On August 31, 2012, Japanese mathematician Shinichi Mochizuki posted four papers on the Internet.
The titles were inscrutable. The volume was daunting: 512 pages in total. The claim was audacious: he said he had proved the ABC Conjecture, a famed, beguilingly simple number theory problem that had stumped mathematicians for decades.
Then Mochizuki walked away. He did not send his work to the Annals of Mathematics. Nor did he leave a message on any of the online forums frequented by mathematicians around the world. He just posted the papers, and waited.
Two days later, Jordan Ellenberg, a math professor at the University of Wisconsin-Madison, received an email alert from Google Scholar, a service which scans the Internet looking for articles on topics he has specified. On September 2, Google Scholar sent him Mochizuki’s papers: You might be interested in this.
“I was like, ‘Yes, Google, I am kind of interested in that!’” Ellenberg recalls. “I posted it on Facebook and on my blog, saying, ‘By the way, it seems like Mochizuki solved the ABC Conjecture.’”
The Internet exploded. Within days, even the mainstream media had picked up on the story. “World’s Most Complex Mathematical Theory Cracked,” announced the Telegraph. “Possible Breakthrough in ABC Conjecture,” reported the New York Times, more demurely.
On MathOverflow, an online math forum, mathematicians around the world began to debate and discuss Mochizuki’s claim. The question which quickly bubbled to the top of the forum, encouraged by the community’s “upvotes,” was simple: “Can someone briefly explain the philosophy behind his work and comment on why it might be expected to shed light on questions like the ABC conjecture?” asked Andy Putman, assistant professor at Rice University. Or, in plainer words: I don’t get it. Does anyone?
The problem, as many mathematicians were discovering when they flocked to Mochizuki’s website, was that the proof was impossible to read. The first paper, entitled “Inter-universal Teichmuller Theory I: Construction of Hodge Theaters,” starts out by stating that the goal is “to establish an arithmetic version of Teichmuller theory for number fields equipped with an elliptic curve…by applying the theory of semi-graphs of anabelioids, Frobenioids, the etale theta function, and log-shells.”
This is not just gibberish to the average layman. It was gibberish to the math community as well.
“Looking at it, you feel a bit like you might be reading a paper from the future, or from outer space,” wrote Ellenberg on his blog.
“It’s very, very weird,” says Columbia University professor Johan de Jong, who works in a related field of mathematics.
Mochizuki had created so many new mathematical tools and brought together so many disparate strands of mathematics that his paper was populated with vocabulary that nobody could understand. It was totally novel, and totally mystifying.
As Tufts professor Moon Duchin put it: “He’s really created his own world.”
It was going to take a while before anyone would be able to understand Mochizuki’s work, let alone judge whether or not his proof was right. In the ensuing months, the papers weighed like a rock in the math community. A handful of people approached it and began examining it. Others tried, then gave up. Some ignored it entirely, preferring to observe from a distance. As for the man himself, the man who had claimed to solve one of mathematics’ biggest problems, there was not a sound.