Mathematics is fun! Timothy Gowers inspires enthusiasm for a subject that is not often met with excitement: using the trajectory of a ball, he explains what constitutes a mathematical model. What role do numbers and abstraction play in mathematics? Why can a successful mathematical proof be described as "beautiful"? What are limits and infinity used for? And how do geometry and probability work? His introduction becomes a thought adventure that alleviates apprehensions and can show the reader (perhaps for the first time) the joy of this fascinating subject.