Shinichi Mochizuki

Shinichi Mochizuki (born March 29, 1969) is a Japanese mathematician working in number theory and geometry.

Quotes

• One fundamental and frequently discussed theme in the further development of inter-universal Teichmüller theory is the issue of increasing the number of professional mathematicians who have a solid, technically accurate understanding of the details of inter-universal Teichmüller theory. ... in order to achieve such a solid, technically accurate understanding of the theory, it is necessary to devote a substantial amount of time and effort over a period of roughly half a year to two or three years, depending on various factors. It also requires the participation of professional mathematicians or graduate students who are
  • sufficiently familiar with numerous more classical theories in arithmetic geometry ...
  • sufficiently well motivated and enthusiastic about studying inter-universal Teichmüller theory, and
  • sufficiently mathematically talented, and who have a
  • sufficient amount of time to devote to studying the theory.
  • On the Essential Logical Structure of Inter-universal Teichmüller Theory in Terms of Logical AND “∧”/Logical OR “∨” Relations: Report on the Occasion of the Publication of the Four Main Papers on Inter-universal Teichmüller Theory. Kyoto University (kurims.kyoto-u.ac.jp) (March 2024). (quote from p. 19)

Quotes about Mochizuki

Academic prowess is not the only characteristic that distinguishes Mochizuki among modern mathematicians. One other characteristic is his ability to concentrate on long-term work. He worked on his IUT theory for 20 years. One could see the potential for that in the early 1990s, when Mochizuki was still an undergraduate student at Princeton. Minhyong Kim, one of his colleagues at that time, recalls Mochizuki making his way through the works of the famous Alexander Grothendieck, “Most of us gradually come to understand [Grothendieck’s works] over many years, after dipping into it here and there ... It adds up to thousands and thousands of pages... Mochizuki...just read them from beginning to end sitting at his desk ... He started this process when he was still an undergraduate, and within a few years, he was just completely done.” The Paradox of the Proof. Project Wordsworth.

Another characteristic is his perfect knowledge of two different cultures, North American and Japanese, and their intricate influence on his mathematical work. Ivan Fesenko writes, "When the language (in this case English) used in a text written to describe a very complex theory (IUT) arises from a substantially different cultural and historical background from that of the author of the theory, the text may be perceived by mathematicians at a substantial cultural distance from the author in the following way: the text may appear rather foreign and psychologically impenetrable, even if it is free of flaws. Moreover, somewhat paradoxically, the lack of technical linguistic flaws may even make the text feel all the more foreign to such mathematicians." Fukugen. Inference:International Review of Science.

There are various versions of the abc conjecture. The strongest among them have the effect of implying proofs of other famous problems, including the famous results of Roth, Baker, Faltings, and Wiles. The current version of IUT does not imply these stronger versions of the abc conjecture, however, there are good perspectives that its refined versions may imply them. Arithmetic deformation theory via arithmetic fundamental groups and nonarchimedean theta functions, notes on the work of Shinichi Mochizuki, Europ. J. Math. 2015.