who is Blaise Pascal and what he contrubutin to mathematics and it's invention
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Answer:
blaise Pascal is a mathematician . he was born on June 19 1623
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Blaise Pascal (/pæˈskæl/ pask-AL, also UK: /-ˈskɑːl, ˈpæskəl, -skæl/ -AHL, PASK-əl, -al, US: /pɑːˈskɑːl/ pah-SKAHL,[3][4][5][6][7] French: [blɛz paskal]; 19 June 1623 – 19 August 1662) was a French mathematician, physicist, inventor, writer and Catholic theologian. He was a child prodigy who was educated by his father, a tax collector in Rouen. Pascal's earliest work was in the natural and applied sciences where he made important contributions to the study of fluids, and clarified the concepts of pressure and vacuum by generalising the work of Evangelista Torricelli. Pascal also wrote in defence of the scientific method.In 1642, while still a teenager, he started some pioneering work on calculating machines. After three years of effort and 50 prototypes,[8] he built 20 finished machines (called Pascal's calculators and later Pascalines) over the following 10 years,[9] establishing him as one of the first two inventors of the mechanical calculator.[10][11]
Pascal was an important mathematician, helping create two major new areas of research: he wrote a significant treatise on the subject of projective geometry at the age of 16, and later corresponded with Pierre de Fermat on probability theory, strongly influencing the development of modern economics and social science. Following Galileo Galilei and Torricelli, in 1647, he rebutted Aristotle's followers who insisted that nature abhors a vacuum. Pascal's results caused many disputes before being accepted.
In 1646, he and his sister Jacqueline identified with the religious movement within Catholicism known by its detractors as Jansenism.[12] Following a religious experience in late 1654, he began writing influential works on philosophy and theology. His two most famous works date from this period: the Lettres provinciales and the Pensées, the former set in the conflict between Jansenists and Jesuits. In that year, he also wrote an important treatise on the arithmetical triangle. Between 1658 and 1659, he wrote on the cycloid and its use in calculating the volume of solids.
Throughout his life, Pascal was in frail health, especially after the age of 18; he died just two months after his 39th birthday.[13]Pascal continued to influence mathematics throughout his life. His Traité du triangle arithmétique ("Treatise on the Arithmetical Triangle") of 1654 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)th row and (n + 1)th column tmn. Then tmn = tm–1,n + tm,n–1, for m = 0, 1, 2, ... and n = 0, 1, 2, ... The boundary conditions are tm,−1 = 0, t−1,n = 0 for m = 1, 2, 3, ... and n = 1, 2, 3, ... The generator t00 = 1. Pascal concludes with the proof,
{\displaystyle t_{mn}={\frac {(m+n)(m+n-1)\cdots (m+1)}{n(n-1)\cdots 1}}.} {\displaystyle t_{mn}={\frac {(m+n)(m+n-1)\cdots (m+1)}{n(n-1)\cdots 1}}.}
In 1654, he proved Pascal's identity relating the sums of the p-th powers of the first n positive integers for p = 0, 1, 2, ..., k.[18]
In 1654, prompted by his friend the Chevalier de Méré, he corresponded with Pierre de Fermat on the subject of gambling problems, and from that collaboration was born the mathematical theory of probabilities.[19] 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 Pensées) used a probabilistic argument, Pascal's Wager, to justify belief in God and a virtuous life. The work done by Fermat and Pascal into the calculus of probabilities laid important groundwork for Leibniz' formulation of the calculus.[20]
After a religious experience in 1654, Pascal mostly gave up work in mathematics.
Philosophy of mathematics
Pascal's major contribution to the philosophy of mathematics came with his De l'Esprit géométrique ("Of the Geometrical Spirit"), originally written as a preface to a geometry textbook for one of the famous "Petites-Ecoles de Port-Royal" ("Little Schools of Port-Royal"). The work was unpublished until over a century after his death. Here, Pascal looked into the issue of discovering truths, arguing that the ideal of such a method would be to found all propositions on already established truths. At the same time, however, he claimed this was impossible because such established truths would require other truths to back them up—first principles, therefore, cannot be reached. Based on this, Pascal argued that the procedure used in geometry was as perfect as possible, with certain principles assumed and other propositions developed from them. Nevertheless, there was no way to know the assumed principles to be