So for years, like all of you, I’ve been idly wondering if it’s true that For every ε > 0, there are only finitely many triples of coprime positive integers a + b = c such that c > d1+ε, where d denotes the product of the distinct prime factors of abc. I figure that’s a question that occurs to everyone in the small hours of the morning, now and again. Once, when I was stuck in the métro during a wildcat strike, I reckoned I’d figured out a marvellous little proof. But I scribbled it down on the back of a pack of Gitanes, shoved it into the Pile of Papers, and never found it again.

Anyway, in 2012, Shinichi Mochizuki had one of those restless nights, then quietly posted 2,000 pages of scribblings on his website:

In them, Mochizuki claimed to have solved the abc conjecture, a 27-year-old problem in number theory that no other mathematician had even come close to solving. If his proof was correct, it would be one of the most astounding achievements of mathematics this century and would completely revolutionize the study of equations with whole numbers.

But the thing is, like everyone else, I couldn’t make heads or tails of it. So I didn’t know whether to envision Mochizuki as one of the great geniuses in the history of mathematics or as a complete fraud and a lunatic (not that these categories are necessarily mutually exclusive).

The curious part is that it’s now late 2015 — and still, apparently, no one knows:

… Probably the first person to notice the papers was Akio Tamagawa, a colleague of Mochizuki’s at RIMS. He, like other researchers, knew that Mochizuki had been working on the conjecture for years and had been finalizing his work. That same day, Tamagawa e-mailed the news to one of his collaborators, number theorist Ivan Fesenko of the University of Nottingham, UK. Fesenko immediately downloaded the papers and started to read. But he soon became “bewildered”, he says. “It was impossible to understand them.”

Mochizuki speaks fluent English, but declines all invitations to discuss his work in English. He won’t speak to journalists. He’s generally described as surprisingly “articulate and friendly,” but I figure the suppressed qualifier is “for a mathematician.” So that’s probably code for, “at least his fingernails don’t look like Grisha Perelmen’s.”

Mochizuki has replied to e-mails from other mathematicians and been forthcoming to colleagues who have visited him, but his only public input has been sporadic posts on his website. In December 2014, he wrote that to understand his work, there was a “need for researchers to deactivate the thought patterns that they have installed in their brains and taken for granted for so many years.”

To mathematician Lieven Le Bruyn of the University of Antwerp in Belgium, Mochizuki’s attitude sounds defiant. “Is it just me,” he wrote on his blog earlier this year, “or is Mochizuki really sticking up his middle finger to the mathematical community?”

Recently, a few mathematicians have finished reading his proof — and they claim it’s solid. Fesenko finally got through it: “Fesenko has studied Mochizuki’s work in detail over the past year, visited him at RIMS again in the autumn of 2014 and says that he has now verified the proof … ‘We had mathematics before Mochizuki’s work — and now we have mathematics after Mochizuki’s work, Fesenko says.”

But here’s the really weird part:

… so far, the few who have understood the work have struggled to explain it to anyone else. “Everybody who I’m aware of who’s come close to this stuff is quite reasonable, but afterwards they become incapable of communicating it,” says one mathematician who did not want his name to be mentioned. The situation, he says, reminds him of the Monty Python skit about a writer who jots down the world’s funniest joke. Anyone who reads it dies from laughing and can never relate it to anyone else.

Mochizuki wrote a progress report last year. He notes, in a more-in-sorrow-than-in-anger tone, that “the most essential stumbling block” to appreciating his work

lies not so much in the need for the acquisition of new knowledge, but rather in the need for researchers (i.e., who encounter substantial difficulties in their study of IUTeich and related topics) to … start afresh, that is to say, to revert to a mindset that relies only on primitive logical reasoning, in the style of a student or a novice to a subject.

He hints in the paper that if you merely study it haphazardly, you’ll never be able to understand it. As his collaborator puts it,

… if you attempt to study IUTeich by skimming corners and “occasionally nibbling” on various portions of the theory, then you will not be able to understand the theory even in 10 years; on the other hand, if you study the theory systematically from the beginning, then you should be able to understand it in roughly half a year.

Roughly half a year? What do you think? Worth the investment? It’s at least plausible that this is one of the century’s great intellectual achievements, right? Six months — that’s not such a huge investment. I’ve spent longer waiting for a guy to call me back.

What about you? If you could take six months to do anything in the world you wanted to do, would you consider devoting the next six months to seeing whether this was worth reading?

Doesn’t it make you curious?