Mathematics was Huygens’ chief field of interest. He was taught the subject in his youth by Jan Stampioen and by Frans van Schooten, a professor in Leiden.
Part of Huygens’ work can be classified under what we now call pure mathematics, such as squaring the circle. However, the greater part of his mathematical work was based on his theories about the workings of nature and his practical work. For example, he developed his theory of involutes and evolutes because he needed something to determine how to construct an isochronic pendulum.
Huygens’ mathematical work was primarily influenced by classical geometry, and most of his theses were founded on the science of geometry. But in Huygens’ time, others were already developing in a more analytical direction. One of these was the German mathematician Gottfried Wilhelm Leibniz. Leibniz learnt the basics of mathematics from Huygens but went on to follow a path of his own, one which Huygens was rather uncomfortable with.
However, Huygens was no stranger to breaking new ground either. One uncharted field he threw himself into was probability. When visiting Paris in 1655, he heard of an ongoing discussion between the French mathematicians Pascal and Fermat about the chances of winning or losing in gambling games (in particular, how the winnings should be divided if a game was stopped halfway through). He became immediately interested in the subject. This resulted in a short treatise, entitled De Ratiociniis in Ludo Aleae (The Value of all Chances in Games of Fortune, or Van rekeningh in spelen van geluck in Dutch). This work was published by his tutor Van Schooten in 1657 and long remained the only introduction to this branch of mathematics.