The proof of the abc conjecture I recently heard that there was a workshop on Inter-universal Teichmuller theory in the Clay institute from 7-11 December 2015.This field of mathematics offers a potential proof of the abc conjecture.If anyone knows, what is the progress of the confirmation of Mochizuki's papers?
I attended a talk by Brian Conrad at my University recently regarding the $abc-$Conjecture. He informed us that the only people who have the faintest idea about Mochizuki's proof are Mochizuki himself and some of his closest understudies who claim its validity. Apparently they are completely unable to explain the work to outsiders. You may have already known that.

Here is a link to Conrad's own words: http://mathbabe.org/2015/12/15/notes-on-the-oxford-iut-workshop-by-brian-conrad/.
Most mathematicians when they read a new paper they make a diagonal reading first to see what it is about and get a glimpse at the kind of methods and ideas used, and then concentrate on the parts which they feel they need more clarification. This is what happens when experts in one field read a paper in their field of expertise.I once had a professor who told that just by reading the first few pages of an article in his area, he could determine the relevance of what was being discussed and whether the paper was likely to have errors or not.

However, as Mochizuki points out on page 9 of his report http://www.kurims.kyoto-u.ac.jp/~motizuki/IUTeich%20Verification%20Report%202014-12.pdf , there seems to be no one right now that has sufficient expertise in absolute Anabelian Geometry to be able to look at IUT papers with the kind of insight and ease an Arithmetic Geometer looks at other papers in Arithmetic Geometry. For researchers to read their papers, they would have to become complete students again: learn the paper line by line, definition by definition, lemma by lemma like a student does when he's taking a course in a new subject. 

Most researchers, are simply not willing to do that and arrogantly categorize IUT as too abstract - thge truth is that they simply don't have enough background!!

There have been 3 mathematicians - Hoshi, Yamashita and Saidi who have gone through all of the papers of IUT a total of 12 times and they all confirm that the theory is correct.