Isaac Newton’s Philosophiae Naturalis Principia Mathematica, published in 1687, is routinely called the most important scientific book ever written. That claim is difficult to dispute. In a single work, Newton established the laws of motion, derived the law of universal gravitation, explained the orbits of planets and comets, accounted for…

Leonardo da Vinci is remembered as the supreme Renaissance artist, the painter of the Mona Lisa and The Last Supper. But this image, however accurate, is radically incomplete. Leonardo spent more time investigating nature than he ever spent painting. His notebooks, over 7,000 surviving pages of them, contain more science…

Between roughly 1543 and 1687, a transformation occurred in European thought so profound that it has no real precedent or parallel. In a century and a half, the basic framework that educated people used to understand the natural world was dismantled and replaced. The Earth moved from the center of…

A prime number is a whole number greater than 1 that cannot be divided evenly by any number other than 1 and itself. The first few primes are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29. They are simple to define and immediately accessible to anyone who can…

Isaac Newton has been the subject of more portraits, sculptures, engravings, and artistic reinterpretations than any other scientist in history. From the formal oil paintings commissioned during his lifetime to William Blake’s visionary attack on his legacy, from Victorian commemorative busts to modern pop-culture iconography, Newton’s image has been shaped…

When you hear a chord played on a piano, your ear receives a single complex sound wave: a messy, oscillating pressure signal that contains all the notes of the chord mixed together. Yet you can distinguish the individual notes. Your auditory system somehow separates the complex signal into its component…

For most of history, the speed of light was thought to be infinite. Aristotle believed light traveled instantaneously. So did Descartes, who argued in the 17th century that if light had a finite speed, solar eclipses would appear delayed, which (he claimed) they did not. The idea that light takes…

For most of human history, there was no zero. The ancient Egyptians counted without it. The Greeks, who invented geometry and proved the irrationality of the square root of two, had no symbol for nothing. The Romans built an empire with a numeral system (I, V, X, L, C, D,…

The smartphone in your pocket, the laptop on your desk, the servers that run the internet, the supercomputers that simulate climate models, and the chips inside your car’s engine all share a common ancestor. They are all, at their core, implementations of an architecture described in a 101-page document written…

Probability, as it was understood in the 18th century, worked in one direction. If you know the composition of a deck of cards, you can calculate the probability of drawing an ace. If you know the bias of a coin, you can calculate the probability of getting heads ten times…