The universe is nothing like how it appears to us. So, what's it really like? What is it in itself? Neither our senses nor any experiments can reveal the ultimate truth of existence. Fortunately, one thing can: reason. We inhabit the Mathmos: the mathematical cosmos. This book reveals the compelling secrets of the hidden reality that we will never once "see", but we can surely know - thanks to mathematics. Do we live in a rational universe or a random universe? This is the choice between a mathematical universe and a scientific universe. The mathematical universe has a rational ultimate answer, the scientific universe does not. The scientific universe is magicked out of non-existence, as if out of a magician's top hat. Are you a member of the magicians' cult of science? Nothing is more alchemical than modern science. You can generate a cosmos out of randomness in nothingness, which is a much greater trick than merely manufacturing gold from lead.