- Prize

# 1st IUT innovator award winning paper decided IUGC (Inter-universal Geometry Center) awarded US$100,000

On April 2, 2024, the Preparatory Association of The Nippon Foundation and DWANGO Educational Institute (Representative Director: Shinichi Yamanaka) reported that 1st IUT innovator award winning paper decided at the Inter-universal Geometry Center (IUGC, Director: Fumiharu Kato) of ZEN University (provisional name, awaiting for establishment approval).

The IUT Innovator Prize aims to encourage the development of researches related to IUT theory and the research activities of the younger generation. The IUT innovator award will be awarded annually to the best paper that includes new and significant developments in the field of IUT theory and its related areas, with prize money ranging from $20,000 to $100,000, starting from 2024 and for a period of 10 years.

After a strict examination by a panel of experts commissioned by the Inter-universal Geometry Center, the first IUT Innovator Award will be awarded to the paper

*“Explicit estimates in inter-universal Teichmüller theory”, *

*by Shinichi Mochizuki, Ivan Fesenko, Yuichiro Hoshi, Arata Minamide, Wojciech Porowski, published in Kodai Math. J. 45 (2022), pp.175-236*

The authors of the paper, Shinichi Mochizuki, Yuichiro Hoshi, Arata Minamide, and Wojciech Porowski of the Institute for Mathematical Sciences, Kyoto University, will receive a prize of US$100,000 (Ivan Fesenko declined to accept the prize money).

Professor Mochizuki and his co-authors hope to donate the prize money to the Research Institute for Mathematical Sciences, Kyoto University, as funds to support research activities related to inter-universal Teichmüller theory and related anabelian geometry.

**About the winning paper:**

The paper contains an enhanced version of the inter-universal Teichmüller (IUT) theory of Shinichi Mochizuki. This stronger version is applied to prove, for the first time in the history of mathematics, several effective abc inequalities with explicitly given constants.

The first application of the established effective abc inequalities is an entirely new proof of one of the most famous results in mathematics: Fermat’s Last Theorem. The proof uses one of the proven effective abc inequalities, a new lower bound on possible positive integer solutions of the Fermat equation, obtained by P. Mihailescu via more classical number theory arguments, and some computer verifications.

In a similar fashion, integer solutions of various types of equations with integer coefficients can be now studied by deriving, using more classical number theory, lower bounds on their possible solutions and then applying the effective abc inequalities, maybe with some computer verifications. This fundamentally changes the area of number theory called Diophantine geometry, the area which has been studied from antiquity.

The authors of the award-winning paper:

Shinichi Mochizuki: Professor, Research Institute for Mathematical Sciences, Kyoto University

Ivan Fesenko: Distinguished Professor, West Lake University (China), Deputy Director of IUGC

Yuichiro Hoshi: Associate Professor, Research Institute for Mathematical Sciences, Kyoto University

Arata Minamide: Special Assistant Professor, Research Institute for Mathematical Sciences, Kyoto University

Wojciech Porowski: Special Assistant Professor, Research Institute for Mathematical Sciences, Kyoto University

**■ About the IUT Innovator Prize and IUT Challenger Prize**IUGC, which was established on June 6, created The IUT Innovator Prize and IUT Challenger Prize 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. And 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.

**＜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 (founder of Dwango Co., Ltd.) 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.

**Reference**・IUGC：

__https://zen-univ.jp/iugc__

・ZEN University (provisional name, awaiting for establishment approval)：

__https://zen-univ.jp/__