The Philosophiæ Naturalis Principia Mathematica, published in 1687, is widely regarded as the most important scientific book ever written. It contains Newton’s laws of motion, his law of universal gravitation, his derivation of Kepler’s laws of planetary motion, his theory of tides, his calculation of the speed of sound, and…

In the year 2000, the Clay Mathematics Institute in Cambridge, Massachusetts, announced seven “Millennium Prize Problems,” the most important unsolved problems in mathematics. Each carried a prize of one million dollars. As of today, only one has been solved (the Poincaré Conjecture, by Grigori Perelman in 2003, who declined the…

Nikola Tesla’s completed inventions changed the world. The alternating current motor, the polyphase power system, the Tesla coil, and the rotating magnetic field are foundations of modern electrical technology. But Tesla’s ambitions extended far beyond what he managed to build. Throughout his career, he announced, designed, and sometimes partially constructed…

Before electronic calculators, before mechanical adding machines, before slide rules, all serious computation was done by hand. Astronomers, navigators, surveyors, and engineers spent enormous amounts of time performing arithmetic, particularly multiplication and division of large numbers. A single astronomical calculation might require dozens of multiplications of six or seven digit…

The laboratory where Marie Curie isolated radium was not a laboratory at all. It was an abandoned dissecting shed at the School of Physics and Chemistry in Paris, on the Rue Lhomond. The building had a glass roof that leaked when it rained, no proper ventilation, and no floor, just…

In 1687, Isaac Newton published a law of universal gravitation that described how every object in the universe attracts every other object with a force proportional to their masses and inversely proportional to the square of the distance between them. The law was spectacularly successful. It explained the orbits of…

By the early twentieth century, physicists knew that atoms existed, that they contained electrons, and that the bulk of an atom’s mass was concentrated in a tiny, dense, positively charged nucleus. This last fact had been established in 1911 by Ernest Rutherford, whose scattering experiments at the University of Manchester…

The computer that guided Apollo 11 to the Moon and back had a clock speed of about 2 MHz, roughly 74 kilobytes of memory, and weighed 32 kilograms. A modern smartwatch is thousands of times more powerful. A basic calculator has more processing capability. And yet the Apollo Guidance Computer…

In 1864, the Scottish physicist James Clerk Maxwell published a set of equations that unified electricity, magnetism, and light into a single theory. The equations predicted that oscillating electric charges should produce waves of electromagnetic energy that travel through space at the speed of light. These waves, if they existed,…

When you look at the night sky, every star appears to be the same distance away. The ancient Greeks imagined the stars as points of light embedded in a crystal sphere. They had no way to measure how far away the stars actually were, and for two thousand years, neither…