This is unfair. Yes, his website looks ridiculous, but it is not part of the culture of academia to care much (and I think such websites are especially popular in East Asia). Very few academics spend much time or effort on the design of their website (or are impressed with the same from others). Also keep in mind he is not a native speaker of English.
Laugh at his website if you want, but please do not infer that he's some eccentric who has no idea what he's talking about.
Clearly he isn't a crank, and I didn't mean for a minute to imply that he was one. I just found the design aesthetics of his web page to be an... interesting coincidence.
But that said -- just trust your gut instincts here. There's a long history in mathematics of brilliant people going off into the dark for frighteningly long periods of time, and coming back with announcements of major results that turn out to be... interesting, but ultimately to contain irreparable gaps. And the fact that nobody -- not even people like Tao or Conrad -- seems to know what exactly he's talking about (even though they obviously respect the guy) doesn't sound too encouraging, either.
Tao doesn't know exactly what Mochizuki is talking about because it is not in any of the (many) areas that Tao is an expert in. Even Fields medalists have their limits.
The people that do work in his area don't know exactly what he's talking about because he's been going in a very deep and difficult direction. No one has been following, because they've been waiting to see if he finds anything in there. There was a good description at "Not Even Wrong":
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What Mochizuki is claiming is that he has a new set of techniques, which he calls “inter-universal geometry”, generalizing the foundations of algebraic geometry in terms of schemes first envisioned by Grothendieck. In essence, he has created a new world of mathematical objects, and now claims that he understands them well enough to work with them consistently and show that their properties imply the abc conjecture.
What experts tell me is that, very much unlike the case of Szpiro’s proof, here it may take a very long time to see if this is really a proof. They can’t just rely on their familiarity with the usual scheme-theoretic world, but need to invest some serious time and effort into becoming familiar with Mochizuki’s new world. Only then can they hope to see how his proof is supposed to work, and be able to check carefully that a proof is really there, not just a mirage. It’s important to realize that this is being taken seriously because such experts have a high opinion of Mochizuki and his past work. If someone unknown were to write a similar paper, claiming to have solved one of the major open questions in mathematics, with an invention of a strange-sounding new world of mathematical objects, few if any experts would think it worth their time to figure out exactly what was going on, figuring instead this had to be a fantasy. Even with Mochizuki’s high reputation, few were willing in the past to try and understand what he was doing, but the abc conjecture proof will now provide a major motivation.
> I didn't mean for a minute to imply that he was one
Ok, fair enough.
But I am trusting my gut instincts here. Not so much having read the paper, but reading the way Ellenberg, Conrad, and Tao discuss the paper. To argue by analogy, if PG and Mark Zuckerberg both came out and said they were both intrigued by a new startup, that certainly wouldn't mean it was a shoo-in for success, but I imagine that VC's would be lining up to take that gamble.
Please also keep in mind that Perelman's proof of the Poincare conjecture confused the hell out of everyone, and I think it was a couple of years before experts came to a consensus that it was correct.
Of course, your pessimism could well be accurate. In any case, the consensus view in the mathematical community will be that ABC "may have been" proved (unless a mistake is found immediately). For better or worse, we are pretty damn cautious.
Laugh at his website if you want, but please do not infer that he's some eccentric who has no idea what he's talking about.