Community Initiative by Mathematicians Already Endorsed by the International Mathematical Union

Several researchers from Rényi Institute have already signed the Leiden Declaration, whose significance extends well beyond the field of mathematics.

The Leiden Declaration on AI and Mathematics is a statement published in June 2026 that was created by an international group of scholars working on the subject, including not only mathematicians. The consultation process began in Leiden, the Netherlands. The Leiden Declaration outlines the current challenges associated with the use of artificial intelligence for research purposes and also provides guidance for navigating them. Although its recommendations are primarily grounded in mathematical research, it is already clear from the preambulum that the document was not written solely for mathematicians but is also intended for the broader public. Around 60 experts representing ten countries, including not only the public sector but also industry, among them research mathematicians, computer scientists, philosophers, historians, as well as social scientists, consulted regularly over the past eight to nine months and formulated the eleven-page Declaration as a consensus proposal. 

“What emerged was not a compromise but a common-ground position. It is neither a belated reaction nor a cry for help; rather, we intend it as a wake-up call,” Bryna Kra, a professor at Northwestern University, former President of the American Mathematical Society, and a member of the preparatory working group, emphasized in response to a question from renyi.hu. “It is time for mathematicians to begin engaging with these issues, because our field of research is changing rapidly, and if we want to have a say in what it becomes, we cannot remain silent."

"In ten years' time, and probably even in five years, the work of a mathematician will look completely different. It is difficult to predict the exact timeframe, but the change itself is undeniable. We have to decide what we want. Many people are voicing strong opinions, but most of them are not mathematicians; they are primarily representatives of companies that have vested interests. We also have interests, but the mathematical community is not loud and sometimes is not even capable of making its voice heard. One of the Declaration's major achievements is that it represents the collective voice of mathematicians: we must be involved in the decision-making process and in preserving and shaping the values that matter. The Leiden Declaration is the result of an exceptional and broad collaborative effort.” 

Bryna Kra is an American mathematician and professor at Northwestern University. She served as President of the American Mathematical Society from 2023 to 2025. She is a member of the American Academy of Arts and Sciences and the National Academy of Sciences. She earned her PhD at Stanford University and, after holding several postdoctoral positions, joined the faculty of Pennsylvania State University in 2000. In 2004, she joined Northwestern University. From 2009 to 2012, she served as Chair of the Department of Mathematics. Her research focuses on ergodic theory and dynamical systems, with particular emphasis on problems motivated by combinatorics and number theory. She recently visited Hungary to participate in one of Rényi Institute's summer schools as a lecturer. (Photo: Northwestern University)

The Leiden Declaration does not call for rejecting AI. Rather, it urges the mathematical community to consciously preserve those core values that make mathematics a “reliable and valuable” scientific discipline. Its authors do not advocate prohibition, but responsible use.

“The work began last September with an in-person meeting in Leiden,” Professor Bryna Kra recalls. “Alongside active research mathematicians, some of whom use AI and others who do not, we brought together computer scientists, including both theoretical researchers and those who develop and use artificial intelligence, as well as historians of mathematics and philosophers. We called the meeting Mechanization of Mathematics. It was not organized like a typical scientific conference, where there are lectures followed by questions and informal discussions during the breaks. Instead, after short presentations, there were numerous breakout sessions and working groups devoted to discussing specific topics. The working groups were highly diverse, including one that focused on policy issues. It was there that the idea of the Declaration first emerged.
"At first, we envisioned only a short document of no more than two pages. But over the following eight months we met regularly online, and the initial idea evolved considerably as we continuously sought consensus."

"Looking back, I still believe that what emerged was not a compromise but a consensus document. Some of the discussions were difficult, and what we ultimately produced is the result of genuine collaboration and agreement on the most important points. It is a much better document than it would have been if any one of us had written it alone. Different perspectives clashed over what was important to include and why. But every single point was preceded by deep and detailed discussion.”

