17 December 2015
A collective effort to solve a recently discovered problem in mathematics has yielded few clues and no definitive answers.
The problem is entitled the abc conjecture (also known as the Oesterlé–Masser conjecture). It was first proposed by Joseph Oesterlé (1988) and David Masser (1985), and can be stated as follows: For every ε > 0, there are only finitely many triples of coprime positive integers a + b = c such that c > d1+ε, where d denotes the product of the distinct prime factors of the product abc.
Approximately three years ago, an alleged proof for the abc conjecture appeared online. Written by Shinichi Mochizuki, the proof is deep and seemingly impenetrable, according to a team of leading specialists who had gathered at the University of Oxford on 7–11 December earlier this year to discuss the matter.
The quest to understand Mochizuki’s proof dates back to August 2012, when he quietly posted four papers on his website in which he claimed to have solved the abc conjecture.