Mathemagia Arthur Benjamin

I looked at the topic "Do you know how to count in your mind?" And remembered a very informative video from Arthur Benjamin, who calls himself a mathemag. In this video, he squared 3- and 5-digit numbers, but, in my opinion, the magic is not in this, but the fact that he, squaring a 5-digit number, quickly recites all thoughts that go to in his head, that is, we know how he does it in his head.