The Declaration identifies as the characteristic values of mathematical research the primacy of proof and understanding, arguing that a mathematical proof demonstrates not only that something is true, but also why it is true. This, in turn, supports the scientific integrity of mathematics. Equally central to the document is the connection between authorship and responsibility: results are attributable to specific authors who take credit for their discovery and assume responsibility for their correctness. These principles ground the merit-based standards to which we aspire in mathematical research. Finally, transparency and verifiability are also fundamental values, since mathematical arguments are regarded as transparent and subject to independent verification. They may be extremely long or difficult, but in principle no proprietary knowledge or equipment should be required to understand them.

"Mathematics produces not only a body of results, but also understanding, clarity, and judgment among the communities of mathematicians who have shaped them, often in the context of their own autonomously guided research. This expert knowledge is essential, both to effectively use mathematics, and to continue to articulate new and significant research questions. A key source of strength of the discipline has long been the autonomous shaping of the direction of research and the methods used to pursue it," the document states.

According to the authors, recent developments in artificial intelligence threaten each of these values, often in ways that disproportionately affect students and early-career mathematicians, and hence the long term future of the discipline.
 

"The reality is that mathematics has become a target for private companies, which use it to substantiate claims because society pays attention when something is backed by mathematics,” Professor Kra explains. “Moreover, one often reads in the press that mathematical research has reached its end. Nothing could be further from the truth. AI is a new tool that is becoming increasingly widespread, but mathematical research has not come to an end because of it. We need to adapt to this new tool. But mathematics is not over, that is simply a false narrative,” she stresses.

The Leiden Declaration identifies the following as tpotential threats.

(1) Current automated techniques can produce plausible but unreliable (or even incorrect) arguments which are difficult to distinguish from correct mathematical proofs. This applies not only to informal arguments, but also to formalizations, 

(2) Technologies that draw extensively on the published mathematical commons undermine the traditional system of attribution. Models trained on published works frequently return outputs that do not properly cite the human works they synthesize. Many current models are also built on data obtained by systematically exploiting licenses and access arrangements that were not made with artificial intelligence in mind, or indeed by simply violating copyright protections.

(3) Technologies which affect the way in which mathematics is practiced may disturb the current system of incentives. The use of artificial intelligence — and thus also the sort of problems which it can address — may become incentivized for its own sake, disrupting our mechanisms for hiring, funding, and recognition. This disadvantages researchers who do not have access to the technologies or decision-making related to them, or who are unwilling to use technologies controlled by organizations whose values they do not share (such as expensive proprietary AI systems).

(4) Equally concerning is the tendency to overemphasize the significance of automated tools while undervaluing the prior human contributions which made those ttools possible. Increasingly, the successful completion of specific mathematical tasks is presented in a way that not only damages perceptions of mathematics, but also misleadingly uses specific mathematical tasks as metrics for the general reasoning capacities of commercial products.

(5)  The increasing involvement of technology companies in mathematical research raises the risk that research questions may come to be prioritized because of their amenability to automated mathematics, rather than expert judgment of their deeper significance. Indeed, broader understanding of the field may be permanently lost in the process of automation. With university budgets under pressure, this reshaping also changes professional incentives in a manner which encourages the collaboration of researchers with technology companies on asymmetric terms. If left unchecked, these trends go beyond threatening researchers’ autonomy, affecting the scope and depth of mathematical research itself. 

How does the Declaration propose to address these challenges? The document formulates recommendations for individual mathematicians, mathematical organisations and non-profit research funders, policymakers in government and elsewhere as well as for developers of commercial AI systems.  

The ideas above extend far beyond mathematics. They can readily be applied to science as a whole, to education, and even to broader debates about the societal use of artificial intelligence. “I am convinced that many of the observations we have made are equally applicable to other scientific disciplines, and indeed beyond science, to society as a whole,” Professor Kra adds. “We did not address only mathematical research; we also discussed education, research in general, and the use of artificial intelligence in the publication of scientific papers. I believe this document has generated such a strong response precisely because it makes statements that span a very broad spectrum of academic work from teaching and research to the history of mathematics.”

