Thursday, October 08, 2015

The biggest mystery in mathematics: Shinichi Mochizuki and the impenetrable proof

The biggest mystery in mathematics: Shinichi Mochizuki and the impenetrable proof

"Sometime on the morning of 30 August 2012, Shinichi Mochizuki quietly posted four papers on his website. The papers were huge — more than 500 pages in all — packed densely with symbols, and the culmination of more than a decade of solitary work. They also had the potential to be an academic bombshell. 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."

The abc conjecture refers to numerical expressions of the type a + b = c. The statement, which comes in several slightly different versions, concerns the prime numbers that divide each of the quantities a, b and c. Every whole number, or integer, can be expressed in an essentially unique way as a product of prime numbers — those that cannot be further factored out into smaller whole numbers: for example, 15 = 3 × 5 or 84 = 2 × 2 × 3 × 7. In principle, the prime factors of a and b have no connection to those of their sum, c. But the abc conjecture links them together. It presumes, roughly, that if a lot of small primes divide a and b then only a few, large ones divide c.

But 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.

Reminded me first of Snow Crash.

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