Any integer can be factored into prime numbers, its вЂdivisorsвЂ™: for example, 60 = 5 x 3 x 2 x 2. The вЂ abcВ conjectureвЂ™, 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, вЂњI will withhold my judgment on the publication of this work until it actually happens, as new information might emerge.вЂќ Unsolved problem вЂњI think it is safe to say that there has not been much change in the community opinion since 2018,вЂќ 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 MochizukiвЂ™s camp.

$basic number theory problems$

Then, in 2018, two highly respected mathematicians said they were confident that they had found a flaw in MochizukiвЂ™s proof-something many saw as death blow to his claims. 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.Д®ight years ago, Mochizuki posted four massive papers online, claiming to have solved the abcВ conjecture. When asked how Mochizuki reacted to news of the paperвЂ™s acceptance, Kashiwara said, вЂњI think he was relieved.вЂќ The paper вЂњwill have a big impactвЂќ, 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.ДЄcceptance of the work in Publications of the Research Institute for Mathematical SciencesВ (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 controversyВ over the mathematiciansвЂ™ proof. After an eight-year struggle, embattled Japanese mathematician Shinichi Mochizuki has finally received some validation.

Basic number theory problems