# Thesis: Blaise Pascal Biography

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Blaise Pascal Bio

Blaise Pascal's Biography

Blaise Pascal was a French mathematician, physicist, and religious philosopher. As a person, Pascal integrated different qualities in a nearly inconsistent manner. He held a position of basic skepticism, directed not in favor of that of Descartes, who was employing primary philosophical doubt only to get hold of a secure basis for his philosophy. At the same time, on the other hand, Pascal contributed path-breaking thoughts to applied mathematics. He laid the foundation of probability theory and invented the first digital calculator (Rooney 43). He was a child phenomenon who was educated by his father, a public servant. The first commercial attempt at a calculating machine was made by Blaise Pascal to help his father, an administrator in Rouen, France, who had to deal with complicated tax figures (Rooney 41-42). It caused a consciousness all over Europe, having a mechanical automation seemed to be able to bring out tasks of human intelligence during those times. Pascal's earliest effort was in the natural and applied sciences where he made significant offerings to the production of mechanical calculators, the study of fluids, and shed light on the theories of pressure and vacuum by taking a broad view the work of Evangelista Torricelli.

Pascal also wrote in defence of the scientific method. Pascal was a mathematician of the first order and helped form two most important new areas of research and wrote an extensive treatise on the area under discussion of projective geometry at the age of sixteen, and later corresponded with Pierre de Fermat on probability theory, strongly influencing the improvement of modern economics and social science. Following Galileo and Torricelli, in 1646 he refuted Aristotle's followers who do not take no for an answer and said that nature detests a vacuum. His results caused many difference of opinions before being accepted.

In 1646 his family converted to Jansenism and his father died in 1651. Following a spiritual experience in late 1654, he had his second conversion, disposed of his scientific work, and dedicated himself to philosophy and theology. His two most well-known works date from this time, the Lettres provinciales and the Pensees, the former set in the disagreement involving the Jansenists and Jesuits. In this year, he also wrote an essential treatise on the arithmetic of triangles. Between 1658 and 1659 he wrote on the cycloid and its use in calculating the volume of solids. Pascal was in poor health throughout his life and his death came just two months after his 39th birthday (Hald 44).

Early Life and Education

In the middle of the contemporaries of Descartes none demonstrated better natural genius than Pascal, but his mathematical reputation rests more on what he might have done than on what he actually effected, as during a considerable part of his life he deemed it his duty to allocate his whole time to religious exercises. Born in Clermont, France, Blaise Pascal lost his mother, Antoinette Begon, at the age of three. His father, etienne Pascal (1588-1651), was a local judge and member of the noblesse de robe, who also had an interest in science and mathematics. Pascal had two sisters, the younger Jacquelin and the elder Gilberte and in 1631, following the death of his wife, etienne Pascal traveled with his children to Paris.

The newly arrived family soon hired Louise Delfault, a maid who in due course became an influential member of the family. etienne, who never remarried, decided that he alone would educate his children, for they all showed astounding intellectual ability, above all his son Blaise. The young Pascal showed a remarkable propensity for mathematics and science. At the age of eleven, he composed a short treatise on the sounds of vibrating bodies, and etienne responded by forbidding his son to further pursue mathematics until the age of fifteen so as not to spoil his study of Latin and Greek. One day, nevertheless, etienne found Blaise writing a self-determining proof that the sum of the angles of a triangle is equal to two right angles by means of a piece of coal on a wall.

From then on, the boy was allowed to study Euclid. Conceivably more importantly, he was allowed to sit in as a silent on looker at the gatherings of some of the greatest mathematicians and scientists in Europe -- such as Roberval, Desargues, Mydorge, Gassendi, and Descartes -- in the monastic cell of Pere Mersenne. Particularly of interest to Pascal was a work of Desargues on conic sections. Following Desargues's thinking, the sixteenyearold Pascal produced, as a means of proof, a short treatise on what was called the "Mystic Hexagram," Essai pour les coniques ("Essay on Conics") and sent it -- his first serious work of mathematics -- to Pere Mersenne in Paris? It is known still today as Pascal's theorem.

Pascal's work was so intelligent that Descartes, when shown the manuscript, declined to accept it as true, and that the composition was not by the elder Pascal. When assured by Mersenne that it was, indeed, the product of the son not the father, Descartes dismissed it.

In France at that time offices and positions could be and were bought and sold. In 1631 etienne sold his position as second president of the Cour des Aides for 65,665 livres (Connor 42). The money was invested in a government bond which provided if not a lavish then without doubt a comfortable income which allowed the Pascal family to move to, and enjoy, Paris. But in 1638 Richelieu, desperate for money to carry on the Thirty Year War, defaulted on the government's bonds. Suddenly etienne Pascal's worth had dropped from nearly 66,000 livres to less than 7,300.

Like so many others, etienne was eventually forced to flee Paris because of his disagreement to the fiscal policies of Cardinal Richelieu, leaving his three children in the care of his neighbor Madame Sainctot, a great beauty with an renowned past who kept one of the most scintillating and scholarly salons in all France. It was only when Jacqueline performed well in a children's play with Richelieu in attendance that etienne was pardoned. In time etienne was back in good graces with the cardinal, and in 1639 had been appointed the king's commissioner of taxes in the city of Rouen -- a city whose tax records, thanks to uprisings, were in utter chaos.

In 1642, in an effort to ease his father's endless, exhausting calculations, and recalculations, of taxes owed and paid, Pascal, not yet nineteen, constructed a mechanical calculator capable of addition and subtraction, called Pascal's calculator or the Pascaline. The Musee des Arts et Metiers in Paris and the Zwinger museum in Dresden, Germany, exhibit two of his original mechanical calculators. Though these machines are early forerunners to computer engineering, the calculator failed to be a great commercial success. For the reason that it was extraordinarily expensive, the Pascaline became little more than a toy, and status symbol, for the very rich both in France and throughout Europe. On the other hand, Pascal continued to make enhancements to his design through the next decade and built fifty machines in total.

Contribution to Mathematics

In addition to the childhood marvels previously mentioned, Pascal continued to influence mathematics throughout his life. In 1653, Pascal wrote his Traite du triangle arithmetique ("Treatise on the Arithmetical Triangle") in which he described a convenient tabular presentation for binomial coefficients, now called Pascal's triangle. He defines the numbers in the triangle by recursion: Call the number in the (m+1)st row and (n+1)st column tmn. Then tmn = tm1, n + tm,n1, for m = 0, 1, 2... And n = 0, 1, 2... The boundary conditions are tm, 1 = 0, t1, n for m = 1, 2, 3... And n = 1, 2, 3... The generator t00 = 1. Pascal concludes with the proof and in 1654, prompted by a friend interested in gambling problems, he corresponded with Fermat on the subject, and from that collaboration was born the mathematical theory of probabilities.

Italian writers of the fifteenth and sixteenth centuries, notably Pacioli (1494), Tartaglia (1556), and Cardan (1545), had discussed the problem of the division of a stake between two players whose game was interrupted before its close. The problem was proposed to Pascal and Fermat, probably in 1654, by the Chevalier de Mere, a gambler who is said to have had unusual ability even for the mathematics. The correspondence which ensued between Fermat and Pascal, was fundamental in the development of modern concepts of probability.

The specific problem was that of two players who want to finish a game early and, given the current circumstances of the game, want to divide the stakes fairly, based on the chance each has of winning the game from that point. From this discussion, the notion of expected value was introduced. Pascal later (in the Pensees) used a probabilistic argument, Pascal's Wager, to justify belief in God and a virtuous life.

He challenged Pascal to solve a puzzle…
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