

The Paradox of the Proof (2013) - wz1000
http://projectwordsworth.com/the-paradox-of-the-proof/?src=longreads

======
kurotetsuka
“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'."

So I guess that's your explanation?

[0] ::
[https://en.wikipedia.org/wiki/Anathem](https://en.wikipedia.org/wiki/Anathem)

[1] :: [http://www.kurims.kyoto-u.ac.jp/~motizuki/thoughts-
english.h...](http://www.kurims.kyoto-u.ac.jp/~motizuki/thoughts-english.html)

[3] ::
[https://en.wikipedia.org/wiki/Anabelian_geometry](https://en.wikipedia.org/wiki/Anabelian_geometry)

[4] :: [https://en.wikipedia.org/wiki/Inter-
universal_Teichm%C3%BCll...](https://en.wikipedia.org/wiki/Inter-
universal_Teichm%C3%BCller_theory)

------
kozak
So, any news on that since 2013?

~~~
wz1000
> 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]

[http://en.wikipedia.org/wiki/Abc_conjecture#Attempts_at_solu...](http://en.wikipedia.org/wiki/Abc_conjecture#Attempts_at_solution)

------
highCs
The _unreadable_ paper is here:
[http://www.kurims.kyoto-u.ac.jp/~motizuki/Inter-
universal%20...](http://www.kurims.kyoto-u.ac.jp/~motizuki/Inter-
universal%20Teichmuller%20Theory%20I.pdf)

------
mutatismutandis
does anyone know why he'd have one of these:
[http://www.kurims.kyoto-u.ac.jp/~motizuki/anpi-kakunin-
jouho...](http://www.kurims.kyoto-u.ac.jp/~motizuki/anpi-kakunin-jouhou.html)

on his site?

