Born June 19, 1623, in Clermont-Ferrand; died Aug. 19, 1662, in Paris. French religious philosopher, writer, mathematician, and physicist.

Pascal’s father was a highly educated jurist and an accomplished mathematician, and in rearing his children he was influenced by the pedagogical ideas of Montaigne. Pascal demonstrated outstanding mathematical aptitude at an early age and appears in the history of science as a classic example of an adolescent prodigy.

Pascal’s first mathematical treatise, Essai pour les coniques (Essay on Conics), was written in 1639 and published in 1640. It was a development of the works of G. Desargues and contained one of the basic theorems of projective geometry—Pascal’s theorem. In 1641 (according to some data, 1642) Pascal constructed a calculating machine. In 1654 he completed a number of works on arithmetic, number theory, algebra, and probability theory; these works were published in 1665. The range of Pascal’s mathematical interests was broad. He discovered a common algorithm for testing the divisibility of any integer by any other integer (On the Character of the Divisibility of Numbers). He is often credited with the discovery of Pascal’s triangle, which is a means of calculating binomial coefficients, and he formulated a number of basic theses of elementary probability theory (Traité du triangle arithmetique, published 1665, and his correspondence with P. Fermat). In these works, Pascal was the first to define precisely the method of mathematical induction and to use that method for proofs. His studies of the cycloid were an important step in the development of the analysis of infinitesimals. Pascal used geometric form to describe an integral calculus for determining areas of figures, volumes of solids, and areas of surfaces and to solve other problems connected with cycloids. His theorem on the characteristic triangle was one of the sources for G. von Leibniz’ differential and integral calculus.

Along with Galileo and S. Stevin, Pascal is considered a founder of classical hydrostatics. He established the fundamental law of hydrostatics, now called Pascal’s law, and discovered the operating principle of the hydraulic press. Pascal pointed out the common nature of the basic laws of equilibrium of liquids and gases. An experiment carried out in 1648 under his direction confirmed E. Torricelli’s hypothesis of the existence of atmospheric pressure.

[Preceding section based on the 2nd edition of the Bol’shaia Sovetskaia Entsiklopediia]

Pascal’s work in the exact sciences dates mainly from the 1640’s and 1650’s. Later he grew disappointed with the abstract nature of these sciences and turned to religious interests and philosophical anthropology. Becoming closely associated with the Jansenists, he began leading a semimonastic way of life in the Jansenist Convent of Port-Royal des Champs in 1655. He conducted an energetic polemic against the Jesuits on questions of religious ethics. The fruit of this polemic, his Lettres provinciales (Provincial Letters), was published in 1657 and is a masterpiece of French satirical prose. In the last years of his life, Pascal’s concerns centered on an attempt at an apology for Christianity through philosophical anthropology. This work was never finished; aphoristic notes for it were posthumously published in 1669 in “amended” form under the title Pensées de M. Pascal surla religion et sur quelques autres sujets (Thoughts of M. Pascal on Religion and on Some Other Subjects). Only with the textological work of the 19th and 20th centuries has it become possible to restore the authentic text of the Pensées.

Pascal’s place in the history of philosophy lies in his being the first thinker to pass through the experience of 17th-century mechanistic rationalism and to formulate clearly the question of the boundaries of the scientific. He drew attention to the “reasons of the heart,” as opposed to the “reasons of the mind,” and thus anticipated the later irrationalist current in philosophy—ranging from F. H. Jacobi and romanticism to the existentialists. Pascal’s view of Christianity was based on its traditional synthesis with cosmology and Aristotelian or Neoplatonic metaphysics and with the political ideology of monarchism (the alliance of throne and altar); nevertheless, Pascal refused to construct an artificially harmonized theological model of the world. His perception of the cosmos was expressed in the words “this eternal silence of the infinite spaces terrifies me.” His view of man was dynamic: “Man’s state is inconstancy, melancholy, and uneasiness.” Pascal does not tire of speaking of the tragic nature and the frailness of man. At the same time, he stresses man’s worth, which lies in the act of thinking. Man, Pascal says, is a “thinking reed,” and “in space, the universe embraces and swallows me up; in thought I embrace it.” Pascal’s concentration on anthropological problems anticipates S. Kierkegaard’s and F. M. Dostoevsky’s conception of the Christian tradition.

Pascal played an important role in the formation of French classicist prose. His influence extended to La Rochefoucauld, La Bruyère, Mme. de Sévigné, and the Comtesse de La Fayette.