Legend has it that the first magic square, where all lines and diagonals add up to the same figure, was revealed more than 2,000 years ago when a river turtle appeared to have ancient Chinese numerals inscribed on sections of its shell. Patterns are everywhere in nature, and counting, measuring, and calculating changes are as old as civilization itself, as are many of the theorems and laws of math. The Pythagorean Theorem was used to plot out fields for planting crops before Pythagoras was even born, but the story begins long before that, with tally marks on rock and bone surviving from the Stone Age. Here is the essential guide to mathematics, an authoritative reference book and timeline that explores the work of history's greatest mathematicians. From the genius of Pierre de Fermat, who said he knew the answers but rarely gave them up, to the fractal pattern discovered by Waclaw Sierpinski now used to plan the route a mailman takes, here are 100 landmark moments in this intensely rigorous discipline, seen through the eyes of the people who lived them. Glimpse the abstract landscape of infinite numbers and multi-dimensional shapes as you learn about the most famous math men of all. Pythagoras had a love of numbers so strong it led to a violent death. Then there is Fibonacci, whose guide for bookkeepers changed the way we add and Descartes, who took inspiration from a fly to convert numbers into shapes and back again, changing math forever. Over many centuries, great minds puzzled over the evidence and, step-by-step, edged ever closer to the truth. Behind every one of these breakthrough moments there's a story about a confounding puzzle that became a discovery and changed the way we see the world.