Blaise Pascal (19 June 1623 – 19 August 1662) was a French mathematician, physicist, inventor, philosopher, and Catholic writer.

Pascal was a child prodigy who was educated by his father, Étienne Pascal, a tax collector in Rouen. His earliest mathematical work focused on projective geometry; he wrote a significant treatise on conic sections at the age of 16. He later corresponded with Pierre de Fermat on probability theory, strongly influencing the development of modern economics and social science. In 1642, he began pioneering work on calculating machines (called Pascal's calculators and later Pascalines), helping him become one of the first two inventors of the mechanical calculator.

Like his contemporary René Descartes, Pascal was also a pioneer in the natural and applied sciences. Pascal wrote in defense of the scientific method and produced several important discoveries. He made significant contributions to the study of fluids and clarified the concepts of pressure and vacuum by generalizing the work of Evangelista Torricelli. The SI unit for pressure is named for Pascal. Following Torricelli and Galileo Galilei, in 1647, he rebutted the ideas of Aristotle and Descartes, who claimed that nature abhors a vacuum.

He is also credited as the inventor of modern public transportation, having established the carrosses à cinq sols, the first modern public transport service, shortly before his death in 1662.

In 1646, he and his sister Jacqueline joined a religious movement within Catholicism known by its critics as Jansenism. After a religious experience in late 1654, he began writing influential works on philosophy and theology. His two most famous works from this period are the Lettres provinciales and the Pensées, the former addressing the conflict between Jansenists and Jesuits. The Pensées includes Pascal's wager, originally called the Discourse on the Machine, a probabilistic argument for why one should believe in God. In that year, he also wrote an important treatise on the arithmetical triangle. Between 1658 and 1659, he studied the cycloid and its use in calculating the volume of solids. After several years of illness, Pascal died in Paris at the age of 39.

Early life and education

Blaise Pascal was born in Clermont-Ferrand, a city in France’s Auvergne region, near the Massif Central. He lost his mother, Antoinette Begon, when he was three years old. His father, Étienne Pascal, was also an amateur mathematician and a local judge who belonged to the "Noblesse de Robe." Pascal had two sisters: Jacqueline, the younger, and Gilberte, the older.

In 1631, five years after his wife’s death, Étienne moved with his children to Paris. The family soon hired Louise Delfault, a maid who became an important part of their lives. Étienne, who never married again, decided to educate his children himself.

As a young boy, Pascal showed great intellectual talent, especially in mathematics and science. Étienne tried to stop his son from studying math, but by age 12, Pascal had rediscovered, on his own, the first 32 geometric ideas from Euclid using charcoal on a tile floor. Because of this, Étienne gave him a copy of Euclid’s Elements.

Pascal was especially interested in a work by Desargues about conic sections. At 16, he wrote a short mathematical paper called Essai pour les coniques (Essay on Conics), which explained a rule now known as Pascal’s theorem. This rule states that if a hexagon is drawn inside a circle or conic shape, the three points where opposite sides cross will always lie on a straight line, called the Pascal line.

Pascal’s work was so advanced that René Descartes believed Étienne had written it. When Mersenne confirmed it was Pascal’s work, Descartes said, “It is not strange that he has offered demonstrations about conics more appropriate than those of the ancients,” but added, “other matters related to this subject can be proposed that would scarcely occur to a 16-year-old child.”

At the time, government jobs in France could be bought and sold. In 1631, Étienne sold his position as second president of the Cour des Aides for 65,665 livres. The money was invested in a government bond that provided a steady income, allowing the family to live comfortably in Paris. However, in 1638, Cardinal Richelieu defaulted on the bond, reducing Étienne’s wealth from nearly 66,000 livres to less than 7,300.

Because of his disagreement with Richelieu’s financial policies, Étienne was forced to leave Paris, leaving his children in the care of Madame Sainctot, a well-known woman who hosted an influential salon in France. Later, when Jacqueline performed well in a play attended by Richelieu, Étienne was pardoned. Eventually, he regained favor with the Cardinal and was appointed the king’s commissioner of taxes in Rouen, a city with chaotic tax records due to uprisings.

In 1642, to help his father with the difficult task of calculating taxes, Pascal, who was not yet 19, created a mechanical calculator called the Pascaline. This device could add and subtract. Eight Pascalines are known to have survived, with four displayed at the Musée des Arts et Métiers in Paris and one at the Zwinger Museum in Dresden, Germany.

