In July 1948, a thirty-two-year-old engineer at Bell Labs published a paper in the Bell System Technical Journal titled “A Mathematical Theory of Communication.” It was forty-four pages long, dense with equations, and addressed a problem that seemed narrowly technical: how to transmit messages efficiently through a noisy communication channel.…

In the summer of 1752, a forty-six-year-old printer from Philadelphia walked into a thunderstorm with a kite, a key, and an idea that most of Europe’s leading scientists considered absurd. Benjamin Franklin wanted to prove that lightning is electricity. The experiment, if it worked, would unify two phenomena that had…

For over a thousand years, the best minds in the ancient world believed that human vision worked by emission. The eye, according to Euclid, Ptolemy, and most Greek philosophers, sent out invisible rays that touched objects and returned with information about their shape and color. Seeing was an active process:…

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…