
Ask HN: Understanding inter-universal Teichmüller theory? - valera_rozuvan
Hi! My name is Valera Rozuvan, and I want to understand inter-universal Teichmüller theory. For those of you who never heard of this theory, please take a look at the Wikipedia&#x27;s entry https:&#x2F;&#x2F;en.wikipedia.org&#x2F;wiki&#x2F;Inter-universal_Teichm%C3%BCller_theory .<p>Why is this important? This theory might have a proof for the abc conjecture.<p>My background is in physics, optics. I finished the Taras Shevchenko National University of Kyiv. I am a hobbyist mathematician.<p>What should be my path of learning that will lead to understanding this theory? Any advice on specific texts, courses, online resources, etc. will be appreciated!
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impendia
It would take an _extraordinary_ effort. I doubt there is _anyone_ who could
learn this material given anything less than a year of solid study -- and I am
thinking of the leading researchers in the world, who are already experts in
everything related. I am a professional mathematician myself, and I doubt I
could manage it even within a year.

This is dictated by the difficulty of the subject, and it is even more so
since Mochizuki's papers are notoriously difficult to read. What I have heard
from other research mathematicians is that Mochizuki doesn't make much of an
effort to make himself comprehensible, to answer questions, or in general to
explain his results to the community.

Also please be warned that the consensus is generally that Mochizuki's theory
is probably incorrect.

That said, if you want to learn the stuff, there is no reference other than
Mochizuki's papers themselves. If you would like to learn some general
background theory I would recommend learning some algebraic geometry, for
which see Ravi Vakil's book:

[http://math.stanford.edu/~vakil/216blog/FOAGapr2915public.pd...](http://math.stanford.edu/~vakil/216blog/FOAGapr2915public.pdf)

and maybe Milne on etale cohmology:

[http://www.jmilne.org/math/CourseNotes/LEC210.pdf](http://www.jmilne.org/math/CourseNotes/LEC210.pdf)

If you find that incomprehensible, start with Dummit and Foote's _Abstract
Algebra_ (read it cover to cover), Neukirch's _Algebraic Number Theory_ ,
Atiyah and Macdonald's _Commutative Algebra_ , and Fulton and Harris's
_Representation Theory_.

If you indeed want to read all that, you may as well enroll in a Ph.D. program
in math....

~~~
valera_rozuvan
After reading many articles, posts, communication channels, etc. on the
Internet about IUT Theory of Shinichi Mochizuki, I think I am starting to
understand why some people believe that the theory doesn't prove the ABC
conjecture. It can be summed up by a phrase I found on some blog: "I believe
in a proof if I understand it.". I have done some research, and came upon the
source of that idea:

Pierre Deligne was first to express: "I don't believe in a proof done by a
computer ... I believe in a proof if I understand it."

[George G. Szpiro, Kepler's Conjecture, John Wiley, 2003. p.21]

~~~
valera_rozuvan
"I don't believe in a proof done by a computer, says Pierre Deligne of the
Institute for Advanced Study, an algebraic geometer and 1978 Fields Medalist.
“In a way, I am very egocentric. I believe in a proof if I understand it, if
it’s clear.” While recognizing that humans can make mistakes, he adds: “A
computer will also make mistakes, but they are much more diffcult to find."

THE DEATH OF PROOF by John Horgan
[http://www.math.uh.edu/~tomforde/Articles/DeathOfProof.pdf](http://www.math.uh.edu/~tomforde/Articles/DeathOfProof.pdf)

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upwg24
see [http://www.claymath.org/events/iut-theory-shinichi-
mochizuki](http://www.claymath.org/events/iut-theory-shinichi-mochizuki) and
[https://www.maths.nottingham.ac.uk/personal/ibf/files/symcor...](https://www.maths.nottingham.ac.uk/personal/ibf/files/symcor.iut.html)
for more information, including the 1st letter to its participants.

~~~
valera_rozuvan
There are several open-ended questions for Shinichi Mochizuki:

1.) What is a Frobenioid? [http://mathoverflow.net/questions/195353/what-is-a-
frobenioi...](http://mathoverflow.net/questions/195353/what-is-a-frobenioid)

2.) What is an étale theta function?
[http://mathoverflow.net/questions/195841/what-is-
an-%C3%A9ta...](http://mathoverflow.net/questions/195841/what-is-
an-%C3%A9tale-theta-function)

I hope the workshops planned will shed some light on them!

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asdftemp
hi there, you might start with this mathoverflow thread:
[http://mathoverflow.net/questions/106560/philosophy-
behind-m...](http://mathoverflow.net/questions/106560/philosophy-behind-
mochizukis-work-on-the-abc-conjecture)

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valera_rozuvan
A very-very good YouTube video explaining what the abc conjecture is:
[https://www.youtube.com/watch?v=RkBl7WKzzRw](https://www.youtube.com/watch?v=RkBl7WKzzRw)
.

