As children, we all learn about numbers. We start with counting, followed by addition, subtraction, multiplication and division. But mathematicians know that the number system we study in school is but one of many possibilities. Other kinds of numbers are important for understanding geometry and physics. Among the strangest alternatives is the octonions. Largely neglected since their discovery in 1843, in the past few decades they have assumed a curious importance in string theory. And indeed, if string theory is a correct representation of the universe, they may explain why the universe has the number of dimensions it does.