Christiaan Huygens, Lord of Zeelhem (14 April 1629 – 8 July 1695) was a Dutch mathematician, physicist, engineer, astronomer, and inventor who is regarded as a key figure in the Scientific Revolution. In physics, Huygens made seminal contributions to optics and mechanics, while as an astronomer he studied the rings of Saturn and discovered its largest moon, Titan. As an engineer and inventor, he improved the design of telescopes and invented the pendulum clock, the most accurate timekeeper for almost 300 years. A talented mathematician and physicist, Huygens authored the first modern treatise where a physical problem was idealized using mathematical parameters, while his work on light contains the first mathematical and mechanistic explanation of an unobservable physical phenomenon.
Huygens first identified the correct laws of elastic collision in his work De Motu Corporum ex Percussione, completed in 1656 but published posthumously in 1703. In 1659, Huygens derived geometrically the formula in classical mechanics for the centrifugal force in his work De Vi Centrifuga, a decade before Isaac Newton. In optics, he is best known for his wave theory of light, which he described in his Traité de la Lumière (1690). His theory of light was initially rejected in favour of Newton's corpuscular theory of light, until Augustin-Jean Fresnel adapted Huygens's principle to give a complete explanation of the rectilinear propagation and diffraction effects of light in 1821. Today this principle is known as the Huygens–Fresnel principle.
Huygens invented and patented the pendulum clock in 1657, which was manufactured in Paris by Isaac II Thuret. Huygens's horological research led to an extensive analysis of the pendulum in Horologium Oscillatorium (1673), regarded as one of the most important 17th-century works on mechanics. While it contains descriptions of clock designs, most of the book is an analysis of pendular motion and a theory of curves. In 1655, Huygens began grinding lenses with his brother Constantijn to build refracting telescopes. He discovered Saturn's biggest moon, Titan, and was the first to explain Saturn's strange appearance as due to "a thin, flat ring, nowhere touching, and inclined to the ecliptic". In 1662, he developed what is now called the Huygenian eyepiece, a telescope with two lenses to diminish the amount of dispersion.
As a mathematician, Huygens developed his theory of evolutes and wrote on games of chance and the problem of points in Van Rekeningh in Spelen van Gluck, which Frans van Schooten translated and published as De Ratiociniis in Ludo Aleae (1657). The use of expected values by Huygens and others would later inspire Jacob Bernoulli's work on probability theory.
Christiaan Huygens was born into a wealthy, influential Dutch family in The Hague on 14 April 1629, the second son of Constantijn Huygens. Christiaan was named after his paternal grandfather. His mother, Suzanna van Baerle, died shortly after giving birth to Huygens's sister. The couple had five children: Constantijn (1628), Christiaan (1629), Lodewijk (1631), Philips (1632) and Suzanna (1637).
Constantijn Huygens was a diplomat and advisor to the House of Orange, in addition to being a poet and a musician. He corresponded widely with intellectuals across Europe, including Galileo Galilei, Marin Mersenne, and René Descartes. Christiaan was educated at home until the age of sixteen, and from a young age liked to play with miniatures of mills and other machines. He received a liberal education from his father, studying languages, music, history, geography, mathematics, logic, and rhetoric, alongside dancing, fencing and horse riding.
In 1644, Huygens had as his mathematical tutor Jan Jansz Stampioen, who assigned the 15-year-old a demanding reading list on contemporary science. Descartes was later impressed by his skills in geometry, as was Mersenne, who christened him the "new Archimedes".
At sixteen years of age, Constantijn sent Huygens to study law and mathematics at Leiden University, where he enrolled from May 1645 to March 1647. Frans van Schooten Jr., professor at Leiden's Engineering School, became private tutor to Huygens and his elder brother, Constantijn Jr., replacing Stampioen on the advice of Descartes. Van Schooten brought Huygens's mathematical education up to date, particularly on the work of Viète, Descartes, and Fermat.
After two years, starting in March 1647, Huygens continued his studies at the newly founded Orange College, in Breda, where his father was a curator. Constantijn Huygens was closely involved in the new College, which lasted only to 1669; the rector was André Rivet. Christiaan Huygens lived at the home of the jurist Johann Henryk Dauber while attending college, and had mathematics classes with the English lecturer John Pell. His time in Breda ended around the time when his brother Lodewijk, who was enrolled at the school, duelled with another student. Huygens left Breda after completing his studies in August 1649 and had a stint as a diplomat on a mission with Henry, Duke of Nassau. After stays at Bentheim and Flensburg in Germany, he visited Copenhagen and Helsingør in Denmark. Huygens hoped to cross the Øresund to see Descartes in Stockholm but Descartes died before he could do that.
Although his father Constantijn had wished his son Christiaan to be a diplomat, circumstances kept him from becoming so. The First Stadtholderless Period that began in 1650 meant that the House of Orange was no longer in power, removing Constantijn's influence. Further, he realized that his son had no interest in such a career.
Huygens generally wrote in French or Latin. In 1646, while still a college student at Leiden, he began a correspondence with his father's friend, Marin Mersenne, who died soon afterwards in 1648. Mersenne wrote to Constantijn on his son's talent for mathematics, and flatteringly compared him to Archimedes on 3 January 1647.
The letters show Huygens's early interest in mathematics. In October 1646 he wrote about the shape of a suspension bridge, demonstrating that a hanging chain is not a parabola, as Galileo thought. Huygens would later label that curve the catenaria (catenary) in 1690 while corresponding with Gottfried Leibniz.
In the next two years (1647–48), Huygens's letters to Mersenne covered various topics, including a mathematical proof of the law of free fall, the claim by Grégoire de Saint-Vincent of circle quadrature, which Huygens showed to be wrong, the rectification of the ellipse, projectiles, and the vibrating string. Some of Mersenne's concerns at the time, such as the cycloid (he sent Huygens Torricelli's treatise on the curve), the centre of oscillation, and the gravitational constant, were matters Huygens only took seriously later in the 17th century. Mersenne had also written on musical theory. Huygens preferred meantone temperament; he innovated in 31 equal temperament (which was not itself a new idea but known to Francisco de Salinas), using logarithms to investigate it further and show its close relation to the meantone system.
In 1654, Huygens returned to his father's house in The Hague and was able to devote himself entirely to research. The family had another house, not far away at Hofwijck, and he spent time there during the summer. Despite being very active, his scholarly life did not allow him to escape bouts of depression.
Subsequently, Huygens developed a broad range of correspondents, though with some difficulty after 1648 due to the five-year Fronde in France. Visiting Paris in 1655, Huygens called on Ismael Boulliau to introduce himself, who took him to see Claude Mylon. The Parisian group of savants that had gathered around Mersenne held together into the 1650s, and Mylon, who had assumed the secretarial role, took some trouble to keep Huygens in touch. Through Pierre de Carcavi Huygens corresponded in 1656 with Pierre de Fermat, whom he admired greatly. The experience was bittersweet and somewhat puzzling since it became clear that Fermat had dropped out of the research mainstream, and his priority claims could probably not be made good in some cases. Besides, Huygens was looking by then to apply mathematics to physics, while Fermat's concerns ran to purer topics.