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A Message from the President: AI and Mathematics — New Possibilities and Challenges

In recent years, artificial intelligence (AI) has advanced rapidly and is having a profound impact on society. Mathematics is no exception. Recently, an AI-assisted argument has been presented claiming that solutions to the Navier–Stokes equations can develop singularities in finite time, even under smooth external forcing. This concerns the Navier–Stokes existence and smoothness problem, one of the Millennium Prize Problems. On October 6, 2026, OpenAI also released numerous mathematical manuscripts, including work on unsolved problems. Although the validity and mathematical significance of these results remain to be evaluated, these developments suggest that AI is bringing major changes to mathematical research.

Mathematics advances through solving problems, discovering new structures, and developing theories. These achievements give rise to new questions and theories, deepen existing theories, and sometimes lead beyond established frameworks. This process will continue even as AI changes the way mathematical research is conducted. AI can serve as a new tool supporting this process.

As AI develops, the roles of mathematicians may also evolve. Identifying important questions, understanding the significance of mathematical results, formulating new problems and developing new theories, and connecting mathematics with other disciplines and societal challenges will become increasingly important. We also expect new opportunities to apply mathematical knowledge and ways of thinking across a wide range of fields.

At the same time, the use of AI raises important challenges. We believe that it remains important to uphold academic integrity, maintain the reliability of mathematical research, and value deep mathematical understanding by researchers themselves. Mathematical claims and proofs presented by AI are not necessarily correct and require careful verification. In research involving AI, it is also important to ensure transparency and the possibility of independent verification, to properly acknowledge and cite previous work, and to clarify contributions and responsibilities. These principles should guide further discussions on the disclosure of AI use, copyright, and research ethics.

Mathematics education presents another important challenge: how to make effective use of AI while fostering independent thinking. This is particularly important in graduate education and the training of young researchers. We should continue to emphasize deep mathematical understanding, the ability to formulate questions independently, and learning through trial and error, while taking advantage of the new possibilities offered by AI.

We believe that it is important to share these fundamental principles and continue discussions on AI and mathematics, drawing on a wide range of experiences and perspectives from research, education, publishing, and other areas.

We hope that the appropriate use of AI, combined with human mathematical thinking and creativity, will further enrich mathematics and expand the applications of mathematical knowledge and ideas across a wide range of fields.

October 16, 2026

ISHIGE Kazuhiro
President, Mathematical Society of Japan