Blaise Pascal: The Boy Who Wanted Reasons

A boy of about twelve is alone in the room in Paris where he is allowed to play. He has a piece of charcoal in his hand, and he is drawing on the floor tiles.

He is not drawing pictures. He is drawing shapes: circles, triangles, straight lines, and then more lines between them. He is trying to work out how to make a circle that is perfectly round, a triangle whose sides and angles are all equal, and how one shape relates to another. He does not know the proper names for any of these things, because nobody has ever taught him. So he has made up his own. A circle he calls a “round”. A line he calls a “bar”. From these he has built his own definitions, then his own rules, and from the rules his own proofs, each one leading to the next.

He is so absorbed that he does not hear the door open. His father walks in and stands behind him for a long while before the boy notices.

The boy’s name is Blaise Pascal, and he is not supposed to be doing this. His father has strictly forbidden him to study mathematics, has hidden all the books on it, and has told him not even to think about it. Both of them are startled. When his father asks what he is doing, Blaise explains that he is looking for a way to prove a particular thing. His father realises, with a shock, that it is the thirty-second proposition of the first book of Euclid, the famous ancient textbook of geometry: the proof that the three angles of any triangle add up to two right angles. When his father asks how he got there, the boy explains the step before it, and the step before that, all the way back to his “rounds” and “bars”.

His father leaves the room without a word. He goes straight to the house of a friend, a learned man named Le Pailleur, and stands there so stunned that the friend, seeing tears in his eyes, is alarmed. “I am not weeping for sorrow, but for joy,” his father tells him.

We know this story because Blaise’s older sister, Gilberte, wrote it down in a short life of her brother after he died. Some historians think it may have grown a little in the telling; a big sister proud of a famous brother is not the most neutral witness. But no one doubts the heart of it. Blaise Pascal had a mind that would not stop asking why, and would not be satisfied with anything less than a real answer.

That mind would one day make him famous across Europe. It would also bring him, by a long road, to a night when he found that the most important answers were not the kind you can prove on a floor in charcoal.

A Father’s Plan

Blaise was born on 19 June 1623 in Clermont, a town in the volcanic hills of the Auvergne in central France. His father, Étienne Pascal, was a senior royal official in the tax courts and a gifted amateur mathematician. His mother, Antoinette Begon, died when Blaise was three. He had two sisters: Gilberte, three years older, and Jacqueline, two years younger, who was nearly as brilliant as he was.

Étienne never remarried. Instead, he decided to educate his son himself. In 1631, when Blaise was eight, he moved the family to Paris so that he could give himself to the task. Blaise never went to school or college. Everything he learned came from his father, from books, and from his own restless head.

Étienne’s plan was careful. He did not want to overload the boy, so Latin would wait until Blaise was twelve. Meanwhile, he talked with him about everything: how languages work, why grammar has rules, the strange effects of nature, like gunpowder. And here, according to Gilberte, the boy showed what kind of mind he had. She wrote that “he wanted to know the reason for everything.” When his father did not know, or gave the usual answers that were really just ways of avoiding the question, Blaise was not satisfied. He went looking for himself, and would not let go until he found a reason that held. In all things, she said, “truth was the sole object of his mind.”

Once, at dinner, someone struck an earthenware dish with a knife. It rang loudly, and then went silent the moment a hand was laid on it. Most people would not have noticed. Blaise wanted to know why. He began experimenting with sounds, and at about eleven or twelve he wrote a short treatise about them.

Mathematics was the one thing his father kept from him, because he feared it would swallow everything else. Blaise kept begging. His father told him only that geometry was the way of making figures correctly and finding the proportions between them, and then forbade him to think about it. It was a bit like telling a hungry person what food is and then locking the kitchen. That is how the charcoal came out.

Among the Mathematicians

After the day on the playroom floor, Étienne gave up. He handed his son a copy of Euclid’s Elements to read in his free time. Blaise worked through it, Gilberte says, without needing anyone to explain it.

Soon he was going with his father to a weekly gathering of the best scientific minds in Paris, which met around a friar named Marin Mersenne. Mathematicians and scientists brought their latest work there to be examined, and problems arrived by letter from Italy, Germany and further afield. In that room of grown men, the teenage Blaise held his own. He brought new work of his own, and sometimes spotted mistakes that the others had missed.

Picture what that must have been like. Most people your age are not asked for their opinion by the leading experts of their country. Blaise was. It is easy to see how a young person in that position might become proud, and it would be a long time before he understood how proud he was.

At sixteen he wrote an essay on conic sections, the curves you get when you slice through a cone at different angles, such as circles, ellipses and parabolas. A short summary was printed in 1640, and one of its results is still taught as “Pascal’s theorem”. The older mathematicians were astonished. Gilberte says some of them said nothing so powerful had been seen since Archimedes, the greatest mathematician of the ancient world. That may be a sister’s pride again, but the essay is real, and it was genuinely new.

