Shinichi Mochizuki of Kyoto University, Japan, has tried to prove the ABC conjecture, a long-standing pure maths problem, but now says fellow mathematicians are failing to get to grips with his work. The ABC conjecture is deceptively complicated. It roughly states that three numbers a, b and c, which have no common factor and satisfy a + b = c cannot be too smooth (more detailed explanation here). In 2012 Mochizuki posted a 500-page paper online that claimed to solve the puzzle, but it required a dense framework of new maths dubbed "Inter-universal Teichmüller Theory" that even experienced mathematicians found difficult to follow. Mochizuki is a highly-respected mathematician and his work is taken seriously, says Minhyong Kim of the University of Oxford, but in the years since he posted the proof no one has been able to give a definitive answer on whether it is correct. Now, he has released a report in which he says that mathematicians working with him studying his theory have yet to find a flaw, but he criticized the community, saying that most researchers are “simply not qualified” to issue a definitive statement on the proof because they don’t truly understand his theory – and haven’t tried hard enough. Advertisement “It’s a bit disappointing that no one has come out and said it’s right or wrong,” he says. “I sympathise with his sense of frustration but I also sympathise with other people who don’t understand why he’s not doing things in a more standard way,” says Kim. It isn’t really sustainable for Mochizuki to teach people one-on-one, he adds, and any journal would probably require independent reviewers who have not studied under Mochizuki to verify the proof. “This sense of stubbornness, dignity and pride is a part of what gives him the personality necessary to embark on a project like this,” says Kim. But for now, the proof remains in limbo. “It’s a curious state.”
– A Japanese mathematician swears he's solved one of the biggest problems in the world of math. The problem is, nobody, not even fellow mathematicians of the highest caliber, can understand Shinichi Mochizuki's proof of something called the ABC conjecture, reports New Scientist. It doesn't help that the proof itself is 500 pages long or that Mochizuki developed his own set of mathematical principles called the Inter-Universal Teichmuller Theory that must be mastered first. (Those who don't are "simply not qualified" to weigh in, says Mochizuki.) Mathematicians aren't saying that Mochizuki's resolution of the theory is wrong, but they're not saying it's right, either. As a result, it's been in a kind of math limbo since 2012, despite attempts by the Kyoto University professor as recently as last month to shed light on it. As for the ABC conjecture, it's a longstanding math problem that also happens to be "deceptively complicated," explains ZME Science. "It roughly states that three numbers a, b, and c, which have no common factor and satisfy a + b = c cannot be too smooth. ... In number theory, a smooth number is an integer which factors completely into small prime numbers." Got that? The upshot, according to both sites, is that the theory raises fundamental questions about the "nature of numbers," and thus its proof would be a major milestone. "It's a bit disappointing that no one has come out and said it's right or wrong," says Oxford professor Minhyong Kim. (Elsewhere, a beating seems to have turned this man into a math whiz.)