As artificial intelligence (AI) models advance in their ability to solve complex mathematical problems, experts in mathematics have raised alarms about the challenges posed by the increasing integration of AI in the discipline. These challenges include the production of unreliable mathematical proofs, insufficient citation practices, improper information disclosure, and the potential for research bias.

This set of concerns has been articulated in a groundbreaking document known as the ‘Leiden Declaration on Artificial Intelligence and Mathematics,’ crafted by a team of 16 researchers over the past eight months, following a conference at Leiden University in the Netherlands in September 2025. The declaration has garnered support from hundreds of signatories and has received endorsement from the International Mathematical Union.

The document emphasizes that recent advancements in AI jeopardize the fundamental values of mathematical research, often impacting students and early-career mathematicians disproportionately, which could have long-term consequences for the field.

The declaration was released shortly after major technology companies such as OpenAI and Google DeepMind announced breakthroughs in solving longstanding mathematical challenges. OpenAI claimed that its model had successfully disproven a notable geometry conjecture introduced by the renowned mathematician Paul Erdős in 1946. Shortly after, researchers at Google DeepMind stated that their model, AlphaProof Nexus, had resolved nine of the 353 unresolved Erdős problems.

Despite these claims of progress, a growing contingent of mathematicians has expressed skepticism regarding the validity of these AI achievements. Kevin Buzzard, a mathematician at Imperial College London, remarked, “It’s noteworthy that tech companies are suddenly showing interest in mathematical research. The Leiden Declaration serves as a thoughtful response to the current developments as AI continues to transform this area.”

Leslie Ann Goldberg, head of computer science at the University of Oxford, added, “The ease with which inaccurate AI-generated drafts can be produced poses a risk of inundating the literature with erroneous claims. Once misinformation takes root, it may lead to further errors as new findings are built on these flawed foundations.”

Key concerns raised in the Leiden Declaration include:

• Unreliable proofs: The declaration states that AI models can generate convincing yet dubious arguments that are challenging to differentiate from valid mathematical proofs. This situation increases pressure on reviewers and jeopardizes traditional standards of correctness, transparency, and independent verification of proofs.
• Citation issues: The document points out that models trained on existing literature often fail to adequately cite the human sources they draw upon.
• Inequitable access: The use of AI might incentivize its own adoption, disrupting established hiring, funding, and recognition practices, while excluding researchers who lack access or choose not to engage with technologies from organizations misaligned with their values.
• Disclosure shortcomings: Mathematics research is often communicated through informal channels, such as press releases or blogs, without the necessary formal documentation for scientific evaluation, the declaration cautions.
• Threats to autonomy: The declaration highlights concerns that research questions suitable for AI approaches may be prioritized due to increased collaboration with technology firms, undermining the independence of mathematical inquiry during a time of budget constraints in universities.

In response to the AI surge, the Leiden Declaration recommends the following actions for mathematicians:

• Promote transparency: Mathematicians should openly disclose their use of AI tools, maintain accountability for the accuracy of their work, credit human authors appropriately despite challenges in attribution, and prioritize AI tools that align with the values outlined in the declaration.
• Make ethical choices: Mathematicians are urged to consider ethical implications when forming partnerships with tech companies involved in AI development for purposes that could lead to warfare, oppression, mass surveillance, or threats to democracy.
• Establish AI use guidelines: The declaration calls on professional mathematical organizations to create guidelines governing the use of AI and automated tools in publishing and peer review, safeguard authors’ rights through licensing agreements to prevent unauthorized use of their work for training data, and support peer-reviewed processes. It also suggests that organizations be prepared to engage if significant mathematical results are claimed through unconventional means.
• Standardize tech partnerships: While recognizing that the tech industry offers attractive employment opportunities and resources for mathematicians, collaborations must adhere to the principles set forth in the declaration, especially in light of the challenges posed by underfunded higher education and unstable academic job markets.