Blaise Pascal

• 1. Introduction

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  Blaise Pascal was born on the 19th of June, 1623, in Clermont-Ferrand, in France's Auvergne region by the Massif Central, and he died 39 years later having reshaped mathematics, physics, theology, and literature. He lost his mother, Antoinette Begon, at age three. By 12, without any formal instruction in the subject, he had independently rediscovered the first thirty-two geometric propositions of Euclid, scratching them out with charcoal on a tile floor. At 16, he wrote a treatise on conic sections that René Descartes refused to believe a boy had produced. At 18, he built one of the world's first mechanical calculators. Before dying in Paris in August 1662, he had also founded the first public bus service, corresponded with Pierre de Fermat to birth probability theory, and written works of French prose that critics still rank among the finest the language has ever produced. How does one life contain so many beginnings? And what drove this brilliant, sick, restless man toward God as fiercely as he had once driven himself toward science?

• 2. The Prodigy's Education

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  Étienne Pascal moved his three children from Clermont-Ferrand to Paris in 1631, five years after his wife's death, bringing along a maid named Louise Delfault who became a lasting member of the household. Étienne was an amateur mathematician himself, a local judge, and a member of the Noblesse de Robe, and he decided to educate his children himself. Strangely, he tried to withhold mathematics from young Blaise entirely, apparently fearing it would distract from other studies. The attempt failed spectacularly. The boy deduced Euclidean geometry on his own from first principles, using a tile floor as his notebook, and his father relented and handed him a copy of Euclid's Elements.

  At 16, Pascal encountered the work of Girard Desargues on conic sections and immediately produced a short proof called the Essai pour les coniques, or Essay on Conics. He sent it to Père Mersenne in Paris. It is still known today as Pascal's theorem: if a hexagon is inscribed in a circle or conic, the three intersection points of opposite sides lie on a single line. Descartes, shown the proof, was so skeptical that he told Mersenne the father must have written it. When Mersenne confirmed the author was the son, Descartes offered a grudging half-compliment, writing that while he did not find it strange that Pascal had exceeded the ancients on this subject, there were matters in the field that would scarcely occur to a 16-year-old. The family's finances had, by this point, grown precarious. In 1638, Cardinal Richelieu defaulted on government bonds to fund the Thirty Years' War, collapsing Étienne's investment from nearly 66,000 livres to less than 7,300. Étienne eventually had to flee Paris, leaving his children with a neighbour named Madame Sainctot. It was only when Jacqueline, Pascal's younger sister, performed well in a children's play attended by Richelieu that Étienne was pardoned and restored to favour, later appointed the king's commissioner of taxes in Rouen in 1639.

• 3. The Calculating Machine

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  Rouen's tax records were in utter chaos when Étienne arrived to sort them out, thanks to a history of uprisings in the city. The teenage Pascal was recruited into this exhausting work of calculation and recalculation. In 1642, not yet 19, he set out to build a device that would do the arithmetic for his father. The result was a mechanical calculator capable of addition and subtraction, later called the Pascaline.

  Pascal spent the following decade refining the design, eventually building around 50 machines according to his own account, with 20 finished units constructed. Eight Pascalines are known to have survived: four are held by the Musée des Arts et Métiers in Paris, and one more is at the Zwinger museum in Dresden. Pascal also presented one to Christina, Queen of Sweden. Despite the machine's ingenuity as a forerunner to four centuries of mechanical calculation, and ultimately to computer engineering, it was not a commercial success. It was cumbersome and extraordinarily expensive, making it little more than a status symbol for the wealthy in France and elsewhere in Europe. The Pascaline pointed the way toward the future without quite reaching it on its own terms.

• 4. Pressure, Vacuum, and the Puy de Dome

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  By 1647, Pascal had learned of Evangelista Torricelli's experiments with barometers. Replicating the experiment himself, he found a tube filled with mercury inverted in a bowl of mercury, with an empty space above the mercury column. Most scientists of the day, including Descartes, held to the Aristotelian view that nature abhors a vacuum and that some invisible matter filled all space. Pascal was unconvinced.

  He published Experiences nouvelles touchant le vide, or New Experiments with the Vacuum, that same year, laying out rules for how various liquids respond to air pressure and arguing the space above the mercury column was genuinely empty. Then he went further. If air has weight, he reasoned, Earth's atmosphere must thin with altitude, meaning air pressure should be lower on a mountaintop than at sea level. Pascal lived near the Puy de Dome but his health was too poor to climb it. He enlisted his brother-in-law Florin Périer, husband of his elder sister Gilberte, who finally carried out the experiment on the 19th of September, 1648, after months of what the account describes as friendly but insistent prodding from Pascal. Périer found that the mercury column was shorter at the mountain's summit than at its base, confirming Pascal's prediction. Pascal replicated the result in Paris by climbing the bell tower of the church of Saint-Jacques-de-la-Boucherie, a height of about 50 metres, where the mercury dropped two lines. He calculated that an ascent of 7 fathoms lowers the mercury by half a line. In a letter to Étienne Noël, a defender of the plenum, Pascal articulated a principle of scientific falsifiability: a single contrary phenomenon is sufficient to establish a hypothesis's falsity. The SI unit of pressure bears his name today.

