Blaise Pascal: Thoughts, Letters, and Minor Works

French Mathematician Blaise Pascal did much to set in motion what is known today as modern mathematics. An unusually creative mathematician, he developed a number of theorems and mathematical structures, including the beginnings of probability theory and a more sophisticated understanding of the geometry of conic structures. At the age of 16, Pascal wrote a brilliant paper on conics; the paper consisted of one single printed page on which he states his major theorem - the opposite sides of any hexagon inscribed in a cone intersect in a straight line. This theorem led Pascal to develop several hundred related theorems in geometry. Pascal's activities, however, were not confined to pure mathematics. When he was about 19 years old, he built a calculating machine that he demonstrated to the king of France. It worked well enough to allow him to build and sell about 50 of them over a few years' time. His work on problems in atmospheric pressure eventually resulted in an early version of the gas law. At the age of 25, Pascal entered a Jansenist monastery to begin an ascetic life of study and argument. However, he continued his mathematical work. With Pierre de Fermat, Pascal laid the foundation for the theory of probability. In 1654, Pascal's friend, the Chevelier de Mere, had asked him to analyze a problem arising from a game of chance. Pascal in turn exchanged a number of letters with Fermat about the problem. This correspondence became the starting point for a theory of probability. However, neither published the ideas developed in the correspondence. The letters did inspire one of Pascal's contemporaries, Christian Huygens of Holland, to publish in 1657 a short tract on the mathematics of games involving dice. Pascal's name is now attached to "Pascals' Triangle" of binomial coefficients which plays and important role in the study combinations and probability. The triangle was known at least 600 years before Pascal became interested in it, but because of his contributions to its study, the triangle eventually became associated with his name. A sensitive and temperamental man, Pascal was obsessed with religious philosophy, a subject on which he wrote extensively. In his general philosophy he was very much taken with the concept of the infinite, which unsettled him and inspired in him a sense of awe. Over a period of years, he wrote on many religious, philosophical, and mathematical subjects. His notes and letters were edited and published posthumously as his Pensees.