# 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 $\epsilon$, there are only a finite number of triples (a,b,c) such that $c \gt d^{1+\epsilon}.$

(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.

### Metaculus help: Predicting

Predictions are the heart of Metaculus. Predicting is how you contribute to the wisdom of the crowd, and how you earn points and build up your personal Metaculus track record.

The basics of predicting are very simple: move the slider to best match the likelihood of the outcome, and click predict. You can predict as often as you want, and you're encouraged to change your mind when new information becomes available. With tachyons you'll even be able to go back in time and backdate your prediction to maximize your points.

The displayed score is split into current points and total points. Current points show how much your prediction is worth now, whereas total points show the combined worth of all of your predictions over the lifetime of the question. The scoring details are available on the FAQ.

Note: this question resolved before its original close time. All of your predictions came after the resolution, so you did not gain (or lose) any points for it.

Note: this question resolved before its original close time. You earned points up until the question resolution, but not afterwards.

This question is not yet open for predictions.

#### Thanks for predicting!

Your prediction has been recorded anonymously.

Want to track your predictions, earn points, and hone your forecasting skills? Create an account today!