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# Will Mochizuki's proof of the "abc conjecture" be formally accepted by the mathematics community by the end of 2017?

The so-called "abc conjecture" (or the Oesterlé–Masse conjecture) states that, given relatively prime numbers *(a,b,c)* such that *a+b=c*, and the product *d* of the unique prime factors of *a,b*, and *c*, then for a specified value of an index , there are only a finite number of triples *(a,b,c)* such that

(That is, almost all the time *d* is substantially greater than *c* -- for instance for *a=5, b=7, c=12,* we have *d=2 x 3 x 5 x 7=210 > c.* An example of the opposite (rare, finitely occuring) kind is *a=3,b=125,c=128,* where *d=2 x 3 x 5=30.* )

The abc conjecture, if true, is regarded as a revelation of deep and surprising connections between the basic arithmetical operations of addition and multiplication, and its truth would have a large number of implications for number theory.

In 2012 the mathematician Shinichi Mochizuki posted several long papers on his website in which he claimed to have found a proof of the conjecture. Mochizuki is a highly respected mathematician, but the papers (and previous results) total more than five hundred pages and the mathematics community has yet to understand Mochizuki's work, let alone verify the proof. A conference of experts in December 2015 that took place in Oxford was unable to resolve the matter, but some progress is being made, and a further conference is scheduled for July 2016.

The question will be regarded as answered in the affirmative if a formal paper (or set of papers) by Mochizuki proving the abc conjecture is accepted by a peer-reviewed mathematics journal by the end of December 2017.

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