The following is an article from the Asahi Shimbun when the Mochizuki paper was published in March 2021. The article here does not mention the proof gap significantly. Many of the researchers’ comments are anonymous.
As far as I could find by google news search, other than the Asahi Shimbun, the Yomiuri Shimbun, Kyodo News, and Nikkan Sports reported the publication of Mochizuki’s paper. The Mainichi Shimbun, NHK, and private TV stations did not report it.
Proof of the ABC Conjecture Finally Published: Eight and a Half Years in the Journal of Mathematics
Tetsuya Ishikura, March 5, 2021 8:00 PM
On March 5, a paper by Shinichi Mochizuki, a professor at Kyoto University’s Research Institute for Mathematical Sciences (RIMS), which claims to have proved the ABC conjecture, an extremely difficult mathematical problem, was published after eight and a half years since it was submitted in 2012. The publisher, European Mathematical Society Publishing House, responded to an inquiry from the Asahi Shimbun. The electronic version of the paper was first published as a special issue of PRIMS, an international mathematics journal published by RIMS, and the printed version will be published in a month.
The paper is titled “Inter-Universal Teichmüller Theory”. The paper is 723 pages long in English, so it was decided to use an entire issue of PRIMS, which usually contains five or more papers. The paper is also difficult to understand, and some mathematicians have doubts about the proofs, so RIMS hopes to use the publication as an opportunity to spread the theory.
The ABC conjecture is a fundamental mathematical question about the addition and multiplication of an infinite number of integers: 1, 2, 3, etc. If proven, it will lead to the solution of many unsolved problems. It has been unsolved for about 35 years since it was first announced in 1985.
A bizarre idea that surprised the world
Professor Mochizuki developed a novel idea of manipulating numbers by connecting the worlds (universes) of addition and multiplication in all directions, and spent more than 10 years alone to create the Inter-Universal Teichmüller Theory. When he submitted his paper to PRIMS in 2012 and published it on his website, mathematicians around the world were amazed.
However, the paper was so bizarre and difficult to understand that even mathematicians complained that they couldn’t even understand what they couldn’t understand. The paper was feared to be “a paper from the future”. The verification process took an unusually long seven and a half years, as some prominent mathematicians voiced their doubts, saying, “There is an uncorrectable gap in the way the proof proceeds.”
In April last year, the PRIMS editorial board declared that the “peer review” process to verify the correctness of the papers was over. It had announced that it would proceed with the work for publication. The editorial board revealed that the paper had been substantially revised 10 times for this special issue, explaining that the paper was long and it took a long time to decide on its publication.
The fact that Professor Mochizuki was the editor-in-chief of the editorial board of PRIMS caused the British science journal Nature to report, “We were shocked that a puzzling paper could be officially published, and the claim that the ABC prediction had been solved remains controversial.” The editorial board explained that “Professor Mochizuki was removed from the committee from the beginning.”
“It will take more than 10 years for the mathematical community to recognize it”
A mathematician, whose field is close to Prof. Mochizuki’s, said, “In order for the majority of the mathematical community to accept that the proof is correct, it will be necessary to increase the number of people who understand the paper. It will probably take more than 10 years for that to happen.” Papers explaining the Inter-Universal Teichmüller theory have been published one after another, but it is said that there are still only about 10 people in the world who understand the theory. RIMS plans to promote the theory, and has established a research center headed by Professor Mochizuki, and has begun recruiting researchers and assistant professors.
Professor Mochizuki has already been working on the application of the IUT theory, and published a paper claiming that Fermat’s Last Theorem, which took more than 350 years to solve, can be proved in a different way. Professor Ivan Fesenko of the University of Nottingham in the U.K., a supporter of Mochizuki, said, “The IUT theory will lead to incredible breakthroughs in mathematics in the future.”
Nobushige Kurokawa, professor emeritus of number theory at the Tokyo Institute of Technology, said, “Professor Mochizuki’s theory is not limited to the proof of the ABC conjecture, but may become a powerful weapon that will affect other difficult problems and other fields. Now that his paper has been confirmed, we hope for further progress.”