Pascal 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, 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. At the age of eleven, he composed a short treatise on the sounds of vibrating bodies, and Étienne responded by forbidding his son to further pursue mathematics until the age of fifteen so as not to harm his study of Latin and Greek. One day, however, Étienne found Blaise (now twelve) writing an independent proof that the sum of the angles of a triangle is equal to two right angles with a piece of coal on a wall. From then on, the boy was allowed to study Euclid; perhaps 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 Père Mersenne.

Particularly of interest to Pascal was a work of Desargues on conic sections. Following Desargues' thinking, the sixteen-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 it-his first serious work of mathematics-to Père Mersenne in 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, when shown the manuscript, refused to believe 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 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 sixteen-year-old child."[3]

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 the Cour des Aides for 65,665 livres.[4] The money was invested in a government bond which 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 the Thirty Year 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 neighbor Madame Sainctot, 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 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 Musée des Arts et Métiers 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. Because 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. However, Pascal continued to make improvements to his design through the next decade and built fifty machines in total.

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