Christiaan Huygens (1629-1695)

Christiaan Huygens was born in Hague, Netherlands. He originally studied law and mathematics at Leiden University. He then continued his study of law at Orange College in Breda while he advanced his study of mathematics through private tutors. He went to France to earn a doctorate from the Protestant University at Angers and passed through Paris in his travels. He did not interact with Fermat (who was in Toulouse at the time) or Pascal (who had started his religious hiatus from math) but interacted with their colleagues from whom he learned of the problem of points. However, those who presented the problem to him were not able to explain the solution. He derived his own solution to the problem as well as to probability problems related to dice games. Later, Carcavi, one of the Parisian mathematicians, wrote to Huygens to explain Fermat's solution to the problem of points, and it was the same solution Huygens had found.

Huygens, however, had used a slightly different approach. While the problems he discussed, including the problem of points, are often seen purely as probability prompts, he did not use the term probability; rather, he thought of the solution as the expectation and used the new algebra invented by Viète and Descartes in his calculations. To Huygens and those of his time, chance meant uncertain and unpredictable, which did not fit the idea of calculated values in given problems. He solved such problems by reducing them to equiprobable scenarios.

He and his brother, Lodewijk, learned of John Graunt's Observations Made upon the Bills of Mortality (1681) and discussed their own life expectancies through letters. Each calculated a different life expectancy because one of them used the mean and the other used the median. These letters were instructive to those studying mortality problems once they were published.

Likely, Huygens' largest contribution to the development of probability theory was his 1657 tract, De ratiociniis in ludo aleae. It included the problem of points with his explanation and other probability problems that were popular or that he had created. It made problems that inspired the study of probability available to more people than previously had access. Proofs for his calculations were rigorous. Jacob Bernoulli's annotated version of the tract became the first section in his famous Ars Conjectandi (1713). Huygens' 1657 tract provided a basis from which other mathematicians developed probability theory.