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Scientific debut

Like some of his contemporaries, Huygens was often slow to commit his results and discoveries to print, preferring to disseminate his work through letters instead. In his early days, his mentor Frans van Schooten provided technical feedback and was cautious for the sake of his reputation.

Between 1651 and 1657, Huygens published a number of works that showed his talent for mathematics and his mastery of classical and analytical geometry, increasing his reach and reputation among mathematicians. Around the same time, Huygens began to question Descartes's laws of collision, which were largely wrong, deriving the correct laws algebraically and later by way of geometry. He showed that, for any system of bodies, the centre of gravity of the system remains the same in velocity and direction, which Huygens called the conservation of "quantity of movement". While others at the time were studying impact, Huygens's theory of collisions was more general. These results became the main reference point and the focus for further debates through correspondence and in a short article in Journal des Sçavans but would remain unknown to a larger audience until the publication of De Motu Corporum ex Percussione (Concerning the motion of colliding bodies) in 1703.

In addition to his mathematical and mechanical works, Huygens made important scientific discoveries: he was the first to identify Titan as one of Saturn's moons in 1655, invented the pendulum clock in 1657, and explained Saturn's strange appearance as due to a ring in 1659; all these discoveries brought him fame across Europe. On 3 May 1661, Huygens, together with astronomer Thomas Streete and Richard Reeve, observed the planet Mercury transit over the Sun using Reeve's telescope in London. Streete then debated the published record of Hevelius, a controversy mediated by Henry Oldenburg. Huygens passed to Hevelius a manuscript of Jeremiah Horrocks on the transit of Venus in 1639, printed for the first time in 1662.

In that same year, Sir Robert Moray sent Huygens John Graunt 's life table, and shortly after Huygens and his brother Lodewijk dabbled on life expectancy. Huygens eventually created the first graph of a continuous distribution function under the assumption of a uniform death rate, and used it to solve problems in joint annuities. Contemporaneously, Huygens, who played the harpsichord, took an interest in Simon Stevin's theories on music; however, he showed very little concern to publish his theories on consonance, some of which were lost for centuries. For his contributions to science, the Royal Society of London elected Huygens a Fellow in 1663, making him its first foreign member when he was just 34 years old.