From the New York Times, an article about Shinichi Mochizuki, a math professor at Kyoto U., who three weeks ago uploaded 500 pages of papers to the Internet in which he claims to not only prove a conjecture that has been around for decades, but to do it, he uses a whole bunch of new math that he made up. It may (or may not) be the biggest leap forward in math in decades. Or, it could be all wrong. Nobody can tell yet.
For other recent mathematical tours de force — the proofs of Fermat’s last theorem, by Andrew Wiles at Princeton in 1995, and the Poincaré conjecture, by Grigory Perelman, a Russian mathematician, in 2003 — other experts could not immediately tell whether the proofs were valid, but “at least in some outline version, they understood how this approach made sense,” said Nets Katz, a mathematician at Indiana University
For Dr. Mochizuki’s abc conjecture proof, “that seems to be completely missing, and I’ve never seen that in my life,” Dr. Katz said. “It just seems a little odd that most of the people who say positive things about it cannot say what are the ingredients of the proof.”
While they cannot yet make heads or tails of it, many are nonetheless taking it seriously, because Dr. Mochizuki already has a number of significant proofs to his credit. “He has a long track record, and he has a long track record of being original,” Dr. Ellenberg said.
Indeed, much of the buzz is around the new techniques the mathematicians do not understand, potentially useful in unraveling similar problems and revealing deeper connections between numbers and geometry.