In August of 2012, mathematician Shinichi Mochizuki posted a series of four papers online that purported to prove the ABC Conjecture, “a famed, beguilingly simple number theory problem that had stumped mathematicians for decades”. Then, nothing. Or nearly nothing.
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.
But seeming jibberish by a genius might just be solid mathematics, but Mochizuki isn’t doing much to help other mathematicians confirm or refute his assertions. Which raises an interesting point: mathematics isn’t all just logic and truth…there’s a social element to it as well.
“You don’t get to say you’ve proved something if you haven’t explained it,” she says. “A proof is a social construct. If the community doesn’t understand it, you haven’t done your job.”