La Declaración de Leiden crea un marco normativo para la IA en matemáticas

The International Mathematical Union (IMU) and thousands of mathematicians have endorsed the Leiden Declaration, a new framework aimed at guiding the ethical and transparent use of artificial intelligence (AI) in mathematical research. The declaration was officially introduced at the International Congress of Mathematicians (ICM) in Philadelphia on Sunday. It outlines fundamental recommendations for researchers, institutions, and public authorities regarding AI integration into mathematics. The initiative emerged from a conference held in September 2025, titled Mechanization and Mathematical Research, organized by the Lorentz Centers at Leiden University in the Netherlands. During this gathering, a working group led by Jim Portegies formed, comprising mathematicians from universities in the United Kingdom, the Netherlands, Poland, the United States, and Switzerland. This team developed the Leiden Declaration through collaborative efforts over several months. According to the declaration, mathematicians retain the choice to use AI in their research or not. Regardless of this decision, each researcher bears responsibility for the health and integrity of the discipline. Human involvement remains essential. While humans created the foundational principles upon which AI-based research results rest, they should also claim credit for these outcomes and ensure the accuracy of their work. Moreover, human insight is crucial for posing new questions and defining relevant research problems. The declaration warns that recent advancements in AI pose a threat to mathematical research and its core values. Students and aspiring mathematicians are disproportionately affected, potentially undermining the long-term prospects of the field. AI-generated theses can appear plausible yet remain unreliable, sometimes even false, making them difficult to distinguish from correct mathematical proofs. These outputs often lack proper attribution, endangering the current system of scientific peer review and traditional standards of correctness, transparency, and independent verification of proofs. Media coverage has also been influenced by AI-assisted research findings, often simplifying complex results and emphasizing automated tools excessively. Contributions made by individuals can be overlooked, harming the reputation of mathematics. Additionally, certain mathematical tasks are being used misleadingly as benchmarks for evaluating large reasoning models (LRMs). Major corporations are investing heavily in AI development while simultaneously advancing mathematical research. However, they tend to select research topics based on how well they align with AI capabilities rather than their deeper significance. This trend threatens academic autonomy, especially given shrinking university budgets and reliance on external funding sources. The declaration includes eleven key guidelines for mathematicians: 1. Disclose all tools used in research. 2. Support peer review processes. 3. Adhere to open-science principles. 4. Take responsibility for the accuracy of one’s work. 5. Highlight human authors, not AI. 6. Ensure proper citation practices. 7. Participate in public discourse. 8. Stay informed about emerging technologies. 9. Welcome collaborators from other disciplines. 10. Choose tools thoughtfully. 11. Evaluate the ethical consequences of one's work and take appropriate measures. The final guideline addresses the appeal of lucrative private-sector research contracts. Mathematics underpins many technological developments that ease daily life, but it can also be misused for warfare, oppression, mass surveillance, or undermining democracy. Mathematicians are urged to withdraw from harmful activities. Preventative measures include fostering awareness and promoting responsible research practices.