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. Hipparchus catalogued those points around 130 BC and ranked them by brightness on a scale astronomers still use. They…

When Galileo first turned his telescope toward Saturn in 1610, he saw something strange. The planet appeared to have two companions, one on each side, like a large ball flanked by two smaller ones. He described Saturn as having “ears.” Two years later, when he looked again, the ears had…

In 1887, the American physicist Albert Michelson and the chemist Edward Morley conducted what is often called the most important failed experiment in the history of science. They set out to detect the luminiferous ether, the invisible substance that 19th-century physicists believed filled all of space and served as the…

Carl Friedrich Gauss, widely regarded as the greatest mathematician since antiquity, is credited with a famous declaration: “Mathematics is the queen of the sciences, and number theory is the queen of mathematics.” The phrase has been repeated so often that it has become a cliché. But Gauss meant something precise…