Cambridge and Oxford Warn: AI Threatens Mathematical Rigor

Mathematicians' Warning on AI

Renowned mathematicians from the universities of Cambridge, Oxford, Columbia, and ETH Zurich have published an eleven-page document highlighting the dangers that artificial intelligence (AI) poses to their field. They warn about the ability of AI systems to produce arguments that resemble mathematical proofs, but whose validity cannot be guaranteed without thorough examination.

Current automated techniques generate arguments that seem credible but lack reliability. These arguments are difficult to distinguish from genuine mathematical proofs, which concerns the signatories of the Leiden Declaration.

AlphaProof and the Lack of Transparency

In July 2024, Google DeepMind announced that AlphaProof had solved three problems at the International Mathematical Olympiad, thereby receiving recognition equivalent to a silver medal. However, the detailed methodology was only made public on November 12, 2025, in the journal Nature, leaving the mathematical community without the necessary information to evaluate these solutions for over a year.

Although mathematicians Tim Gowers and Joseph Myers verified the solutions presented during the competition, this does not replace a comprehensive evaluation of the method used. The Leiden Declaration emphasizes that this practice of announcing results on commercial timelines before the community can weigh in is not limited to Google DeepMind, but affects the entire sector.

Copyright and Citation Issues

The Leiden Declaration also points out that AI models, often trained on mathematical publications, frequently fail to cite the human works they rely on. These models are sometimes built from data obtained through licenses and access agreements that are not suitable for AI, or even in violation of copyright.

In mathematics, it is essential to cite prior works to ensure the verifiability of reasoning. Leslie Ann Goldberg, head of the computer science department at Oxford, signed the Declaration stating that mathematical research almost always relies on previous work. She fears that drafts generated by AI may flood the literature with incorrect results, leading to the spread of errors.

Call for Responsibility from Tech Companies

The signatories of the Declaration urge tech companies not to use mathematical publications as training data without the explicit consent of their authors. The Declaration, developed over eight months by a working group of seventeen members, was initiated during a workshop in September 2025 at the Lorentz Center in Leiden. It remains open for signatures from the mathematical community.