If a programmer locked himself away for 14 years and then emerged and announced he'd written a completely bug free OS, there would be skepticism. Code needs to be battle tested by other people to find the bugs.
Mathematics is the same, to an extent; one guy working alone for 14 years is likely to have missed ideas and perspectives that could illuminate flaws in his reasoning. Maths bugs. If he's produced hundreds of pages of complex reasoning, on his own, however smart he is I'd say there's a high chance he's missed something.
Humans need to collaborate in areas of high complexity. With a single brain, there's too high a chance of bias hiding the problems.
It's a shame that you've disregarded all of the replies to your original comment. tl;dr there are degrees of bugs and many are easily fixed.
edit: more constructively, Imagine that you're working on the NYT crossword and I come along and point out that 45 across is wrong and tell you what the answer should be. Do you then throw away the rest of your work? No, you fix the part that's wrong and then check the rest of the puzzle to figure out the scope of the error.
I don't really accept the notion that inconsistencies in a giant mathematical proof will always show themselves. That does happen sometimes, but if you're breaking new ground (as Mochizuki seems to be) its much more likely that things will seem consistent to you, but are actually inconsistent because you made a mistake somewhere.
Right, that's why other people are trying to verify the proof and aren't just taking it on faith. They're almost certainly going to find errors, the question is whether or not those errors are easily fixed, difficult to fix, or fundamentally impossible to fix.
"...Mochizuki is holding a private seminar with Yamashita, and Kim hopes that Yamashita will then go on to share and explain the work."
The issues are complex. Mochizuki apparently has some diffidence about communicating with the wider mathematical community. Yamashita may have to act as spokesman (and an initial checker). Then once communicated the checking and sifting can begin (and the recycling of new tools start).
Assuming the work is intelligible and valid of course.
Wiles was much more involved in the Math community at large than Mochizuki. He continued to publish non-FLT papers, go to conferences, etc. Even then, the general consensus is that FLT would have been proven much faster if Wiles shared his work earlier.
Mathematics is the same, to an extent; one guy working alone for 14 years is likely to have missed ideas and perspectives that could illuminate flaws in his reasoning. Maths bugs. If he's produced hundreds of pages of complex reasoning, on his own, however smart he is I'd say there's a high chance he's missed something.
Humans need to collaborate in areas of high complexity. With a single brain, there's too high a chance of bias hiding the problems.
(Repost of my previous comment https://hackertimes.com/item?id=4829806)