- Prize
- Event

# Establishment of International Award for IUT Theory and First IUGC Conference on IUT Theory

On July 7, 2023, the Preparatory Association of The Nippon Foundation and DWANGO Educational Institute (Representative Director: Shinichi Yamanaka) reported the following at the Inter-universal Geometry Center (IUGC, Director: Fumiharu Kato) of ZEN University (provisional name) (currently under planning for establishment), which was established on June 6, 2023, to promote and develop the Inter-universal Teichmüller Theory (IUT Theory) by Professor Shinichi Mochizuki of the Research Institute for Mathematical Science, Kyoto University.

- The IUT Innovator Prize will be awarded annually within a scope from $20,000 to $100,000 to the best paper containing new and important developments in IUT theory and related fields.
- Next year in April 2024, the first IUGC conference will be held in Tokyo, gathering researchers in IUT theory and related fields.

Nobuo Kawakami (founder of Dwango Co., Ltd.) will provide the prize money for the IUT Innovator Prize to IUGC, as well as create the following award as an individual:

- The IUT Challenger Prize of $1,000,000 will be awarded to the first mathematician to write a paper on the IUT theory that shows an inherent flaw in the theory.

**■ About the IUT Innovator Prize and IUT Challenger Prize**

**＜Background of the prizes＞**

The IUT theory, officially called the Inter-universal Teichmüller Theory, was published on the Internet in 2012 by Professor Shinichi Mochizuki of the Institute for Mathematical Analysis, Kyoto University. Since its publication, the IUT theory has caused a great deal of discussion in the mathematical community because it solves the abc conjecture, which is said to be “the most difficult of all unsolved problems" in the field of mathematical theory that deals with integers. The paper was published in 2021 in a peer-reviewed journal (PRIMS, an international journal edited by the Research Institute for Mathematical Science, Kyoto University).

On the other hand, the IUT theory has been the subject of a very unusual amount of confusion in the mathematical community, with some mathematicians skeptical about the correctness of the theory, while there has been no mathematical debate about whether or not it is correct.

Despite the importance of the theory, one of the main reasons for this situation is that Professor Mochizuki's theory is not only huge but also highly original, and understanding the claims of the IUT theory requires a great deal of time and effort, even for a superlative mathematician.

We are pleased to announce the establishment of the above prizes to reward mathematicians who are committed to the IUT theory, even if only to a small extent. We hope that this endeavor will encourage more mathematicians to study the IUT theory.

**＜How the IUT Innovator Prize will be judged＞**

The IUT Innovator Prize will be awarded annually for 10 years starting in 2024 to a paper that contains a new and important development in the IUT theory and related fields.

The prize will be awarded to a paper that has been submitted to a mathematical journal and contains a new version or application of the IUT theory, a new analysis of the logical structure of the theory, or an important contribution to a closely related field.

The amount of the prize money will be determined according to the novelty of the paper and the importance of the contribution.

The papers will be evaluated by a panel of experts in the IUT theory appointed by IUGC in a closed review process independent of peer review in the journal to which the paper is submitted. The evaluation results will be determined and announced by IUGC.

**＜How the IUT Challenger Prize will be judged＞**

The judging will be conducted by Nobuo Kawakami on his own initiative.

The method of judging will not be made public, but the papers to be judged must be peer-reviewed and published in a mathematical journal that is covered by MathSciNet and has published at least 10 papers on arithmetic geometry in the past 10 years.

**■ About the 1st IUGC Conference**

The IUGC Conference aims to bring together leading mathematicians in IUT to present and discuss their latest research results. The first IUGC conference is scheduled to be held in April 2024, and invitations will be sent out this month to important mathematicians involved in the IUT theory, including Professor Shinichi Mochizuki, the founder of the IUT theory, and mathematicians working in related fields.

The conference will be held in Tokyo, but will be broadcast worldwide via the Internet.

The first winner of the IUT Innovator Prize will also be announced at the conference.

Please refer to the IUGC web page(https://zen-univ.jp/iugc) for more detailed information, which will be updated as needed.

**■ Comments from the people involved**

**Fumiharu Kato** (Director of IUGC, Professor Emeritus of the Tokyo Institute of Technology)

IUGC is a new institute for mathematics with the mission of conducting various activities to promote the dissemination and development of the IUT theory. We hope to sponsor and support a variety of activities from the viewpoint of promoting research not only in the IUT theory itself but also in related fields such as anabelian geometry, as well as career development of researchers and feedback from society. IUGC believes that the creation of the award and the holding of the international conference will contribute effectively to

- encouraging the development and promotion of the IUT theory, especially the participation of the younger generation, and
- encouraging the global mathematical community to engage in a sound discussion of the IUT theory in a mathematically precise and well-defined form.

** **

**Ivan Fesenko **(Deputy Director of IUGC, Professor and Visiting Professor of University of Warwick and Tsinghua University)

In the last 11 years, the IUT theory has been studied by many, thoroughly tested, and discussed and explained in several international workshops, and no mathematical paper has yet been published that proves any substantial flaw in the IUT theory. It is the standard rule in the mathematical world that new theories are evaluated by experts in the field. In the case of the IUT theory, its main prerequisite is the field of anabelian geometry, in which Japanese mathematicians are world leaders. It was therefore most appropriate that the IUT papers were refereed and published in the Japanese mathematical journal PRIMS. Some confusion about the IUT theory exists among a few mathematicians who do not have research experience in anabelian geometry. Making public statements about alleged faults in IUT without providing mathematical evidence of them is a violation of Article 6 of the EMS Code of Practice (https://euromathsoc.org/code-of-practice). The new announced prizes will inspire mathematicians to study the IUT theory and develop it further.

** **

**Kawakami Nobuo **(founder of Dwango Co., Ltd.)

It is a common phenomenon in politics and society that things that are supposed to be true or false continue to be debated without ever being settled.

However, I am honored to have witnessed, as a witness of history, a rare case in which the same thing is happening in mathematics, where such a thing should not happen.

In my opinion, the root of the problem is that the cost of learning to argue the correctness of the IUT theory has become too high, even for superlative mathematicians.

It is my hope that the modest reward I am offering will help to increase the number of mathematicians who decide to become involved in the IUT theory.

As for the IUT Challenger Prize, I have decided to make it my personal prize. I will decide who to give it to. Of course, I am not a mathematician, so I am not competent to judge the correctness or incorrectness of the arguments. My hope is that the IUT theory, if it is wrong, will be settled in the mathematical community under a sound mathematical debate.

**Reference**

・IUGC： https://zen-univ.jp/iugc

・ ZEN University (provisional name) (currently under planning for establishment)： https://zen-univ.jp/

**【For inquiries】 ****IUGC Press officer ／ Preparatory Association of The Nippon Foundation and DWANGO Educational Institute**：

Toshihiko Nakazawa, E-mail： iugc@zen-univ.jp