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…

In an age before telescopes, before photography, before any instrument could magnify the stars, one man achieved astronomical measurements so precise that they remained unsurpassed for a century. Tycho Brahe (1546 to 1601), a Danish nobleman with a silver nose, a pet elk, and an ego to match, built the…

Sometime around 1637, the French lawyer and amateur mathematician Pierre de Fermat was reading a copy of Diophantus’s Arithmetica, a third-century Greek text on number theory. Next to a passage about Pythagorean triples (whole numbers that satisfy a² + b² = c²), Fermat wrote a note in the margin. He…

An equation is a statement that two things are equal. It is the simplest possible form of a mathematical sentence. Yet equations have reshaped civilizations, launched technological revolutions, and revealed truths about the universe that no amount of verbal argument could have uncovered. The ten equations below are not merely…

On November 8, 1895, Wilhelm Conrad Röntgen was working alone in his laboratory at the University of Würzburg, experimenting with cathode rays (streams of electrons in a vacuum tube). He noticed that a fluorescent screen across the room was glowing, even though the tube was covered with black cardboard. Something…

Before photography, every scientific image was drawn by hand. Anatomists, botanists, astronomers, and naturalists depended on artists to make the invisible visible: the internal structure of a human body, the form of a newly discovered plant, the surface of the Moon as seen through a telescope. The best scientific illustrations…

In October 1950, the British journal Mind published a paper by Alan Turing titled “Computing Machinery and Intelligence.” It began with a sentence that would become one of the most quoted in the history of science: “I propose to consider the question, ‘Can machines think?’” The paper was unlike anything…

On October 4, 1957, the Soviet Union launched a polished aluminum sphere the size of a beach ball into orbit around the Earth. The satellite, called Sputnik, carried no instruments of scientific value. It simply transmitted a radio beep. But that beep, audible to anyone with a shortwave receiver, announced…