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…

Nikola Tesla filed his first United States patent in 1886 and his last in 1928. The 112 patents he received during that span cover an extraordinary range of electrical inventions: motors, generators, lighting systems, power transmission, radio, remote control, and energy conversion. All of these patents have long since expired.…

At the height of World War II, approximately 10,000 people worked at Bletchley Park, Britain’s top-secret codebreaking center in Buckinghamshire. Roughly 75 percent of them were women. They operated the machines that broke German and Japanese ciphers. They analyzed intercepted messages. They translated decoded intelligence. They maintained the filing systems…

In a 1988 poll of readers of the Mathematical Intelligencer, mathematicians voted it the most beautiful theorem in all of mathematics. The physicist Richard Feynman called it “the most remarkable formula in math.” The mathematician Keith Devlin wrote that “like a Shakespearean sonnet that captures the very essence of love,…

In the early 1920s, young women in factories across the United States painted watch dials with luminous radium paint. The paint glowed in the dark, making the watches readable at night. The work was considered glamorous. The paint was harmless, the companies assured them. The women were encouraged to lick…