The IMU’s Leiden Declaration: AI’s Growing Threats and Opportunities for Mathematics

Background

On June 2, 2026 the International Mathematical Union (IMU) released the "Leiden Declaration on Artificial Intelligence and Mathematics," signed by 16 mathematicians from 15 universities and supported by over 130 scholars.

Earlier, OpenAI announced that its general‑reasoning model independently disproved Erdős’s "plane unit distance conjecture," an 80‑year‑old open problem, without human‑provided hints and by linking the problem to algebraic number theory—a milestone described by Fields Medalist Timothy Gowers as "AI mathematics milestone." Two days later DeepMind reported solving nine Erdős problems, and a team from Peking University solved the Anderson conjecture in exchange algebra, formally verified in Lean 4.

Declaration Content

The declaration first lists five core values of mathematics:

Proof is the foundation of mathematics, providing the highest certainty.

Results belong to specific authors, who are responsible for correctness.

Mathematical arguments should be transparent and independently verifiable without proprietary knowledge.

The community must assess research by depth, difficulty, and value.

Autonomous choice of research directions sustains the discipline’s long‑term vitality.

It then identifies five layers of AI‑related threats:

AI may generate seemingly convincing but subtly erroneous "proofs," pressuring peer‑review processes.

AI models trained on vast corpora often fail to correctly cite the human work they synthesize, raising copyright concerns.

Unequal access to AI tools could create new academic inequities, privileging those with compute resources.

Increasingly, results are announced via press releases and blogs rather than peer‑reviewed journals, exemplified by AlphaProof’s publicized solutions to International Mathematical Olympiad problems, which can overstate AI contributions and obscure prior human work.

The declaration warns that AI companies are attracted to mathematics because formal proofs provide an almost unlimited feedback source for training, a hypothesis still unverified; some resulting general models are already commercialized for ethically sensitive applications such as warfare, oppression, mass surveillance, and democratic erosion.

What the Declaration Does Not Say

It does not call for banning AI in mathematics; instead it urges clear community norms, disclosure of AI usage, rigorous review, and honest attribution.

It does not deny AI’s achievements; the preface acknowledges that recent AI advances may mark a significant new chapter in the discipline.

It does not claim to represent all mathematicians. While Fields Medalist Peter Scholze publicly supports the declaration, emphasizing human‑centered understanding of mathematics, other mathematicians view the document as overly cautious and lacking foresight.

New Challenges

Reliability of proofs —Mathematics relies on proofs that anyone can verify, yet AI‑generated proofs erode this guarantee. A 1,000‑step proof with a subtle error at step 573 may require highly specialized expertise to detect, raising questions about the net value of such proofs.

The declaration notes that integrating AI‑generated proofs into existing argumentation, presentation, and verification pipelines is difficult, whether the proofs are informal or formal.

Attribution complexity —Mathematical knowledge builds cumulatively over decades. Traditional citation practices underpin intellectual credit and legal rights. AI models, trained on massive literature, produce outputs without following citation norms, creating both copyright and fundamental "who contributed what" dilemmas. The declaration asserts that responsibility does not disappear with AI involvement; human authors must remain fully accountable and provide detailed acknowledgments.

Mathematics as an AI testbed —AI companies heavily invest in mathematics because provable statements can be automatically verified, offering an ideal substrate for training general reasoning. This creates a structural shift: research priorities may be driven by algorithmic feasibility rather than mathematicians’ judgment, threatening the discipline’s autonomy.

Understanding the Declaration’s Position

The declaration can consolidate consensus, highlight concerns, and guide individual and institutional behavior, but it cannot dictate technological trajectories or bind those who ignore it.

It serves as a starting point for broader discussion, with the IMU planning further debate at the International Congress of Mathematicians (ICM 2026) in Philadelphia.

Historically, mathematics has weathered multiple tool‑driven transformations—from the advent of computers to the computer‑assisted proof of the Four‑Color Theorem—without being extinguished, yet each shift left lasting controversy. The current wave is faster, larger, and backed by substantial commercial interests, making the declaration’s call for careful scholarly attention especially significant.