*“Knowing God without knowing our wretchedness leads to pride. Knowing our wretchedness without knowing God leads to despair. Knowing Christ gives the balance.”*Among the contemporaries of Descartes none displayed greater 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 devote his whole time to religious exercises.

Blaise Pascal was born at Clermont on June 19, 1623, and died at Paris on Aug. 19, 1662. His father, a local judge at Clermont, and himself of some scientific reputation, moved to Paris in 1631, partly to prosecute his own scientific studies, partly to carry on the education of his only son, who had already displayed exceptional ability. Pascal was kept at home in order to ensure his not being overworked, and with the same object it was directed that his education should be at first confined to the study of languages, and should not include any mathematics. This naturally excited the boy's curiosity, and one day, being then twelve years old, he asked in what geometry consisted. His tutor replied that it was the science of constructing exact figures and of determining the proportions between their different parts. Pascal, stimulated no doubt by the injunction against reading it, gave up his play-time to this new study, and in a few weeks had discovered for himself many properties of figures, and in particular the proposition that the sum of the angles of a triangle is equal to two right angles.

His father, struck by this display of ability, gave him a copy of Euclid's Elements, a book which Pascal read with avidity and soon mastered.

Blaise Pascal was born at Clermont on June 19, 1623, and died at Paris on Aug. 19, 1662. His father, a local judge at Clermont, and himself of some scientific reputation, moved to Paris in 1631, partly to prosecute his own scientific studies, partly to carry on the education of his only son, who had already displayed exceptional ability. Pascal was kept at home in order to ensure his not being overworked, and with the same object it was directed that his education should be at first confined to the study of languages, and should not include any mathematics. This naturally excited the boy's curiosity, and one day, being then twelve years old, he asked in what geometry consisted. His tutor replied that it was the science of constructing exact figures and of determining the proportions between their different parts. Pascal, stimulated no doubt by the injunction against reading it, gave up his play-time to this new study, and in a few weeks had discovered for himself many properties of figures, and in particular the proposition that the sum of the angles of a triangle is equal to two right angles.

His father, struck by this display of ability, gave him a copy of Euclid's Elements, a book which Pascal read with avidity and soon mastered.

*“The Knowledge of God is very far from the love of Him”*Before Pascal turned 13 he had proven the 32nd proposition of Euclid and discovered an error in Rene Descartes geometry. At 16, Pascal began preparing to write a study of the entire field of mathematics, but his father required his time to hand total long columns of numbers. Pascal began designing a calculating machine, which he finally perfected when he was thirty, the pascaline, a beautiful handcrafted box about fourteen by five by three inches. The first accurate mechanical calculator was born. The Pacaline was not a commercial success in Pascal's lifetime; it could do the work of six accountants and people feared it would create unemployment.

At the age of fourteen he was admitted to the weekly meetings of Roberval, Mersenne, Mydorge, and other French geometricians; from which, ultimately, the French Academy sprung. At sixteen Pascal wrote an essay on conic sections; and in 1641, at the age of eighteen, he constructed the first arithmetical machine, an instrument which, eight years later, he further improved. His correspondence with Fermat about this time shows that he was then turning his attention to analytical geometry and physics. He repeated Torricelli's experiments, by which the pressure of the atmosphere could be estimated as a weight, and he confirmed his theory of the cause of barometric variations by obtaining at the same instant readings at different altitudes on the hill of Puy-de-Dôme.

In 1650, when in the midst of these researches, Pascal suddenly abandoned his favorite pursuits to study religion, or, as he says in his Pensées, "contemplate the greatness and the misery of man''; and about the same time he persuaded the younger of his two sisters to enter the Port Royal society.

