> When an error in one of the articles was pointed out by Vesselin Dimitrov and Akshay Venkatesh in October 2012, Mochizuki posted a comment on his website acknowledging the mistake, stating that it would not affect the result, and promising a corrected version in the near future.[15] He revised all of his papers on "inter-universal Teichmüller theory", the latest of which is dated November 2014.[11] Mochizuki has refused all requests for media interviews, but released progress reports in December 2013[16] and December 2014.[17] According to Mochizuki, verification of the core proof is "for all practical purposes, complete." However, he also stated that an official declaration shouldn't happen until some time later in the 2010s, due to the importance of the results and new techniques. In addition, he predicts that there are no proofs of the abc conjecture that use significantly different techniques than those used in his papers.[17] There was a workshop on IUT at Kyoto University in March 2015 and another one will be held at Clay Mathematics Institute in December 2015.[18]
“Inter-universal Geometer" - This seems to refer to the Geometers from Neal Stephenson's Anathem[0], or is at least inspired by the same concept. "Inter-universal" probably refers to the fact that math, analogous to geometry, holds true regardless of the rules of one's universe. (Math is a set of "if these rules apply to a system, then these other rules must apply" statements.) Just seems a little weird to me that the article was so specific about so much, but left that bit ambiguous ("What does it mean? His website offers no clues.").
Edit - Did some digging, apparently his website offers direct clues:
> "inter-universal geometry", which may be thought of as a sort of generalization of anabelian geometry and, in particular, "absolute p-adic anabelian geometry"[1]
Idk what the "absolute p-adic" part means, but anabelian geometry is described here: [3].
Edit2 - Dunno why i'm spending so much time on this, but here's Mochizuki's explanation for the term (stolen from this wiki page on Inter-universal Teichmüller theory[4]).
> "in this sort of a situation, one must work with the Galois groups involved as abstract topological groups, which are not equipped with the 'labeling apparatus' . . . [defined as] the universe that gives rise to the model of set theory that underlies the codomain of the fiber functor determined by such a basepoint. It is for this reason that we refer to this aspect of the theory by the term 'inter-universal'."
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[ 242 ms ] story [ 637 ms ] threadhttp://en.wikipedia.org/wiki/Abc_conjecture#Attempts_at_solu...
Edit - Did some digging, apparently his website offers direct clues:
> "inter-universal geometry", which may be thought of as a sort of generalization of anabelian geometry and, in particular, "absolute p-adic anabelian geometry"[1]
Idk what the "absolute p-adic" part means, but anabelian geometry is described here: [3].
Edit2 - Dunno why i'm spending so much time on this, but here's Mochizuki's explanation for the term (stolen from this wiki page on Inter-universal Teichmüller theory[4]).
> "in this sort of a situation, one must work with the Galois groups involved as abstract topological groups, which are not equipped with the 'labeling apparatus' . . . [defined as] the universe that gives rise to the model of set theory that underlies the codomain of the fiber functor determined by such a basepoint. It is for this reason that we refer to this aspect of the theory by the term 'inter-universal'."
So I guess that's your explanation?
[0] :: https://en.wikipedia.org/wiki/Anathem
[1] :: http://www.kurims.kyoto-u.ac.jp/~motizuki/thoughts-english.h...
[3] :: https://en.wikipedia.org/wiki/Anabelian_geometry
[4] :: https://en.wikipedia.org/wiki/Inter-universal_Teichm%C3%BCll...
on his site?