Sigismund, the Mad Mathemagician, first introduced as Madman in Hex and the City, was a highly intelligent NASA scientist in the 60's who turned to study mysticism and mathematical description theory trying to find a new way to view reality. Eventually, he did, and whatever he saw drove him insane, earning him the nickname Madman.
Madman's powers have an undefined origin. But essentially, reality is manipulated around him by his will. Reality distorts itself in order to follow his thoughts and imagination. He seems to have a soundtrack playing almost constantly, depending on the mood he's in. At one point in the book, he uses his imagination to imagine himself as a samurai with a katana and chopped one of Walker's Reasonable Men into tiny bits.