18/09/27 06:20:04.04 xNwcF5GI.net
>>64
URLﾘﾝｸ(galoisrepresentations.wordpress.com)
Persiflage Galois Representations and more!
The ABC conjecture has (still) not been proved
Posted on December 17, 2017
(抜粋)
34 Responses to The ABC conjecture has (still) not been proved
Terence Tao says:
December 18, 2017 at 2:46 pm
Thanks for this.
I do not have the expertise to have an informed first-hand opinion on Mochizuki’s work, but on comparing this story with the work of Perelman and Yitang Zhang you mentioned that I am much more familiar with, one striking difference to me has been the presence of short “proof of concept” statements in the latter but not in the former,
by which I mean ways in which the methods in the papers in question can be used relatively quickly to obtain new non-trivial results of interest (or even a new proof of an existing non-trivial result) in an existing field.
In the case of Perelman’s work, already by the fifth page of the first paper Perelman had a novel interpretation of Ricci flow as a gradient flow which looked very promising, and by the seventh page he had used this interpretation to establish a “no breathers” theorem for the Ricci flow that,
while being far short of what was needed to finish off the Poincare conjecture, was already a new and interesting result, and I think was one of the reasons why experts in the field were immediately convinced that there was lots of good stuff in these papers.
つづく