ZEN Mathematics Center

About ZMC

ZMC（ZEN Mathematics Center) is an international research institute established with the aim of promoting and developing modern mathematics with a focus on arithmetic geometry and the formalization of modern mathematics using computer languages.

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OUR SCOPE

Arithmetic geometry is a branch of modern mathematics that aims to elucidate various problems in number theory using algebraic geometry methods, and research is being conducted all over the world. Among them, Japan’s research in the field of so-called “anabelian geometry,” including algorithmic anabelian geometry, is world leading. Generally speaking, progress in modern mathematics is speeding up, not slowing down. It is becoming more difficult for mathematicians to follow new important papers and results. On the other hand, in recent years, research on proof-supporting systems using computer languages has progressed, and in fact, some modern mathematical theories, including theorems in arithmetic geometry, have been “formalized.” The formalization of mathematical theories here means rewriting theorems and their proofs into computer programs. This is an example of synergy between modern mathematics and computer science. The relationship between artificial intelligence (AI) and mathematics is also an important topic in modern society. In light of this situation, we would like to create a new relationship between modern society and mathematics through the activities that promote modern mathematics, such as arithmetic geometry represented by anabelian geometry, and its formalization.We would also like to provide support to young researchers around the world who are aiming to work in modern mathematics and related fields.

MESSAGE

ZMC Director Kato Fumiharu

In the 21st century, is modern mathematics not entering a transitional period? And is it not only professional mathematicians who will lead us to what the future should be, but also all the people living in modern society?
Traditional modern mathematics has been driven by the daily research of professional mathematicians. In each of these specialized fields, extremely advanced specialized research has been conducted. Even now, research is progressing rapidly. At the same time, computer science has advanced to a high level in modern times, and the relationship with pure modern mathematics has gradually expanded. Not only that, but recent research in artificial intelligence (AI) is increasingly becoming a driving force in connecting modern mathematics to society.
It seems to me that this new movement will be the catalyst for modern mathematics to change into a newer discipline. I think that modern mathematics will be closely linked to fields that are originally close to mathematics but have not been involved in the study of modern mathematics in the past, such as computer science, deep neural networks, and large language models.
The impact of artificial intelligence on modern mathematics is even greater. For example, there is a problem of what it means for mathematicians to “understand” something that is difficult to understand in detail with conventional mathematical methods, such as deep learning. Serious thinking about this problem may have the power to change mathematics from its fundamental foundations. In addition, through AI, mathematics will become increasingly interactive with various aspects of modern society.
The goal of promoting modern mathematics and related fields suggests an important point not only in terms of research promotion, but also in terms of the state of theoretical research in modern society. The ZMC will host and support a variety of activities from the perspective of disseminating theoretical research to society and providing feedback to researchers to develop their careers and give back to society.