Although the Pascaline was an early example of mechanical calculation and influenced future developments in computing, it was not commercially successful. It was too expensive and difficult to use, making it more of a luxury item for the wealthy. Pascal also gave one of the first Pascalines to Christina, Queen of Sweden, in 1632. Over the next decade, he improved his design and built about 50 machines, with 20 completed over the following 10 years.

Mathematics

In 1654, encouraged by his friend the Chevalier de Méré, Pascal wrote letters to Pierre de Fermat about problems related to gambling. Their collaboration led to the creation of the mathematical theory of probability. The specific problem involved two players who wanted to end a game early and split the money fairly based on their chances of winning from that point. This discussion introduced the idea of expected value. John Ross wrote, "Probability theory and its discoveries changed how people understand uncertainty, risk, decision-making, and how individuals and societies can influence future events." In his work Pensées, Pascal used a probabilistic argument called Pascal's wager to support belief in God and a virtuous life. However, Pascal and Fermat did not fully develop the field of probability. Christiaan Huygens, learning about their work, wrote the first book on probability. Later, Abraham de Moivre and Pierre-Simon Laplace continued to expand the theory. The work of Fermat and Pascal on probability calculations provided important ideas for Leibniz’s development of calculus.

Pascal’s Traité du triangle arithmétique, written in 1654 but published later in 1665, described a simple table for organizing binomial coefficients. He called this table the "arithmetical triangle," now known as Pascal’s triangle. The triangle can also be shown as follows:

Pascal defined the numbers in the triangle using a rule based on previous numbers. He called the number in the (m + 1)th row and (n + 1)th column tₘₙ. The rule is tₘₙ = tₘ₋₁,ₙ + tₘ,ₙ₋₁, for m = 0, 1, 2, … and n = 0, 1, 2, … The boundary conditions are tₘ,₋₁ = 0 and t₋₁,ₙ = 0 for m = 1, 2, 3, … and n = 1, 2, 3, … The starting number, t₀₀, is 1. Pascal included a proof of this in his work.

In the same treatise, Pascal clearly stated the principle of mathematical induction. In 1654, he proved Pascal’s identity, which connects the sums of the p-th powers of the first n positive integers for p = 0, 1, 2, …, k.

That same year, Pascal had a religious experience and largely stopped working on mathematics.

In 1658, while suffering from a toothache, Pascal began studying problems related to the cycloid. When his toothache stopped, he saw this as a sign from heaven to continue his research. Eight days later, he finished his essay and proposed a contest to share his findings.

Pascal asked three questions about the cycloid, including its center of gravity, area, and volume. Winners would receive prizes of 20 and 40 Spanish doubloons. Pascal, Gilles de Roberval, and Pierre de Carcavi judged the contest. The two submissions, by John Wallis and Antoine de Lalouvère, were not judged to be correct. While the contest was ongoing, Christopher Wren sent Pascal a proposal for proving the cycloid’s length. Roberval claimed he had known about the proof for years. Wallis later published Wren’s proof, giving Wren credit for the first published solution.

Physics

Blaise Pascal made important contributions to physics, especially in the study of fluids and pressure. In honor of his work, the SI unit of pressure and Pascal's law (a key idea in hydrostatics) are named after him. He created an early version of a roulette wheel while trying to build a perpetual motion machine. Today, Blaise Pascal Chairs are given to top scientists who do research in the Ile de France region.

Pascal studied how liquids move and behave under pressure. He invented the hydraulic press (which uses liquid pressure to increase force) and the syringe. He showed that hydrostatic pressure depends on the height of the liquid, not its weight. He supposedly tested this by attaching a thin tube to a full barrel of water and filling the tube to the third floor of a building. This caused the barrel to leak, an experiment now called Pascal's barrel experiment.

In 1647, Pascal learned about Evangelista Torricelli’s work with barometers. Torricelli placed a tube filled with mercury upside down in a bowl of mercury. Pascal wondered what force kept the mercury in the tube and what filled the space above it. At the time, many scientists, including Descartes, believed space was filled with invisible matter (a plenum), not a vacuum. This idea came from Aristotle’s belief that all motion required a substance. Light passing through the glass tube also suggested a substance like aether filled the space.

