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Conferences were held on the subject in subsequent years, and participants reported partial progress but said it would probably take many years to come to a conclusion. Although, at the time, some of his close collaborators said they found the proof to be correct, experts around the world struggled, often reluctantly, to slog through it, let alone verify it. Mochizuki has declined all invitations to travel abroad and lecture about his work. Written in an impenetrable, idiosyncratic style, the papers seemed to be built entirely on mathematical concepts that were completely unfamiliar to the rest of the community - “like you might be reading a paper from the future, or from outer space”, wrote Jordan Ellenberg, a number theorist at the University of Wisconsin–Madison, on his blog soon after the papers appeared. 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.
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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 an innovative approach to proving Fermat’s last theorem, the legendary problem formulated by Pierre de Fermat in 1637 and solved only in 1994.
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Any integer can be factored into prime numbers, its ‘divisors’: for example, 60 = 5 x 3 x 2 x 2.
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The abc conjecture 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 judgement on the publication of this work until it actually happens, as new information might emerge.” Unsolved problem “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 had spent considerable effort trying to verify Mochizuki’s claimed 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 a 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 at the press conference, and did not make himself available to reporters.Įight years ago, Mochizuki posted four massive papers online, claiming to have solved the abc conjecture. 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, speaking in Japanese, announced the publication at a press conference in Kyoto on 3 April. The journal, of which Mochizuki is chief editor, is published by Japan’s Research Institute for Mathematical Sciences (RIMS) at Kyoto University, where he works. 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) is the latest development in a long and acrimonious controversy over the mathematician’s proof. Credit: Kyoto UniversityĪfter an eight-year struggle, embattled Japanese mathematician Shinichi Mochizuki has finally received some validation.