In 2012, the mathematician Shinichi Mochizuki published four papers on his own website with little fanfare. Together, they totalled more than 500 pages—a hyperdense labyrinth of symbols invoking a brutal new mathematical framework known as inter-universal Teichmüller Theory. Via said framework, Mochizuki claimed to have solved the abc conjecture—a simple-seeming statement about prime numbers that has nonetheless eluded mathematicians since first being proposed in 1985. The catch? No other mathematician could understand the thing. 
 
 Mochizuki had unleashed an impenetrable mathematical hellscape. Understanding it is not simply a matter of being a really great number theorist, one has to become an expert in an entirely new mathematical field as defined in Mochizuki's papers. The only preparation for verifying the new proof is to understand inter-universal Teichmüller Theory, which no one really does. Thus, a paradox is raised: verifying the proof means fully committing to it for years even though it might be wrong. 
 
 
 
 In a verification progress report published in December of 2014, Mochizuki bemoaned: “With the exception of the handful of researchers already involved in the verification activities concerning IUTeich (inter-universal Teichmüller Theory) discussed in the present report, every researcher in arithmetic geometry throughout the world is a complete novice with respect to the mathematics surrounding IUTeich, and hence, in particular, is simply not qualified to issue a definitive (i.e., mathematically meaningful) judgment concerning the validity of IUTeich on the basis of a ‘deep understanding’ arising from his/her previous research achievements.” 
 
 Mathematicians have nonetheless taken up the challenge. At a workshop last week at the University of Kyoto, the normally reclusive Mochizuki presented his work in-person to a gathering of believers, several of whom noted significant progress in untangling the proof. UC San Diego number theorist Kiran Kedlaya at least sees a light at the end of the tunnel, however distant. He told Nature News that we can expect a verification no less than three years from now, but that mathematicians have begun to uncover a general strategy unlying Mochizuki's proof and have isolated passages that seem particularly key. 
 
 Moreover, there are now 10 mathematicians committed to the cause, up from three at the time of a workshop last December at Oxford. 
 
 Skepticism remains, however. “The constructions are generally clear, and many of the arguments could be followed to some extent, but the overarching strategy remains totally elusive for me,” Yale mathematician Vesselin Dimitrov told Nature. “Add to this the heavy, unprecedentedly indigestible notation: these papers are unlike anything that has ever appeared in the mathematical literature.” (Dimitrov, who is a recurring figure in the abc conjecture saga, had previously claimed to have found a contradiction in the proof, but Mochizuki was able to explain it away.) 
 
 
 
 In comments posted to Facebook (via Not Even Wrong), workshop organizer Ivan Fesenko, a mathematician at the University of Nottingham, noted that participants worked hard and kept a friendly atmosphere. At the end, they were "tired but happy." 
 
 Fesenko also lightly chided IUTeich skeptics (of which there are quite a few, including "Mathbabe" Cathy O'Neil), writing, "It is true that people who take relatively negative or sceptical positions towards IUT are often, if not always, the least interested or most reluctant to ask detailed questions. Ample opportunities to ask such questions were available during the workshop. Those who intensively used them visibly progressed in their understanding of IUT." 
 
 Proving the abc conjecture may prove to be worth the effort. A (very gnarly) paper by Dimitrov earlier this year showed how a reduction of Mochizuki's proof, if it is eventually verified, should offer solutions to a large number of other mathematical problems, including a new proof of Fermat's last theorem. 
 
 As for what the abc conjecture actually is, here's what I wrote in 2015: 
 
 Take three (whole) numbers—a, b, and c—of the form a + b = c. These three numbers are what’s known as coprime. This just means that they don’t share any divisors (except for 1, but every number is divisible by 1). If one of the numbers is divisible by, say, 13, none of the others are divisible by 13. It’s an interesting relationship, like three people with no shared ancestors all the way back to the very first human/number (which is 1). 
 
 What we need to prove is that for some other, fourth number d, there will be a finite (countable) number of abc triplet sets (as, bs, and cs fitting the above equation) such that c is greater than d raised to some positive power that is not 1 (a “perfect power”). Finally, this extra number d isn’t just anything; it must be the product of the prime factors of a, b, and c. That’s it. Somehow, these three numbers that aren’t linked by common factors (coprime) are, after all, linked by their factors. It’s weird. 
 
 You could even say that the conjecture is kind of elegant: three seemingly perfect mathematical strangers are related in the end. A simple statement, but with a proof that turns out to be anything but. 

 AP/Press Association Images 
 
 Nearly four years after Shinichi Mochizuki unveiled an imposing set of papers that could revolutionize the theory of numbers, other mathematicians have yet to understand his work or agree on its validity — although they have made modest progress. 
 
 Some four dozen mathematicians converged last week for a rare opportunity to hear Mochizuki present his own work at a conference on his home turf, Kyoto University's Research Institute for Mathematical Sciences (RIMS). 
 
