The Mathemagician sure is an interesting ruler. For one thing, he doesn't take the title of "king," like his brother Azaz does. Instead, his name/title is unique to him. Being part mathematician and part magician makes him "The Mathemagician." Cute, right?
We know right when we meet him that math is this guy's life: "He was dressed in a long flowing robe covered entirely with complex mathematical equations and a tall pointed cap that made him look very wise. In his left hand he carried a long staff with a pencil point at one end and a large rubber eraser at the other" (14.63). For him, numbers are never boring. They're exciting and, actually, incredibly precious.
In fact, rubies and other jewels mean nothing to him compared to numbers. When Milo, Tock, and the Humbug see the Mathemagician's jewel collection, they call it "the most amazing mass of wealth that any of them had ever seen" (14.79). But the Mathemagician just sees the jewels as a pain in the neck: "'They're such a terrible nuisance,' sighed the Mathemagician, 'and no one can think of what to do with them. So we just keep digging them up and throwing them out. Now,' he said, taking a silver whistle from his pocket and blowing it loudly, 'let's have some lunch' (14.80).
Sure, this is funny – very funny, actually. But maybe we're also supposed to learn a little lesson from our friend the Mathemagician. We need to learn to value things other than money: for the Mathemagician, it's numbers. What's valuable to you?
The Mathemagician is also a great teacher, especially compared to his brother. The leader of Digitopolis encourages Milo to discover the answers to questions himself (and as we learn at the end of the book, this is a great way out of the Doldrums). The Mathemagician's gift, in particular, encourages Milo to think for himself. The magic staff isn't a crutch he can use to get out of a few jams and then toss it aside. It's not an answer book: Milo has to use this tool to solve problems for himself.
Oh, and one last thing we like about this guy: he knows when he's been outsmarted. The Mathemagician admits defeat when Milo tricks him – looks like the teacher has become the student!