history
From 1620 to 1972, the slide rule was the calculating tool of every engineer, scientist, navigator, and student of advanced mathematics. The transition to the pocket calculator collapsed a 350-year tradition in a single decade and removed it almost entirely from modern memory.</p>
biology
In a few species of Southeast Asian and American firefly, thousands of insects flash in perfect unison, their rhythms aligned to within milliseconds. The mechanism, worked out over half a century of research, is one of the cleanest examples of decentralized coordination in biology.
mathematics
The Mandelbrot set is perhaps the most-photographed mathematical object in history, but the visualization is the surface of a much deeper theory. The mathematics behind the famous shape includes a still-open major conjecture, a proof that its boundary has Hausdorff dimension 2, and a co...
mathematics
Roger Penrose discovered in 1974 that two simple shapes can tile the plane forever without ever repeating. The discovery solved an open mathematical problem and, a decade later, accidentally revealed a class of crystals that Linus Pauling spent the rest of his career denying existed.
mathematics
Honeybees build hexagonal comb. Pappus of Alexandria conjectured in the 4th century that hexagons were the optimal solution to the problem the bees were solving
mathematics
The relationship between simple frequency ratios and a fixed-pitch keyboard is mathematically impossible to satisfy exactly. Three thousand years of music theory has been a sequence of compromises, each of which sounds wrong in some specific way that another compromise was designed to avoid.
mathematics
Cellular automata are the simplest possible computational systems and they exhibit some of the deepest behavior we know how to study. The schoolroom version is Conway's Game of Life. The mathematical reality is that the simplest known universal computer fits in three lines of pseudocode.
mathematics
When a dog runs at a duck swimming across a pond, the dog's path traces a pursuit curve. Pierre Bouguer worked out the mathematics in 1732. The same equations describe missile guidance, predator-prey dynamics, hot-pursuit problems in epidemiology, and the spiral arms of certain galaxies.
mathematics
Random numbers are simultaneously the most familiar and the most subtle objects in mathematics. The century of false starts, the philosophical puzzle of what randomness even means, the practical engineering of generators that fool sophisticated tests, and the cryptographic stakes when the engin
mathematics
Spirals appear at every scale in nature — galactic arms, hurricanes, ammonites, sunflowers, snail shells, the double helix. The reason is not coincidence; it is that a small number of mathematical processes generate spirals as their natural shape, and these processes recur at every scale where
science
A soap bubble is a small machine for solving a difficult mathematical problem: find the surface of minimum area enclosing a given volume. The fact that bubbles solve this problem instantly, by physics, has occupied mathematicians for two centuries — from Plateau's experiments with iron-wire frame...
mathematics
Every storage device, every transmission, every QR code, every deep-space probe, every CD, every cell phone signal, every satellite link — they all rely on a class of mathematical structures invented in 1950 by a frustrated Bell Labs engineer who could not get his program to run over the weekend....