AmiMoJo shares a report from Nature: After an eight-year struggle, embattled Japanese mathematician Shinichi Mochizuki has finally received some validation. His 600-page proof of the abc conjecture, one of the biggest open problems in number theory, has been accepted for publication. Acceptance 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 mathematicians’ proof. Mochizuki is chief editor but was not involved in the review. Eight years ago, Mochizuki posted four massive papers online, claiming to have solved the abc conjecture. The work baffled mathematicians, who spent years trying to understand it. 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. The “abc conjecture,” the problem Mochizuki claims to have solved, expresses a profound link between the addition and multiplication of integer numbers. Any integer can be factored into prime numbers, its ‘divisors’: for example, 60 = 5 x 3 x 2 x 2. 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. A 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. Some experts say Mochizuki failed to fix the fatal flaw in the solution. “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. 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.”

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