism centered on Epoch AI’s delayed disclosure of OpenAI’s funding and early access to problems, which drew backlash inside the AI research community over transparency norms rather than legality.

Does the Leiden Declaration argue against using AI in mathematics?

No. Commentary around its release specifically noted it is not anti-AI, and several signatories, including Terence Tao, actively use AI tools in their own research every week.

How did mathematicians share values before a written declaration existed?

Informally, according to Tao, who noted that such goals were long “disseminated informally from advisor to student,” along with mechanisms like peer review, rather than through any single written statement.