After more experiments, Pascal wrote New experiments with the vacuum in 1647. This work explained how air pressure supports different liquids and showed that the space above a liquid column in a barometer was a vacuum. He later published Account of the great experiment on equilibrium in liquids in 1648.

Torricelli’s experiments showed air pressure equals the weight of 30 inches of mercury. If air has weight, Earth’s atmosphere must have a maximum height. Pascal reasoned that air pressure should be lower at higher altitudes. He lived near the Puy de Dôme mountain but was too sick to climb it. In 1648, Florin Périer, husband of Pascal’s sister, climbed the mountain to test this idea. Périer’s report confirmed that air pressure decreases with height.

Pascal repeated the experiment in Paris by taking a barometer to the top of a church tower, about 50 meters high. The mercury level dropped. He found that climbing 7 fathoms (a unit of length) lowers the mercury level by half a line. Note: Pascal used pouce and ligne for "inch" and "line," and toise for "fathom."

In a letter to Étienne Noël, who believed in the plenum, Pascal wrote: "To prove a hypothesis is correct, it’s not enough if all observations match it. If even one observation contradicts it, the hypothesis is false."

Adult life: religion, literature, and philosophy

In the winter of 1646, Pascal’s 58-year-old father broke his hip after slipping on an icy street in Rouen. Because of his age and the limited medical knowledge of the 17th century, a broken hip could be very serious, maybe even deadly. Rouen had two of France’s best doctors, Deslandes and de la Bouteillerie. Pascal’s father refused to let anyone else treat him, and this was a good choice because the man survived and could walk again. However, recovery took three months, during which the doctors visited him often.

Both doctors were followers of Jean Guillebert, who supported a small group within Catholic teachings called Jansenism. This group, though small, was gaining influence in France at the time. It promoted strict religious beliefs based on the teachings of Augustine. After his father’s treatment, Blaise Pascal borrowed books written by Jansenist authors from the doctors. Around this time, Pascal had a spiritual awakening and began writing about religious topics the following year.

For a few years, Pascal became less interested in religion and focused on worldly matters (1648–54). His father died in 1651 and left his inheritance to Pascal and his sister, Jacqueline, who Pascal helped care for. Jacqueline announced she would join a Jansenist convent called Port-Royal. Pascal was deeply affected by her decision, though he was more sad about his own poor health than her choice.

By late October 1651, Pascal and Jacqueline reached an agreement. In exchange for an annual payment, Jacqueline gave her share of the inheritance to Pascal. Gilberte, Pascal’s other sister, had already received her inheritance as a dowry. In early January 1652, Jacqueline left for Port-Royal. According to Gilberte, Pascal went to his room without seeing Jacqueline, who was waiting in the convent’s parlor. In early June 1653, after much urging from Jacqueline, Pascal gave his sister’s inheritance to Port-Royal, which he now considered “a cult.” With two-thirds of his father’s estate gone, Pascal, then 29 years old, faced a life of limited financial resources.

For a time, Pascal lived as a bachelor. During visits to his sister at Port-Royal in 1654, he showed little interest in worldly matters but was not drawn to religious devotion.

On November 23, 1654, between 10:30 and 12:30 at night, Pascal had a powerful religious experience. He immediately wrote a short note to himself, beginning with “Fire. God of Abraham, God of Isaac, God of Jacob, not of the philosophers and the scholars…” and ending with a quote from Psalm 119:16: “I will not forget thy word. Amen.” He kept this note sewn into his coat and moved it whenever he changed clothes. A servant found it by accident after his death. This note is now called the Memorial. Some scholars disagree about whether a carriage accident caused the experience described in the Memorial. After this event, Pascal’s religious beliefs grew stronger. In January 1655, he spent two weeks at a convent in Port-Royal. For the next four years, he traveled regularly between Port-Royal and Paris. Shortly after his conversion, he began writing his first major religious work, the Provincial Letters.

Literature

Blaise Pascal is considered one of the most important writers of the French Classical Period and is still studied today as one of the greatest French prose writers. Seymour Eaton called him "the greatest of all French thinkers." His use of satire and wit influenced later writers who argued about important issues.

