Dutch scientist Christiaan Huygens, inspired by investigations of pendulums by Galileo Galilei beginning around 1602, invents the pendulum clock, a clock that uses a pendulum, a swinging weight, as its timekeeping element.
Galileo, who had discovered the key property that makes pendulums useful timekeepers—isochronism, which means that the period of swing of a pendulum is approximately the same for different sized swings—had had the idea for a pendulum clock in 1637, partly constructed by his son in 1649, but neither had lived to finish it.
Having invented the pendulum clock in December 1656, Huygens patents the clock in 1657.
The introduction of the pendulum, the first harmonic oscillator used in timekeeping, increases the accuracy of clocks enormously, from about fiofteen minutes per day to fifteen seconds per day, leading to their rapid spread as existing 'verge and foliot' clocks are retrofitted with pendulums.
These early clocks, due to their verge escapements, have wide pendulum swings of up to one hundred degrees.
The mathematical theory of probability, the branch of mathematics concerned with analysis of random phenomena, has its roots in attempts to analyze games of chance by Gerolamo Cardano in the sixteenth century, and by Pierre de Fermat and Blaise Pascal in the seventeenth century (for example the "problem of points").
Huygens publishes a book on the subject in 1657.
