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":
-----------
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.
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":
-----------
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.
-----------
http://www.math.columbia.edu/~woit/wordpress/?p=5104