Beginning in 1656–57, Pascal published a famous attack on casuistry, a method of ethical reasoning used by Catholic thinkers in the early modern period, especially the Jesuits and Antonio Escobar. Pascal criticized casuistry as a way to use complex arguments to justify moral weakness and sins. The 18-letter series, published between 1656 and 1657 under the name Louis de Montalte, angered King Louis XIV. The king ordered the book to be destroyed in 1660. In 1661, during the formulary controversy, the Jansenist school at Port-Royal was condemned and closed. Those connected to the school had to sign a 1656 papal statement condemning Jansen’s teachings as heretical. Pascal’s final letter in 1657 challenged Pope Alexander VII directly. Even though the pope publicly opposed Pascal, he was convinced by Pascal’s arguments.

The Provincial Letters were popular as a literary work. Pascal’s use of humor, mockery, and sharp satire made the letters widely read and influenced later French writers like Voltaire and Jean-Jacques Rousseau.

Pascal is famous for his apology for writing a long letter, as he had not had time to write a shorter one. From Letter XVI, as translated by Thomas M'Crie: "Reverend fathers, my letters were not usually so long or so frequent. Lack of time must be my excuse for both. This letter is long simply because I had no time to make it shorter."

Charles Perrault praised the Letters, saying they showed "purity of language, nobility of thought, solidity in reasoning, finesse in raillery, and an agrément not found elsewhere." Émile Faguet called Pascal "one of the greatest of French philosophers." Pascal was a dualist and scientist who followed the ideas of René Descartes.

However, Pascal focused most on the philosophy of religion, saying Descartes’ philosophy was "useless and uncertain." He wrote, "I cannot forgive Descartes. In all his philosophy, he would have been willing to ignore God, but he couldn’t avoid letting him start the world in motion; afterwards, he didn’t need God anymore."

Pascal opposed the rationalism of Descartes, saying "reason can decide nothing here," and also rejected empiricism, preferring fideism. For Pascal, God’s nature was such that proofs could not reveal Him. Humans are "in darkness and estranged from God" because "he has hidden Himself from their knowledge." Pascalian theology, as described by Wood, suggests humans are "born into a duplicitous world that shapes us into duplicitous subjects and so we find it easy to reject God continually and deceive ourselves about our own sinfulness."

Pascal’s most influential theological work, the Pensées ("Thoughts"), is widely considered a masterpiece and a landmark in French prose. Sainte-Beuve praised a section of the Pensées (Thought #72) as the finest pages in the French language. Will Durant called the Pensées "the most eloquent book in French prose."

The Pensées was not completed before Pascal’s death. It was meant to be a detailed and organized defense of the Christian faith, originally titled Apologie de la religion Chrétienne ("Defence of the Christian Religion"). After his death, the scattered notes were published in 1669 as Pensées de M. Pascal sur la religion, et sur quelques autres sujets ("Thoughts of M. Pascal on religion, and on some other subjects") and quickly became a classic.

One strategy of the Apologie was to use the conflicting philosophies of Pyrrhonism and Stoicism, as represented by Montaigne and Epictetus, to push unbelievers into despair and confusion until they accepted God.

Pascal’s major contribution to mathematics was De l'Esprit géométrique ("Of the Geometrical Spirit"), originally written as a preface to a geometry textbook for the Petites écoles de Port-Royal. The work was not published until over a century after his death. Here, Pascal explored how truths are discovered, arguing that the ideal method would be to base all propositions on already established truths. However, he claimed this was impossible because established truths would require other truths to support them. Therefore, Pascal believed the geometric method, which assumes certain principles and builds other ideas from them, was as perfect as possible, even though no one could be certain if the assumed principles were true.

In De l'Esprit géométrique, Pascal also developed a theory of definition. He distinguished between definitions created by writers as labels and definitions that are naturally understood by everyone because they clearly refer to something. The second type is characteristic of essentialism. Pascal argued that only the first type of definition was important for science and mathematics, and that these fields should follow Descartes’ philosophy of formalism.

In De l'Art de persuader ("On the Art of Persuasion"), Pascal examined the axiomatic method in geometry, specifically how people come to accept the axioms that support later conclusions. He agreed with Montaigne that achieving certainty through human methods was impossible. He argued that these principles can only be grasped through intuition, and that this fact showed the need to submit to God when seeking truth.