At the age of fourteen he was admitted to the weekly meetings of Roberval, Mersenne, Mydorge, and other French geometricians; from which, ultimately, the French Academy sprung. At sixteen Pascal wrote an essay on conic sections; and in 1641, at the age of eighteen, he constructed the first arithmetical machine, an instrument which, eight years later, he further improved. His correspondence with Fermat about this time shows that he was then turning his attention to analytical geometry and physics. He repeated Torricelli's experiments, by which the pressure of the atmosphere could be estimated as a weight, and he confirmed his theory of the cause of barometric variations by obtaining at the same instant readings at different altitudes on the hill of Puy-de-Dôme.

In 1650, when in the midst of these researches, Pascal suddenly abandoned his favorite pursuits to study religion, or, as he says in his Pensées, "contemplate the greatness and the misery of man''; and about the same time he persuaded the younger of his two sisters to enter the Port Royal society.

*“Let us weigh the gain and the loss, in wagering that God is. Consider these alternatives: if you win, you win all, if you lose you lose nothing. Do not hesitate, then, to wager that he is.”*In 1653 he had to administer his father's estate. He now took up his old life again, and made several experiments on the pressure exerted by gases and liquids; it was also about this period that he invented the arithmetical triangle, and together with Fermat created the calculus of probabilities. He was meditating marriage when an accident again turned the current of his thoughts to a religious life. He was driving a four-in-hand on November 23, 1654, when the horses ran away; the two leaders dashed over the parapet of the bridge at Neuilly, and Pascal was saved only by the traces breaking. Always somewhat of a mystic, he considered this a special summons to abandon the world. He wrote an account of the accident on a small piece of parchment, which for the rest of his life he wore next to his heart, to perpetually remind him of his covenant; and shortly moved to Port Royal, where he continued to live until his death in 1662. Constitutionally delicate, he had injured his health by his incessant study; from the age of seventeen or eighteen he suffered from insomnia and acute dyspepsia, and at the time of his death was physically worn out.

His famous Provincial Letters directed against the Jesuits, and his Pensées, were written towards the close of his life, and are the first example of that finished form which is characteristic of the best French literature. The only mathematical work that he produced after retiring to Port Royal was the essay on the cycloid in 1658. He was suffering from sleeplessness and toothache when the idea occurred to him, and to his surprise his teeth immediately ceased to ache. Regarding this as a divine intimation to proceed with the problem, he worked incessantly for eight days at it, and completed a tolerably full account of the geometry of the cycloid.

Pascal was dismayed and disgusted by society's reactions to his machine and completely renounced his interest in science and mathematics, devoting the rest of his life to God. He is best known for his collection of spiritual essays, Les Pensées. Even though the basic design of the Pascaline lived on in mechanical calculators for over three hundred years. As a counting machine, the Pascaline was not superseded until the invention of the electronic calculating machine. "The arithmetical machine produces effects which approach nearer to thought than all the actions of animals", wrote Pascal in Pensées, (a -customarily- lengthy piece) "but it does nothing which would enable us to attribute will to it, as to animals." Pascal, genius by any measure, died of a brain hemorrhage at the age of 39.

His famous Provincial Letters directed against the Jesuits, and his Pensées, were written towards the close of his life, and are the first example of that finished form which is characteristic of the best French literature. The only mathematical work that he produced after retiring to Port Royal was the essay on the cycloid in 1658. He was suffering from sleeplessness and toothache when the idea occurred to him, and to his surprise his teeth immediately ceased to ache. Regarding this as a divine intimation to proceed with the problem, he worked incessantly for eight days at it, and completed a tolerably full account of the geometry of the cycloid.

Pascal was dismayed and disgusted by society's reactions to his machine and completely renounced his interest in science and mathematics, devoting the rest of his life to God. He is best known for his collection of spiritual essays, Les Pensées. Even though the basic design of the Pascaline lived on in mechanical calculators for over three hundred years. As a counting machine, the Pascaline was not superseded until the invention of the electronic calculating machine. "The arithmetical machine produces effects which approach nearer to thought than all the actions of animals", wrote Pascal in Pensées, (a -customarily- lengthy piece) "but it does nothing which would enable us to attribute will to it, as to animals." Pascal, genius by any measure, died of a brain hemorrhage at the age of 39.