All this time he was still doing his Latin and Greek, and talking with his father about logic and physics over meals.

And what about God? This is the surprising part. In a book about young people who wrestled with doubt, Blaise Pascal’s teenage years contain very little of it. Gilberte says he never went through a phase of mocking religion, as many clever young men of his day did. His father had given him a rule: whatever is an object of faith cannot be an object of reason. Faith was one room; science was another; and the boy who demanded reasons for everything in the second room did not ask many questions in the first. He went to Mass, believed what the Church taught, and gave his mind to mathematics.

It was a respectful faith, and a sincere one. But it was kept in a box. Blaise had not yet asked whether the God he believed in had any claim on the rest of his life: on his ambition, his pride, his brilliant, hungry mind. That question was still waiting for him.

Trouble and a Machine

When Blaise was about fifteen, the family’s comfortable life was suddenly shaken. In 1638 the government of Cardinal Richelieu, the most powerful man in France, cut the interest it paid on government bonds, where Étienne had invested much of his money. Étienne joined a protest, and when the authorities began arresting protesters, he went into hiding. For a time the children were left in Paris without him.

The family’s rescue came from Jacqueline, then about thirteen. She was a talented young poet and performer, and in 1639 she acted in a children’s play in front of Richelieu himself. Afterwards she recited verses asking him to pardon her father. The cardinal was charmed, and he did. More than that, he gave Étienne a new job: overseeing the collection of taxes in Normandy, based in the city of Rouen. Around the start of 1640, the family moved there.

Tax collection meant endless sums, done by hand with pen and counters, often late into the night. Blaise, now about eighteen, watched his father labouring over columns of figures and asked another question: could a machine do this?

He set out to build one. It was a box of gears and wheels in which numbers were dialled in and the machine carried the tens by itself, so that it could add and subtract without its user needing to know any arithmetic. Gilberte called it “something new in nature”: a science that had lived only in the mind, now done by a machine. The idea came to him easily. The hard part, she says, was making the craftsmen understand what he wanted. It took him around two years to get it working, and he went on improving it for years afterwards, through dozens of versions. A handful of his calculating machines still survive in museums today.

But that labour came at a cost. From around this time, his health began to break down: headaches, stomach pain, and later times when he could barely walk. He told his family that “since the age of eighteen he had not passed a day without pain.” For the rest of his life, his brilliant mind would have to work inside a body that was always hurting.

The Winter of the Broken Hip

The question that had been waiting for him arrived in January 1646, in an unlikely way. Étienne slipped on the ice in Rouen and badly injured his hip. Two brothers from a local noble family, the Deschamps brothers, who were skilled at setting bones, came to treat him, and stayed in the house for about three months while he recovered.

They were devout men, part of a renewal movement in the French Catholic Church centred on the convent of Port-Royal near Paris. Its enemies later called it “Jansenism”. The movement taught, much as Augustine had taught twelve centuries before, that human beings are helpless to save themselves and depend completely on the grace of God, and it called Christians to a serious, wholehearted life rather than a respectable Sunday religion. The brothers had brought books, and they talked about them. The Pascals began to read.

For Blaise, who turned twenty-three that summer, it was like a door opening in a wall he had not known was there. For the first time he saw that Christianity was not one room among many, but a claim on the whole house. Gilberte describes it this way: he understood “that the Christian religion obliges us to live for God alone and to have no other object but him.” He began to turn away from what she called his “researches”. Soon the whole family had been drawn in. Even Étienne, the father who had taught him everything, began to follow his son’s lead.

Historians often call this Pascal’s “first conversion”, because something even deeper was to happen eight years later. But it was real. A young man whose whole identity rested on his mind had been confronted with the possibility that his mind was not the most important thing about him.

Certain and Young

It would be nice to say that Blaise immediately became humble and gentle. He did not. Like many people who have just discovered something important, he became very sure of himself.

In 1647, not long after his awakening, he and two friends went to hear a man in Rouen who was teaching a new philosophy. When the man drew conclusions about Christian doctrine that they believed were false, the three young men warned him, then reported him to the church authorities, and kept pressing until he was made to withdraw his views. Gilberte tells the story with approval. Readers today may feel less comfortable. Pascal was right to care about truth, but there is something hard about three clever young men hunting down an older one’s mistakes. Zeal and humility do not always arrive at the same time.

