Blaise Pascal 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 evangelist a 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, he built 20 finished machines (called pascal’s calculators and later Pascalines) over the following 10 years,establishing him as one of the first two inventors of the mechanical calculator.

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.

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 letters provincials sand the pen sees, the former set in the conflict between Jansenist and Jesuits. In that year, he also wrote an important treatise on the arithmetical triangle. Between 1658 and 1659, he wrote on the cyclo jeans 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.

**Pascal** was born in clerk on tufted and, which is in France’s Auvergne region. He lost his mother, Antoinette Begon, at the age of three. His father,Étienne Pascal(1588–1651), who also had an interest in science and mathematics, was a local judge and member of the “Noblesse de Robe”. Pascal had two sisters, the younger Jacqueline and the elder Gilberte.

In 1631, five years after the death of his wife,Étienne Pascal moved with his children to Paris. The newly arrived family soon hired Louise Delfault, a maid who eventually became an instrumental member of the family. Étienne, who never remarried, decided that he alone would educate his children, for they all showed extraordinary intellectual ability, particularly his son **Blaise. The** young Pascal showed an amazing aptitude for mathematics and science.

Particularly of interest to Pascal was a work of departure on comic sections. Following Desargues’ thinking, the 16-year-old 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 I this first serious work of mathematics stopped Mersey win Paris; it is known still today as Pascal’s theorem.

It states that if a hexagon is inscribed in a circle (or conic) then the three intersection points of opposite sides lie on a line (called the Pascal line). Pascal’s work was so precocious that Descartes was convinced that Pascal’s father had written it. When assured by Mersenne that it was indeed the product of the son and not the father, Descartes dismissed it with a sniff: “I do not find it strange that he has offered demonstrations about conics more appropriate than those of the ancients,” adding, “but other matters related to this subject can be proposed that would scarcely occur to a 16-year-old child.”

In France at that time offices and positions could be—and were—bought and sold. In 1631, Étienne sold his position as second president of theCour des Aidesfor 65,665livres.

The money was invested in agovernment bondwhich provided, if not a lavish, then certainly a comfortable income which allowed the Pascal family to move to, and enjoy, Paris. But in 1638 Richelieu, desperate for money to carry on theThirty Years’ War, defaulted on the government’s bonds. Suddenly Étienne Pascal’s worth had dropped from nearly 66,000 livres to less than 7,300.

like so many others, Étienne was eventually forced to flee Paris because of his opposition to the fiscal policies of cardinal Richelieu, leaving his three children in the care of his neighbour Madame Saintly, a great beauty with an infamous past who kept one of the most glittering and intellectual salons in all France. It was only when Jacqueline performed well in a children’s play with Richelieu in attendance that Étienne was pardoned. In time, Étienne was back in good graces with the cardinal and in 1639 had been appointed the king’s commissioner of taxes in the city ofRouen—a city whose tax records, thanks to uprisings, were in utterchaos.

In 1642, in an effort to ease his father’s endless, exhausting calculations, and recalculations, of taxesowed and paid (into which work the young Pascal had been recruited), Pascal, not yet 19, constructed a mechanical calculator capable of addition and subtraction, called Pascal’s calculator or the pascal one. Of the eight Pascal ones known to have survived, four are held by theMusée des Arts et Métiersin Paris and one more by theZwinger museum in Dresden, Germany, exhibit two of his original mechanical calculators.

Although these machines are pioneering forerunners to a further 400 years of development of mechanical methods of calculation, and in a sense to the later field of computer engineering, the calculator failed to be a great commercial success. Partly because it was still quite cumbersome to use in practice, but probably primarily because it was extraordinarily expensive, the Pascaline became little more than a toy, and astatus symbol, for the very rich both in France and elsewhere in Europe. Pascal continued to make improvements to his design through the next decade, and he refers to some 50 machines that were built to his design.

Contributions to mathematics Pascal continued to influence mathematics throughout his life. his traits du triangle arithmétique(“Treatise on the Arithmetical Triangle”) of 1653 described a convenient tabular presentation forbinomial coefficients, now called **Pascal’s triangle**

The triangle can also be represented:

He defines the numbers in the triangle by recursion: Call the number in the (m+ 1)th row and (n+ 1)th columntmn. Thentmn=tm–1,n+tm,n–1, form= 0, 1, 2, … andn= 0, 1, 2, … The boundary conditionsaretm,−1= 0,t−1,n= 0 form= 1, 2, 3, … andn= 1, 2, 3, … The generatort00= 1. Pascal concludes withthe proof,1654, he proved pascal’s identity relating the sums of thep-th powers of the firstnpositive integers forp= 0, 1, 2, …,k.