AI in Mathematical Research Working Group

Objectives

Motivation

The year 2026 has marked a significant turning point in the use of artificial intelligence (AI) in mathematical research. Beginning with solutions to open Erdős problems, we have witnessed major advances in research-level mathematics, including the disproof of the Erdős unit-distance conjecture and an AI-assisted counterexample to the Jacobian conjecture. These developments provide compelling evidence that AI has become a powerful tool for mathematical discovery, reasoning, and formalization of proofs, and its role in mathematical research will continue to grow.

Mathematicians are developing their own ways of incorporating rapidly evolving AI tools into research. By sharing concrete experiences and methods from actual research projects, researchers can learn from one another, develop more effective workflows, and expand the range of problems and techniques they can explore.

At the same time, the growing role of AI raises urgent issues, such as the quality and reliability of AI-generated proofs, transparency and equitable access to powerful AI systems, and potential threats to the sustainability of the research community. The mathematical community should therefore actively discuss not only the effective use of AI, but also its limitations and risks, and develop a shared vision for human–AI collaboration that contributes constructively to mathematical progress.

Scope — What we will and will not do

The main activity of the Working Group will be a seminar held approximately once a month. We will invite researchers from within and outside iTHEMS to share concrete case studies in which AI played a meaningful role in an actual mathematical research project. Rather than presenting only the final results, speakers will be encouraged to explain their research process: what tools they used, how they used them, what worked or did not work, how AI-generated results were verified, and how the use of AI affected the direction or scope of their research. Each seminar will include substantial discussion time to exchange ideas on the presented research, as well as views on opportunities, risks, and the future relationship between AI and mathematics.

The Working Group is not intended as a general seminar series explaining AI technologies or the mechanisms of large language models, unless these are directly relevant to mathematical research.

Expected outcomes

Through these activities, we aim to build a platform where researchers can share practical knowledge, assess new AI tools, and develop new ways of using them in mathematical research. We also hope that the discussions and interactions fostered by the Working Group will lead to new collaborations among participants and invited speakers, potentially resulting in joint research projects, publications, software, or other research outputs related to AI and mathematics.

Beyond mathematics, we expect that the practical methods and research experiences shared in the Working Group will also be valuable to researchers in other fields, and may stimulate broader interdisciplinary collaborations within and beyond iTHEMS.

On the duration of this WG

Given the rapid pace of change in AI and the need to reassess our objectives regularly, the Working Group will initially run until the end of FY 2026, at which point we will review its aims and consider renewal.

Facilitators:

Taketo Sano (RIKEN iTHEMS) – Contact: taketo.sano@riken.jp

Yuya Murakami (RIKEN iTHEMS)

Junnosuke Koizumi (RIKEN iTHEMS)