The ABC Conjecture has not been proved



As I’ve blogged about before, proof is a social construct: it does not constitute a proof if I’ve convinced only myself that something is true. It only constitutes a proof if I can readily convince my audience, i.e. other mathematicians, that something is true. Moreover, if I claim to have proved something, it is my responsibility to convince others I’ve done so; it’s not their responsibility to try to understand it (although it would be very nice of them to try).

A few months ago, in August 2012, Shinichi Mochizuki claimed he had a proof of the ABC Conjecture:

For every $latex \epsilon > 0,$ there are only finitely many triples of coprime positive integers $latex a, b, c$ such that $latex a+b= c$ and $latex c > d^{(1+\epsilon)},$ where $latex d$ denotes the product of the distinct prime factors of the product $latex abc.$

The manuscript he…

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