Artificial intelligence is playing an increasingly visible role in mathematical research: the most advanced models from OpenAI and Anthropic are not only accelerating researchers’ workflows but have also produced independent advances on long-standing problems. OpenAI’s experimental Astra model registered ten advances in mathematics and theoretical computer science, including a counterexample to a conjecture by Alain Connes from the 1980s. Anthropic’s Claude model produced a surprising counterexample to the well-known Jacobi conjecture in algebraic geometry.
François Charles, head of the mathematics department at École Normale Supérieure, says these results are credible: experts have reviewed them, and most have also been checked in the Lean formal proof system. Charles emphasizes that AI does not replace mathematicians, yet it has become an invaluable collaborator: it can autonomously find counterexamples to open conjectures and can be highly effective in interactive use with researchers.
How AI assists mathematics
In practice, AI speeds up research in several ways. Some researchers reach new ideas through dialogue with models — in one case an American researcher arrived at a long-sought counterexample following interaction with ChatGPT. Often the specific solutions proposed by AI contain errors, but they steer human thinking in productive directions. For mathematicians who rely on intuition, AI helps formalize intermediate steps that used to take months or years.
Several factors explain the rapid progress: mathematics is fundamentally text-based and thus well matched to generative language models; the correctness of proofs is objectively verifiable; and mathematical research largely operates within an open science culture, so much of the literature is freely available online. Modern models have also become hybrid systems: they recognize when to call external tools (for example a calculator or web search) and can perform checks on their own output.
Limits and risks
Charles also pointed out current limitations. Models still struggle with continuous, twenty-page arguments, while modern mathematics often involves proofs of a hundred pages or more. Caution is needed regarding citations because AI can obscure or misattribute sources. In education, AI has a dual effect: it can lower students’ reluctance to ask questions and democratize access to advanced mathematical knowledge, but it can also facilitate cheating; mastering mathematical thinking still requires independent work without aids.
Competition and access: European concerns
A major concern is that Europe may fall behind if its researchers cannot access the most advanced AI models. At present, the United States and China develop the leading large language models, and Charles warns that it is possible Washington could at some point restrict access for certain countries — past trade and tariff conflicts show how quickly such decisions can occur. This could open a significant mathematical divide between countries with cutting-edge AI and those without. Charles argues that responses should be coordinated at the European Union level rather than by individual nations.
Ethical and authorship issues
A recent Leiden statement offers guidelines for the ethical use of AI in mathematics, addressing authorship: a machine cannot assume scientific responsibility, but if it made a substantive contribution to a result, that contribution should be acknowledged. The reporting process also reflected AI collaboration: an AI assistant participated in preparing the original article, but the final content was edited and verified by a journalist.
Conclusion
AI-driven, autonomous mathematical results may mark a new phase in scientific research: they accelerate idea generation, help formalize intuition, and assist in verifying proofs. At the same time, technical limits, citation issues, educational challenges, and geopolitical access problems raise important questions. François Charles believes that political and research-policy responses at the European level are needed to address these challenges.
