text: If nobody understands a mathematical proof, does it count? 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 problem gets its name from the simple equation for adding two numbers, a + b = c, but poses deep questions about the true nature of numbers. 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. "It's a bit disappointing that no one has come out and said it's right or wrong," he says. 
   
   Easy as ABC? 
   
   Now Mochizuki has posted a new report describing his efforts to explain his theory to others. He says that three researchers who studied it with his help have yet to find an error, but it will take a few more years for it to be fully confirmed. 
   
   He has also criticised the rest of the community for not studying his work in detail, and says most other mathematicians are "simply not qualified" to issue a definitive statement on the proof unless they start from the very basics of his theory. 
   
   Some mathematicians say Mochizuki must do more to explain his work, like simplifying his notes or lecturing abroad. "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. 
   
   Mochizuki's seeming reticence calls to mind Grigori Perelman, another mathematician who refused to engage with the mathematical community and ultimately turned down a $1 million prize for his solution to a problem called the Poincaré conjecture. "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." 
   
   If you would like to reuse any content from New Scientist, either in print or online, please contact the syndication department first for permission. New Scientist does not own rights to photos, but there are a variety of licensing options available for use of articles and graphics we own the copyright to. ||||| Shinichi Mochizuki of Kyoto University, Japan claims he has proven the ABC conjecture, one of the longest standing mysteries of mathematics. However, even though his 500-page paper was published in 2012, no one has managed to understand it. Mochizuki says his 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 number theory, a smooth number is an integer which factors completely into small prime numbers. 
   
   The beauty of this theory is that it captures the intuitive sense that triples of numbers which satisfy a linear relation, and which are divisible by high perfect powers, are rare. It seems like a bottomless, still lake – it seems very simple, but the more you dive into it, the deeper it gets. In fact, the theory poses some significant questions about the actual nature of numbers, so truly understanding it would be highly significant for mathematics. 
   
   Step in, Mochizuki. In 2012, he published a 500-page paper online that claimed to solve the puzzle. There were two problems however – the first one, that it’s a 500 page paper, and the second (and more important one), that it uses a dense framework of new maths created by him and dubbed “Inter-universal Teichmüller Theory” – a framework that has even experience mathematicians struggling. Inter-universal Teichmüller Theory is basically a whole new way of looking at numbers which he used to prove other conjectures, such as the Szpiro conjecture, and part of the Vojta’s conjecture for the case of hyperbolic curves, as well as Fermat’s Last Theory. 
   
   Mochizuki is a highly-respected mathematician and his work is taken seriously – it’s not like no one has tried to understand his work. It’s just that … no one could. 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. Minhyong Kim of the University of Oxford is one of the many who are still awaiting the verdict in this case. 
   
   Advertisement “It’s a bit disappointing that no one has come out and said it’s right or wrong,” he says. 
   
   The thing is that if you want to understand the proof of this theory, you have to first understand the Inter-universal Teichmüller Theory he developed, and that’s no easy feat in itself. 
   
   “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. 
   
   I’m not exactly sure exactly why Mochizuki chose to work in this complicated way, but hey, if it works, it works. I think the scientific community has a duty to rise up to the event and figure out if this is right or wrong. Sure it’s complicated, but that’s modern math – you’d expect no less. I also believe we’re not going to get any reply from Mochizuki, seeing as he wrote the following: 
   
   “The papers were released in order to make it possible for specialists to study and assess the validity of IUTeich; they were never intended as an announcement to the general public. Moreover, I never envisaged that these papers might elicit reactions consisting of non-mathematical content from non-specialists. I have no intention of responding to such non-mathematical reactions.” 
   
   But until someone figures if Mochizuki is right or wrong, his theories remain in a Schrodinger’s cat like state. 
   
   “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.”
target: – 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.)