At just 20 years old, Gottfried Wilhelm Leibniz earned his doctorate in law, then proceeded to reshape mathematics, philosophy, and physics before the century was out. He invented calculus independently of Newton, introduced binary arithmetic that became the backbone of every modern computer, and coined the word "function" in mathematics. As a philosopher, he advanced rationalism and idealism, and his concept of a universe composed of fundamental units he called monads still sparks debate in metaphysics today. His optimism principle, that we inhabit the best of all possible worlds, so permeated European thought that Voltaire satirized it a generation later. Leibniz died in 1716, largely unrecognized by his peers, yet his fingerprints rest on every smartphone, logic gate, and calculus textbook in the world.