 Mochizuki is “less isolated than he was before the process got started”, says Kiran Kedlaya, a number theorist at the University of California, San Diego. Although at first Mochizuki's papers, which stretch over more than 500 pages1–4, seemed like an impenetrable jungle of formulae, experts have slowly discerned a strategy in the proof that the papers describe, and have been able to zero in on particular passages that seem crucial, he says. 
 
 And Jeffrey Lagarias, a number theorist at the University of Michigan in Ann Arbor, says that he got far enough to see that Mochizuki’s work is worth the effort. "It has some revolutionary new ideas,” he says. 
 
 Still, Kedlaya says that the more he delves into the proof, the longer he thinks it will take to reach a consensus on whether it is correct. He used to think that the issue would be resolved perhaps by 2017. “Now I'm thinking at least three years from now.” 
 
 Others are even less optimistic. “The constructions are generally clear, and many of the arguments could be followed to some extent, but the overarching strategy remains totally elusive for me,” says mathematician Vesselin Dimitrov of Yale University in New Haven, Connecticut. “Add to this the heavy, unprecedentedly indigestible notation: these papers are unlike anything that has ever appeared in the mathematical literature.” 
 
 The abc proof 
 
 Mochizuki’s theorem aims to prove the important abc conjecture, which dates back to 1985 and relates to prime numbers — whole numbers that cannot be evenly divided by any smaller number except by 1. The conjecture comes in a number of different forms, but explains how the primes that divide two numbers, a and b, are related to those that divide their sum, c. 
 
 If Mochizuki’s proof is correct, it would have repercussions across the entire field, says Dimitrov. “When you work in number theory, you cannot ignore the abc conjecture,” he says. “This is why all number theorists eagerly wanted to know about Mochizuki's approach.” For example, Dimitrov showed in January5 how, assuming the correctness of Mochizuki’s proof, one might be able to derive many other important results, including a completely independent proof of the celebrated Fermat’s last theorem. 
 
 But the purported proof, which Mochizuki first posted on his webpage in August 2012, builds on more than a decade of previous work in which Mochizuki worked in virtual isolation and developed a novel and extremely abstract branch of mathematics. 
 
 Mochizuki in the room 
 
 The Kyoto workshop followed on the heels of one held last December in Oxford, UK. Mochizuki did not attend that first meeting, although he answered the audience’s questions over a Skype video link. This time, having him in the room — and hearing him present some of the materials himself — was helpful, says Taylor Dupuy, a mathematician at the Hebrew University of Jerusalem who participated in both workshops. 
 
 There are now around ten mathematicians who are putting substantial effort into digesting the material — up from just three before the Oxford workshop, says Ivan Fesenko, a mathematician at the University of Nottingham, UK, who co-organized both workshops. The group includes younger researchers, such as Dupuy. 
 
 In keeping with his reputation for being a very private person, Mochizuki — who is said to never eat meals in the presence of colleagues — did not take part in the customary mingling and social activities at the Kyoto meeting, according to several sources. And although he was unfailingly forthcoming in answering questions, it was unclear what he thought of the proceedings. “Mochizuki does not give a lot away,” Kedlaya says. “He’s an excellent poker player.” 
 
 Fellow mathematicians have criticized Mochizuki for his refusal to travel. After he posted his papers, he turned down multiple offers to spend time abroad and lecture on his ideas. Although he spent much of his youth in the United States, he is now said to rarely leave the Kyoto area. (Mochizuki does not respond to requests for interviews, and the workshop’s website contained the notice: “Activities aimed at interviewing or media coverage of any sort within the facilities of RIMS, Kyoto University, will not be accepted.”) 
 
 “He is very level-headed,” says another workshop participant, who did not want to be named. “The only thing that frustrates him is people making rash judgemental comments without understanding any details.” 
 
 Still, Dupuy says, “I think he does take a lot of the criticism about him really personally. I’m sure he’s sick of this whole thing, too.”
– Four years after a Japanese mathematician announced he'd cracked an epic math problem, his fellow number crunchers are a step closer to deciding whether he got it right. Yes, his work is that complicated. In 2012, Shinichi Mochizuki of Kyoto University, who's known to work in isolation, published a 500-page proof he said explained the ABC conjecture, a renowned math problem involving prime numbers. The problem is few could understand his proof because it required a grasp on Inter-universal Teichmuller Theory—essentially a new branch of math Mochizuki created—and he refused to travel to explain it to the mathematical community, reports Nature. Finally, a breakthrough came last month in Kyoto, where he lives. During a meeting of four dozen mathematicians, Mochizuki was able to teach his theory to others. As Ivan Fesenko of the University of Nottingham put it on Facebook, some participants "visibly progressed in their understanding" and ended up "tired but happy," per Motherboard. (The latter site gets into the nitty gritty of the "simple-seeming" ABC conjecture.) There are now 10 people who reportedly understand IUT and are working to verify Mochizuki's proof. But it isn't clear how soon that could happen. One number theorist says it could still be years before Mochizuki's theory is proven correct—or not. If he's right, though, it could be "revolutionary," says one mathematician. (Want to be a millionaire? Solve this problem.)