In 1656 Huygens patented the first pendulum clock, which greatly increased the accuracy of time measurement.
Tutored at home by private teachers, Huygens later studied law and mathematics at the University of Leiden from 1637 until
1643. Van Schooten tutored him in mathematics while he was in Leiden. From 1647 until 1649 he studied law at the College of
Orange at Breda. In 1649 he went to Denmark as part of a diplomatic team.
His most productive period (1650-66) was spent at The Hague in relative solitude. However his long stay from 1666 to 1681
at the Académie in Paris was spent with some of the greatest scientists of the age.
Huygens's first publications in 1651 and 1654 considered mathematical problems, but he soon he turned to lens grinding. Using
one of his own lenses, Huygens detected, in 1655, the first moon of Saturn.
The following year he discovered the true shape of the rings of Saturn and in Systema Saturnium (1659), Huygens explained
the phases and changes in the shape of the ring.
In 1656 Huygens patented the first pendulum clock, which greatly increased the accuracy of time measurement. He built several
pendulum clocks to determine longitude and they underwent sea trials in 1662 and again in 1686. In the Horologium
Oscillatorium sive de motu pendulorum (1673) he described the theory of pendulum motion. He also derived the law of
centrifugal force for uniform circular motion. As a result of this Huygens, Hooke, Halley and Wren formulated the
inverse-square law of gravitational attraction
His short tract De Ratiociniis in Ludo Aleae in 1657 was the first printed work on probability. It was prompted by the work
of Pascal and Fermat which Huygens learned of during his time in Paris.
His work on the collision of elastic bodies showed the error Descartes' laws of impact. In his Traité de la lumiere (1678),
Huygens argued in favour of a wave theory of light. Huygens stated that an expanding sphere of light behaves as if each point
on the wave front were a new source of radiation of the same frequency and phase.
In the final years of his life Huygens composed one of the earliest discussions of extraterrestrial life, published after his death as
the Cosmotheoros (1698).
Huygens described the 31-tone equal temperament in Lettre touchant le cycle harmonique . This has led indirectly to a
tradition of 31-tone music in the Netherlands in this century.
Huygens was elected to the Royal Society in London in 1663 and the Académie Royal des Sciences in Paris in 1666.