Last works and death

T. S. Eliot once described Pascal during this time as "a man of the world among ascetics, and an ascetic among men of the world." Pascal believed that suffering was natural and necessary for people. In 1659, Pascal became very ill. During his final years, he often refused help from doctors, saying, "Do not pity me. Sickness is the natural state of Christians, because through it we experience suffering, the loss of worldly pleasures, and freedom from life's passions, without ambition or greed, always expecting death." To follow Jesus’ example of spiritual poverty, Pascal said that if God allowed him to recover, he would dedicate his life to helping the poor.

In 1661, Louis XIV banned the Jansenist movement at Port-Royal. In response, Pascal wrote one of his last works, Écrit sur la signature du formulaire ("Writ on the Signing of the Form"), encouraging Jansenists to remain firm in their beliefs. Later that year, Pascal’s sister Jacqueline died, which led him to stop arguing about Jansenism.

Pascal’s final major achievement was creating one of the first land-based public transportation systems, the carrosses à cinq sols. This system used horse-drawn carriages with multiple seats to carry passengers along five fixed routes. Pascal also established rules for public transport, including fixed prices (five sols, which is why it was named) and fixed schedules, even when no passengers were present. Although the system was not successful financially and ended by 1675, Pascal is often called the inventor of public transportation.

In 1662, Pascal’s illness worsened, and his emotional state worsened after his sister’s death. Knowing his health was failing, he wanted to move to a hospital for those with serious illnesses, but his doctors said he was too weak to be moved. On August 18, 1662, in Paris, Pascal had seizures and received last rites. He died the next morning, saying, "May God never abandon me." He was buried in the cemetery of Saint-Étienne-du-Mont.

An autopsy after his death showed serious problems in his stomach and other abdominal organs, as well as brain damage. However, the exact cause of his poor health was never confirmed. Experts have suggested it may have been tuberculosis, stomach cancer, or a mix of both. The headaches Pascal experienced were likely caused by the brain damage.

Legacy

One of the universities in Clermont-Ferrand, France—Université Blaise Pascal—is named after Blaise Pascal. A school in Lubumbashi, Democratic Republic of the Congo, called Établissement scolaire français Blaise-Pascal, is also named after him.

The 1969 film My Night at Maud's by Eric Rohmer is inspired by Pascal's writings. A biographical film titled Blaise Pascal, directed by Roberto Rossellini, was shown on Italian television in 1971. Pascal was the subject of the first episode of the 1984 BBC Two documentary Sea of Faith, hosted by Don Cupitt. The chameleon in the animated movie Tangled is named Pascal.

A programming language is named Pascal. In 2014, Nvidia introduced a new chip design called Pascal, named after him. The first graphics cards using this design were released in 2016.

In the 2017 video game Nier: Automata, several characters are named after famous philosophers. One character, Pascal, is a peaceful, thinking machine who helps other machines live in harmony with androids they are fighting. He also acts as a caring figure for machines learning to embrace their individuality.

The otter in the Animal Crossing video game series is named Pascal.

A minor planet, numbered 4500, is named Pascal in his honor.

In 1967, Pope Paul VI quoted Pascal’s writings in his letter Populorum progressio. In 2023, Pope Francis released a formal letter titled Sublimitas et miseria hominis, dedicated to Blaise Pascal, to mark the 400th anniversary of his birth.

Blaise Pascal influenced French sociologist Pierre Bourdieu, who wrote a book titled Pascalian Meditations in 1997, and French philosopher Louis Althusser.

Works

• Essai pour les coniques [Essay on conics] (1639)
• Experiences nouvelles touchant le vide [New experiments with the vacuum] (1647)
• Récit de la grande expérience de l'équilibre des liqueurs [Account of the great experiment on liquid balance] (1648)
• Traité du triangle arithmétique [Treatise on the arithmetical triangle] (written around 1654; published 1665)
• Lettres provinciales [The Provincial Letters] (1656–57)
• De l'Esprit géométrique [On the Geometrical Spirit] (1657 or 1658)
• Écrit sur la signature du formulaire (1661)
• Pensées [Thoughts] (unfinished at death; published 1670)
• Discours sur les passions de l'amour [Discourse on the Passion of Love] (possibly a forgery)
• On the Conversion of the Sinner
• Ecrits sur la grace [Writings on Grace]