As many of you know,
Mochizuki now has an alleged recently announced a proof of the ABC conjectureavailable online. This is very exciting news. However, my question is not about the proof itself (which may or may not be true, and It is still incomprehensible far too early to most of the leading mathematicians in the world).
When Grothendieck pursued proving the Weil Conjecture, he had a very particular vision. Namely, given a sufficiently nice cohomology theory, the proof of the Weil conjectures is fairly simplejudge its correctness, and can be sketched within the boundaries but it builds on many years of a few pages. This provided the motivation for his interest in motives, the standard conjectures, and so forthwork by him. In other words, a sketch of Can someone briefly explain the proof was clear in philosophy behind his head, and in order to make that sketch rigorous, he had to invent an arcane and difficult language. (Of course, there is still no motivic proof of the Weil conjectures, but that is besides my point.)
It seems to me that since Mochizuki has come up with an arcane and difficult language himself, work and has involved others in this school of "inter-universal Teichmüller theory", that he must have had a sketch for the proof of the ABC conjecture, in the same sense that Grothendieck had a sketch of the proof of the Weil conjectures. And that this new language (see http://quomodocumque.wordpress.com/2012/09/03/mochizuki-on-abc/ for interesting commentary) is just a way to make this sketch a reality.
It therefore behooves me to ask
Question
What is the underlying vision that Mochizuki pursued when trying comment on why it might be expected to prove shed light on questions like the ABC conjecture? What is the sketch of the proof that he had in mind?
