![basic number theory outcome basic number theory outcome](https://i.ytimg.com/vi/QDiWmCjwnvs/maxresdefault.jpg)
The saga began when Mochizuki, a respected number theorist quietly posted his preprints on 30 August 2012-not on, mathematicians’ preferred repository, but on his own webpage at RIMS. The conjecture roughly states that if a lot of small primes divide two numbers a and b, then only a few, large ones divide their sum, c.Ī proof, if confirmed, could change the face of number theory, by, for example, providing a novel approach to proving Fermat’s last theorem, the legendary problem formulated by Pierre de Fermat in 1637 and solved only in 1995. Any integer can be factored into prime numbers, its ‘divisors’: for example, 60 = 5 x 3 x 2 x 2. The ‘ abc conjecture’, the problem Mochizuki claims to have solved, expresses a profound link between the addition and multiplication of integer numbers. Another mathematician, Edward Frenkel of the University of California, Berkeley, says, “I will withhold my judgment on the publication of this work until it actually happens, as new information might emerge.” Unsolved problem
![basic number theory outcome basic number theory outcome](https://0.academia-photos.com/attachment_thumbnails/32454231/mini_magick20190420-360-lx9oh3.png)
“I think it is safe to say that there has not been much change in the community opinion since 2018,” says Kiran Kedlaya, a number theorist at the University of California, San Diego, who was among the experts who put considerable effort over several years trying to verify the proof. The latest announcement seems unlikely to move many researchers over to Mochizuki’s camp. Then, in 2018, two highly respected mathematicians said they were confident that they had found a flaw in Mochizuki’s proof-something many saw as death blow to his claims.
![basic number theory outcome basic number theory outcome](https://static.docsity.com/documents_first_pages/2009/03/12/bf0bcb6e6909aa36e613b946dd2eb9d3.png)
The work baffled mathematicians, who spent years trying to understand it. Mochizuki, who has denied requests for interviews over the years, did not appear and did not make himself available to reporters.Įight years ago, Mochizuki posted four massive papers online, claiming to have solved the abc conjecture. When asked how Mochizuki reacted to news of the paper’s acceptance, Kashiwara said, “I think he was relieved.” The paper “will have a big impact”, said Kashiwara. Two other RIMS mathematicians, Masaki Kashiwara and Akio Tamagawa, announced in Japanese the publication at a 3 April press conference in Kyoto. His 600-page proof of the abc conjecture, one of the biggest open problems in number theory, has been accepted for publication.Īcceptance of the work in Publications of the Research Institute for Mathematical Sciences (RIMS)-a journal of which Mochizuki is chief editor, published by the institute where he works at Kyoto University-is the latest development in a long and acrimonious controversy over the mathematicians’ proof. After an eight-year struggle, embattled Japanese mathematician Shinichi Mochizuki has finally received some validation.