Nor did he give up science as completely as his sister suggests. Those same years, 1646 to 1648, were the years of his most famous experiments. An Italian scientist, Torricelli, had shown that a glass tube of mercury, turned upside down in a dish, leaves an empty space at the top. Almost everyone at the time believed, following the ancient philosopher Aristotle, that “nature abhors a vacuum” and that truly empty space could not exist. Pascal tested the idea again and again, with tubes of water and wine and mercury, and then in 1648 had his brother-in-law, Florin Périer, carry a tube of mercury up the Puy de Dôme, a mountain near Clermont. As Périer climbed, the mercury fell. The weight of the air was pressing it up, and there was less air above it at the top. The ancient idea had to go.

That is the young Pascal in a single picture: a man who would not accept an idea, however ancient and respected, just because everyone believed it. He wanted to test it. Later, writing about faith, he would turn that same honesty on reason itself. “We must know where to doubt, where to feel certain, where to submit,” he wrote. A person who doubts everything, he thought, is as foolish as a person who doubts nothing. The skill is knowing which is which.

What Came After

In 1651 Étienne died. Jacqueline, who had longed for years to join Port-Royal, entered the convent soon afterwards. Blaise, at first, opposed her, partly from loneliness and partly over money, and it caused real pain between them. His doctors told him to rest and amuse himself, and he did. For about three years he moved in fashionable Paris society, made friends with a young duke, and studied games of chance; out of that came his work with Pierre de Fermat that founded the mathematics of probability. Later he looked back on these years as a time when he had drifted from God. They also left him empty, and by 1654 he was visiting Jacqueline in her convent and telling her so.

On the night of Monday 23 November 1654, when he was thirty-one, something happened to him alone in his room, from about half past ten until about half past midnight. He never spoke of it. After he died, a servant found a piece of parchment sewn into the lining of his coat, with a paper inside it, both in his handwriting. He had carried it with him for eight years, sewing it into each new coat. It is known as the Memorial. It is not in our library, and it was written in French, but in one English translation it begins with a single word in capitals, “FIRE”, and then: “God of Abraham, God of Isaac, God of Jacob, not of the philosophers and the learned.” Further down come the words “Joy, joy, joy, tears of joy.” The Memorial also copies out Jesus’ prayer from John’s Gospel, which a modern Bible renders, “Now this is eternal life, that they may know You, the only true God, and Jesus Christ, whom You have sent” (John 17:3).

That was the answer to the question his teenage years had left unasked. The God he had believed in, at a respectful distance, was not a conclusion to be reached by clever people, like a theorem on a floor. He was a living person who could be met, and he was known through Jesus Christ. “We know God only by Jesus Christ,” Pascal later wrote.

The rest of his life was short, and full. He used his brilliance in The Provincial Letters (1656–57), a series of witty anonymous letters defending his friends at Port-Royal and attacking what he saw as a dishonest, easy-going morality. He began a great book to persuade doubters and the indifferent that Christianity was true, starting not with proofs but with the puzzle of human beings: so great and so wretched, so clever and so lost. He never finished it. His illnesses grew worse; he gave away much of what he had to the poor; and he died in Paris on 19 August 1662, aged thirty-nine. Gilberte says almost his last words were, “May God never forsake me!” His friends gathered the scraps of his unfinished book and published them as the Pensées, or “Thoughts”. They have been read by doubters ever since.

The boy who wanted reasons for everything never stopped wanting them. He simply discovered that reason itself has limits, and that the last thing a really honest mind does is to admit it. “The last proceeding of reason,” he wrote, “is to recognise that there is an infinity of things which are beyond it.”

In Their Own Words

“We must know where to doubt, where to feel certain, where to submit.”

— Blaise Pascal, Pensées (published 1670)

Think It Through

1. Blaise’s father tried to keep mathematics from him, and it only made him more curious. Is it ever right to keep a young person from a subject? What happens to questions that are forbidden?
2. As a teenager, Pascal kept faith and reason in separate rooms. What are the advantages and dangers of doing that? Do you tend to do it?
3. Pascal was right to care about truth, but the way he and his friends pursued the teacher in Rouen seems hard. How can someone hold strong convictions without becoming a hunter of other people’s mistakes?
4. “We must know where to doubt, where to feel certain, where to submit.” What is one thing you think it is right to doubt, one thing you feel certain of, and one thing you might need to submit to?

Read More on Ochorus

Pascal’s unfinished masterpiece, the Pensées, is on Ochorus in full; start with the sections “The Misery of Man Without God” and “Of the Necessity of the Wager”. The Life of Blaise Pascal is his sister Gilberte’s memoir, the source of the stories of the charcoal on the floor and the calculating machine. Letters and Minor Works collects his letters, including the long letter he wrote after his father’s death, and his “Prayer to Ask of God the Right Use of Sickness”. The Provincial Letters shows his wit at full stretch. His full biography is on his author page.