She then poses a question:

„Did we get everything right? Of course not! Will there be a continuation of the document, perhaps even revisions? I certainly hope so. I am travelling around Europe, and what I see in the international mathematical community is that people have genuinely begun discussing the issues raised by the Declaration. Both signatories and readers have told me: ‘Now I'll take this back to my department or my research institute, and we'll discuss what it says and what we should do.’ I consider that a success and a significant impact. We do not all have to agree on every single point. What matters is that people recognise that these issues require attention, and that we mathematicians must take the initiative instead of simply drifting with the current," the professor says.

She illustrates the authors' perspective with two examples. “First, the meaning of being the author of a scientific paper is changing radically. At present, we have one view, many publishers have another, and publishers themselves do not even agree with one another regarding what kinds of AI use should be disclosed and how. What we, as mathematicians, want needs to be communicated to publishers. We need to harmonise our intentions and establish a common understanding of what we consider acceptable.

Second, AI has solved mathematical problems. Genuinely open problems. But it did not solve them independently. It relied on the extraordinarily rich body of mathematical literature, identified novel connections that humans had not previously recognised, and proposed new solutions. However, we must remember that a proof cannot be considered truly interesting if people are unable to understand and explain it. In that case, it is not helpful. This clearly demonstrates that the role of humans is also changing. We will have to take responsibility for providing explanations and for finding new ways to educate future generations. We grew up without these tools, but that is not true of today's high school students. They no longer have the ‘luxury’ of spending long periods wrestling with a problem, because they will always have a system in their pocket ready to answer it for them.”

Professor Bryna Kra also expects that representatives of other academic disciplines will produce similar declarations in their own fields. “I already know of initiatives in the legal profession,” she says. “They are working on something similar because lawyers, too, are being deeply affected by developments related to the use of AI. We are currently living through a period of rapid change, but our task is to adapt and to articulate what we want. This Declaration is an attempt to do exactly that.”

She reiterates that the authors do not expect signatories to agree completely with every word of the document. “We are not trying to persuade anyone to sign it, and there is also an opportunity to provide feedback. Nevertheless, I encourage everyone to sign, because it is extremely important for the mathematical community to develop a common position regarding the use of AI. We know that our interests are not the same as those of large corporations or governments. That is precisely why we need to demonstrate consensus. 

The opinion of Rényi Institute also counts. On the one hand, many international researchers visit the Institute. On the other hand, Rényi Institute is the centre of mathematical research in Hungary. It sets the direction for the next generation of researchers and students. As for my own students in the U.S., they have been incredibly enthusiastic, engaged, and almost touched that their future had actually been taken into consideration: they are the generation that will be most profoundly affected by these developments.” 

Professor Bryna Kra also noted that her working group will meet as early as July at the International Congress of Mathematicians in Philadelphia to discuss the next steps. For the time being, however, they do not expect to revise the text of the Declaration for at least another year. “But given the speed of changes, we simply cannot stop the work or the collective reflection,” she emphasizes.

The central message of the Leiden Declaration is that AI can be a valuable tool in mathematics, but it cannot replace human understanding, responsibility, transparency, or the norms of the scientific community. Mathematics, in the words of the Declaration, remains a human practice.”

The Declaration has already received endorsements from some of the world's largest organisations and most distinguished mathematicians. These include the International Mathematical Union (IMU), the Max Planck Institute for Mathematics, and acclaimed mathematician Terence Tao. (Full list  can be viewed HERE.) The American Mathematical Society (AMS) has also published the Declaration in several venues and will feature it in the September issue of the Notices of the American Mathematical Society. Since its publication, several senior researchers at Rényi Institute, including members of the Hungarian Academy of Sciences and research professors, have signed the Declaration.

This autumn, the Section of Mathematics of the Hungarian Academy of Sciences, Rényi Institute, and János Bolyai Mathematical Society are planning a joint event to discuss, in light of the Leiden Declaration, the guidelines proposed for Hungarian organisations and researchers.