Those papers are where the details of the proof are supposed to be, and it’s exactly those that everyone is having trouble with.

Bernhard,

There are definitely lots of “new ideas”, the problem is understanding them and whether they really are powerful enough to give a proof. They are not being just dismissed, partly because Mochizuki has a serious track record, partly because as people work on them, they are not finding that they are wrong.

I think there is a strong feeling among a lot of people in the field that it is Mochizuki’s responsibility to do a better job of communicating his ideas, so they’re not going to spend more time on this now.

What do you think about Lagarias’ comment that Mochizuki’s work has “some revolutionary new ideas,” ? This seems really odd. Aren’t they still trying to figure out if the alleged proof is right or wrong still? How do they than separate a possible collection of crackpotish ideas from “revolutionary” ones? Is this a case where no matter what the outcome the tools he invited (which?) are already useful?

Also shouldn’t be on Mochizuki’s shoulder the burden to try to prove his work is worthy? Why aren’t these guys reacting like “You have a proof? Make it readable” His refusal to do so, sounds a bit he’s hiding behind formalism.

It’s not like they can do an experiment to verify it so…

]]>I suppose Mochizuki re-writing material has its own problems, as probably according to his understanding the material is complete already. If this is the case, then somebody else has to invest time to make the translation to a more mainstream formulation. The problem might be that the material is so large and so far away from mainstream mathematics that it will take years to understand and re-write it.

]]>I’m not sure what “introductory material” you mean. The problem I think is basically that

1. Mochizuki refuses to rewrite material, on the grounds that this should not be necessary, people should just spend the time it takes to understand what he has written.

2. The small number of people who were supposed to have digested this material, and rewrite it in this manner (e.g. Go Yamashita), have not been able to complete this task.

3. Others have been unable to digest the material. If you can’t understand yourself why a proof works, you’re not going to be able to rewrite it for others to understand.

That, four years later, no one else has been able to write up their own version of the proof is the central mystery here.

]]>The problem here is that such questions as “what are the basic new objects and concepts” have baffled experts, so the non-expert doesn’t have a chance. Knowing anything about the usual Teichmuller theory I don’t think helps. ]]>

So the Mochizuki affair could be summarised by asking: are we dealing with another case of de Branges’ proof of the Riemann hypothesis, or of his proof of Bieberbach’s conjecture?

]]>”

aspects of inter-universal Teichmüller theory may be thought of as arithmetic analogues of the geometric theory surrounding Bogomolov’s proof. Alternatively, Bogomolov’s proof may be thought of as a sort of useful elementary guide, or blueprint [perhaps even a sort of Rosetta stone!], for understanding substantial portions of inter-universal Teichmuller theory.” ]]>