Dr. Art Benjamin’s day job is mathematics professor at Harvey Mudd College. In his free time he likes to square 5 digit numbers in his head in front of a couple thousand people. At the end of this demonstration he thinks out loud so we can see how he does it.
15 minutes. Link to Video
If you’d like to learn to do this, he wrote a book about it: Arthur Benjamin | Secrets of Mental Math. There are a couple of chapters by Michael Shermer and introductions by Bill Nye The Science Guy and James Randi.
His website: www.math.hmc.edu/~benjamin