• 5. The Night of Fire

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  In the winter of 1646, Étienne Pascal, then 58, slipped on an icy street in Rouen and broke his hip. Two doctors, Deslandes and de la Bouteillerie, treated him through a three-month recovery. Both men were followers of Jean Guillebert and adherents of Jansenism, a rigorous Augustinian movement within French Catholicism that had earned strong opposition from the Jesuits. Pascal spoke with them at length and began reading Jansenist authors. He experienced what biographers call a first conversion and started writing on theological topics.

  This initial engagement faded. Pascal's father died in 1651, and Pascal entered what biographers describe as his worldly period, lasting until 1654. His sister Jacqueline, to whom Pascal was deeply attached, announced she would become a postulant at the Jansenist convent of Port-Royal. By October of 1651, a settlement had been reached: in exchange for an annual stipend, Jacqueline signed over her portion of the inheritance to her brother. In early January 1652, she left for Port-Royal. In early June 1653, Pascal formally signed over his sister's entire inheritance to Port-Royal as well, leaving the 29-year-old with what his biographers call genteel poverty.

  Then came the 23rd of November, 1654. Between 10:30 and 12:30 at night, Pascal had an intense religious experience and wrote a brief note that began: "Fire. God of Abraham, God of Isaac, God of Jacob, not of the philosophers and the scholars," concluding with Psalm 119:16, "I will not forget thy word. Amen." He sewed the document, now called the Memorial, into his coat, and transferred it whenever he changed clothes. A servant found it by chance after his death. From that night on, Pascal's intellectual life took a different shape, though it never entirely left behind the habits of a mathematician.

• 6. Letters, Satire, and the Pensees

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  Beginning in 1656, Pascal published an 18-letter series under the pseudonym Louis de Montalte, attacking casuistry, the ethical method popular among the Jesuits and particularly associated with Antonio Escobar. Pascal argued that casuistry was nothing more than complex reasoning deployed to justify moral laxity. The letters, later collected as the Provincial Letters, were sharp, satirical, and widely read. Louis XIV was incensed; in 1660 he ordered the book shredded and burned. In 1661, in the midst of what was called the formulary controversy, the Jansenist school at Port-Royal was condemned and closed. Pascal's final letter from 1657 had defied Pope Alexander VII directly, though the source notes that Alexander, while publicly opposing Pascal, was nonetheless persuaded by his arguments.

  The Provincial Letters left a mark on French prose. Charles Perrault wrote of them that everything was there: purity of language, nobility of thought, solidity in reasoning, and finesse in raillery. Voltaire and Jean-Jacques Rousseau were among the later writers shaped by the letters' style. Pascal himself, in Letter XVI, offered an apology that became one of the most quoted lines in French letters: he had not had time to write a shorter letter.

  The Pensées, published posthumously in 1669 from scraps of paper found after Pascal's death, was intended as a sustained defense of the Christian faith under the title Apologie de la religion Chrétienne. It was never completed. Will Durant called it the most eloquent book in French prose. One of its central arguments is Pascal's wager, originally titled the Discourse on the Machine, a probabilistic case for belief in God. The wager drew on the same mathematical instinct that had produced Pascal's work with Fermat on probability in 1654, applying the logic of expected value to matters of faith. In 2023, Pope Francis released an apostolic letter dedicated to Pascal in commemoration of the fourth centenary of his birth.

• 7. Public Transit and the Final Years

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  In January 1655, following his religious conversion, Pascal retreated to Port-Royal for two weeks. For the next four years he travelled regularly between Port-Royal and Paris, writing and corresponding. In 1658, while suffering from a toothache, he began thinking about the cycloid, a curve traced by a point on the rim of a rolling circle. His toothache disappeared, and he interpreted this as a sign to continue. Eight days later he had completed an essay and announced a contest, offering prizes of 20 and 40 Spanish doubloons for the best solutions to three problems about the cycloid's center of gravity, area, and volume. Neither of the two entries, submitted by John Wallis and Antoine de Lalouvère, was judged adequate. Christopher Wren sent Pascal a proof for the rectification of the cycloid during the contest; Wallis later published it in his Tractus Duo, crediting Wren with the first published proof.

  Shortly before his death in 1662, Pascal launched the carrosses à cinq sols, a network of horse-drawn multi-seat carriages running five fixed routes through central Paris. The carriages ran on fixed schedules, charged a fixed price of five sols, and departed even when no passengers had boarded. The lines were not commercially successful and the last one closed by 1675, but he has been credited as the inventor of modern public transportation for establishing those operating principles.

  By 1662, Pascal's illness had become severe. He sought admission to the hospital for incurable diseases, but his doctors declared him too unstable to be moved. In Paris on the 18th of August, 1662, he went into convulsions and received last rites. He died the next morning. His last words were recorded as "May God never abandon me." He was buried in the cemetery of Saint-Étienne-du-Mont. An autopsy found grave damage to his stomach, other abdominal organs, and his brain; the precise cause remained undetermined, with speculation pointing to tuberculosis, stomach cancer, or a combination. A programming language, a unit of pressure, a minor planet designated 4500 Pascal, and an Nvidia microarchitecture whose first graphics cards shipped in 2016 all carry his name.