No doubt the guy's exceptionally brilliant, and perhaps one day a mathematician with enough motivation to do it will spend a very long time trying to understand and decipher what he constructed, but my take on it is that anyone that wants to communicate a message, no matter how brilliant, should also go to the trouble of making it as legible as possible to others.
This is actually a major gripe of mine when reading papers - not enough effort to communicate the math so it's readable. It's really frustrating to decipher a paper when there's a lot of hand waving. It's 10x worse when buzzwords or unimportant relationships are also included.
If you've gone through paper-publishing, editors ask for pretty large reductions. A 29 page paper can easily be a 50-60 pages paper with "decent details" or a 150 pages paper with clear explanations of all details.
This assumes infinite time to add all minutiae to LaTeX. Not everyone works directly on that, almost everyone thinks on paper, develops ideas on paper and then TeXifies it. In my case, most of the "it is clear that" never made it into any version of the final file.
Well, you certainly don't need all the minutiae, but some hand holding, especially on specific papers that deal with some theorems that might not be so well know would be helpful.
My favorite journal - the electronic journal of combinatorics - doesn't have page limits because it never gets printed. You can also use as many colors as you like in your diagrams!
Meanwhile, a friend of mine uses a bool in their LaTeX files for 'idiot mode'; flip it on and recompile to get the painfully detailed versions of all the proofs. Since the source is on the arxiv, it means each paper has a kind of half-hidden long version.
I've been working on a paper from my PhD thesis. I have 10 pages of derivations before I even get to the solution of the equations, include figures, or perform analysis. It could easily be a 30 to 40 page paper. Cutting it down or splitting it into 2 papers will likely be necessary because of page limits. You kind of need to pick and choose what to leave out.
Of course, it happens without page limits as well. I used work from an older book and between two steps was easily two pages of work and there's another half dozen pages of work that from other parts of the derivation.
I have been seeing this too. Steve Pinker in his books, Sense of Style, has portions which talk about this problem. He calls it -"Curse of Knowledge" and has advise for scientific writers. I wish researchers could spend a bit more time on improving their writing skills for better communication.
Beyond the paper constraints, there's often something of a selective pressure to obfuscate as a way to get through review. Math you don't quite understand seems complex. Math that's clear and concise seems, after the fact, to be trivial.
I read the report linked in the article and Mochizuki et al do not seem to think that studying this would take prohibitively long time. Some select quotes:
> During these lectures, Yamashita warned that if you attempt to study IUTeich by skimming corners and “occasionally nibbling” on various portions of the theory, then you will not be able to understand the theory even in 10 years; on the other hand, if you study the theory systematically from the beginning, then you should be able to understand it in roughly half a year.
> Unfortunately, however, there appear to exist, especially among researchers outside Japan, quite strongly negative opinions and antagonistic reactions to the idea of “studying the theory carefully and systematically from the beginning”.
>From the point of view of achieving an effective solution to this sort of problem [=education], the most essential stumbling block lies not so much in the need for the acquisition of new knowledge, but rather in the need for researchers (i.e., who encounter substantial difficulties in their study of IUTeich and related topics) to deactivate the thought patterns that they have installed in their brains and taken for granted for so many years and then to start afresh, that is to say, to revert to a mindset that relies only on primitive logical reasoning, in the style of a student or a novice to a subject.
If it's in your interest that I understand what you're saying, and you make it too hard for me to parse your stuff down to a comprehensible level - then it's your fault, not mine.
