Leiden Declaration: AI is challenging the core values of mathematics - Leiden University

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In the ‘Leiden Declaration’, an international group of researchers warns that AI is putting fundamental values of the discipline under threat. The rise of AI is forcing mathematics to rethink what makes their field reliable and valuable. This is their proposed way forward.

What happens if a mathematical proof is no longer the work of a human, but of an algorithm that no one fully understands? Who is responsible for errors, and who gets credit for correct results? And how can we tell whether an AI-generated proof is genuinely new, or simply a clever reworking of existing work without proper attribution?

These are no longer hypothetical questions, but real dilemmas mathematicians worldwide are grappling with. That’s why sixteen researchers from fifteen universities have published the Leiden Declaration on Artificial Intelligence and Mathematics: a call to safeguard the core values of mathematics in the age of AI.

From Leiden, Rodrigo Ochigame and David Holmes are involved. ‘We worked on the declaration for several months, bringing together different points of view in search of shared principles. Despite these differences, we reached consensus on the main points,’ says Ochigame, co-organiser of the Lorentz workshop where the idea for the declaration emerged (see below).

The workshop at the Lorentz Center (see the box at the bottom of the page) where the Leiden Declaration emerged. At the center of the front row are Rodrigo Ochigame (left) and Mateja Jamnik (University of Cambridge, right), both co-authors of the Declaration and organisers of the workshop.

Mathematics is rooted in human understanding

Peter Scholze, director of the Max Planck Institute for Mathematics and Fields Medal laureate, calls the Leiden Declaration ‘a wonderful declaration, coming at the right time’. ‘The goal of mathematical research is human understanding of mathematics, so mathematics can only thrive in a community of human researchers. It is crucial to preserve this communal spirit.’

Lack of agreements on responsible use

The Leiden Declaration does not call for AI to be banned from mathematics, but instead urges clear community norms for its use. Researchers already use AI to help write papers, generate proofs, and assist in peer review. According to the authors, the challenge is to ensure that the technology benefits rather than unrecoverably harms the discipline.

The declaration is officially supported by the International Mathematical Union (IMU). Its Vice President Ulrike Tillmann writes: ‘We take the rapid development and impact of AI on our discipline very seriously: It opens new and exciting opportunities, but also raises questions that cannot be left unexamined. By endorsing the declaration, the IMU affirms that the future of mathematical research must be guided by human judgment, fair and transparent practices, and the shared values of the global mathematical community. Mathematics is, and should always remain, a profoundly human endeavour.’

Five threats AI poses to mathematics

The declaration identifies five threats to the mathematical discipline.

1. Unreliable results

Mathematics is built on rigorous proofs that provide clear understanding. However, AI can produce ‘proofs’ that look convincing but contain almost invisible errors.

2. Lack of proper attribution and violation of copyright

AI models often produce results without citing the human work they build on. This raises questions about recognition and intellectual property.

3. Dependence and inequality

There is a risk that mathematicians will soon depend on access to the latest proprietary AI technology and expensive computational resources in order to produce competitive results. This leads to inequality between researchers.

4. Overhyping of results

Press releases and blogs often make AI claims without proper scientific scrutiny. This leads to overestimating AI’s capabilities and underestimating human contributions.

5. Loss of autonomy

When technical feasibility or commercial interests shape research directions, mathematics risks losing autonomy in setting its research agenda.

​​​​​​​What can mathematicians do?

The declaration outlines several responses aimed at reducing these risks. Transparency is central: researchers should clearly disclose which AI tools, prompts, and methods they have used. AI should be treated as a tool rather than an author, with human researchers remaining fully responsible, including for proper attribution.

The authors also encourage mathematicians to engage in the public debate and stay informed about emerging technologies, and to carefully consider the tools they use and their ethical implications.

‘Inaccurate AI-generated drafts are cheap to produce, and there is a risk of cluttering the literature with claimed results that are simply wrong, These errors are then likely to propagate as new results are...