In December, 2007, Mathemagian Arthur Benjamin put on quite a show at TED. I was looking for a microphone in his ear, but didn’t see it, and there frankly wasn’t enough time for him to cheat. As the show went on, he look more and more legit and increasingly impressive. At the 11:20 mark, he talked out the process going through his head as his did his on-the-fly calculations, and he revealed that he uses a word/number system to do his magic. It was a phenomenal wrap-up to his show.
Arthur Benjamin is a math professor during the day (at Harvey Mudd College). He has written and lectured extensively on math agility and mental math.