His Childhood and Early Work

My brother was born at Clermont on the 19th of June in the year 1623. My father's name was Étienne Pascal, president of the Cour des Aides; and my mother's, Antoinette Begon. As soon as my brother was old enough to be talked to, he gave signs of an extraordinary mind by the little retorts he made, very much to the point, but still more by the questions he asked about the nature of things, which surprised everyone. This beginning, which gave such fair hopes, never belied itself; for as he grew he kept increasing in strength of reasoning, so that he was always far beyond his age.

Meanwhile, my mother having died as early as the year 1626, when my brother was only three years old, my father, finding himself alone, applied himself more earnestly to the care of his family; and as he had no other son but this one, his being an only son, together with the great signs of intelligence he recognised in the child, gave him so great an affection for him that he could not bring himself to entrust his education to another, and resolved from that time to teach him himself, as indeed he did, my brother never having entered any college, and never having had any other master than my father.

In the year 1631 my father withdrew to Paris, took us all there, and made his home there. My brother, who was only eight years old, gained a great advantage from this retirement, in view of my father's plan for his upbringing; for there is no doubt that he could not have taken the same care in the provinces, where the duties of his office and the continual company that came to his house would have greatly distracted him; but in Paris he was entirely free; he gave himself wholly to it, and he had all the success that could come of the care of a father as intelligent and as affectionate as a father can be.

His chief maxim in this education was always to keep the child above his work; and it was for this reason that he would not begin to teach him Latin until he was twelve, so that he might learn it with greater ease.

During this interval he did not leave him idle, for he talked with him about everything he saw him capable of understanding. He showed him in a general way what languages were; he showed him how they had been reduced to grammars under certain rules; that these rules had in turn exceptions which people had taken care to note; and that in this way a means had been found of making every language communicable from one country to another.

This general idea cleared his mind and showed him the reason for the rules of grammar, so that when he came to learn it he knew why he was doing so, and he applied himself precisely to the things that most required application.

After this knowledge my father gave him other kinds; he often spoke to him of the extraordinary effects of nature, such as gunpowder, and other things that astonish us when we consider them. My brother took great pleasure in these conversations, but he wanted to know the reason for everything; and since the reasons are not all known, when my father did not give them, or gave those commonly put forward, which are really nothing but evasions, he was not satisfied: for he always had an admirable clearness of mind for discerning what is false; and one may say that always and in all things truth was the sole object of his mind, since nothing could ever satisfy him but the knowledge of it. Thus from his childhood he could yield only to what appeared to him evidently true; so that when he was not given good reasons he looked for them himself, and when he had fastened on something he would not let it go until he had found some reason that could satisfy him. Once, among other occasions, someone at table having struck an earthenware dish with a knife, he noticed that it gave out a loud sound, but that as soon as a hand was laid on it the sound stopped. He wished at once to know the cause, and this experiment led him to make many others on sounds. He observed so many things that he wrote a treatise on them at the age of twelve, which was judged to be altogether well reasoned.

His genius for geometry began to appear when he was still only twelve, through so extraordinary an occurrence that it seems to me well worth relating in detail.

My father was a man learned in mathematics, and through this was acquainted with all the able men in that science, who were often at his house; but since he intended to instruct my brother in languages, and knew that mathematics is a science that fills and greatly satisfies the mind, he did not wish my brother to have any knowledge of it, for fear it should make him neglectful of Latin and the other [sciences] in which he wished to perfect him. For this reason he had put away all the books that dealt with it, and he refrained from speaking of it with his friends in his presence; but this precaution did not prevent the child's curiosity from being aroused, so that he often begged my father to teach him mathematics; but my father refused, holding it out to him as a reward. He promised him that as soon as he knew Latin and Greek he would teach it to him. My brother, seeing this resistance, asked him one day what this science was and what it dealt with: my father told him, in general terms, that it was the means of making figures correctly and of finding the proportions they bore to one another, and at the same time forbade him to speak of it any more or ever to think of it. But this mind, which could not stay within such bounds, no sooner had this simple opening—that mathematics gave the means of making figures that were unfailingly correct—than he began to muse on it by himself in his hours of recreation; and being alone in a room where he was accustomed to play, he would take a piece of charcoal and draw figures on the floor tiles, seeking ways to make, for example, a perfectly round circle, a triangle whose sides and angles were all equal, and other such things. He found all this out by himself; then he sought the proportions of the figures to one another. But as my father had taken such great care to hide all these things from him, he did not even know their names. He was obliged to make up definitions for himself; he called a circle a “round,” a line a “bar,” and so with the rest. After these definitions he made himself axioms, and finally he made perfect demonstrations; and as in these matters one proceeds from one thing to the next, he pushed his inquiries so far that he reached the thirty-second proposition of the first book of Euclid. While he was at this point, my father came into the room where he was, without my brother hearing him; he found him so intently absorbed that it was a long while before he noticed his coming. One cannot say which of them was the more surprised: the son to see his father, because of the express prohibition he had been given, or the father to see his son in the midst of all these things. But the father's surprise was far greater when, having asked him what he was doing, he was told that he was looking for such-and-such a thing, which was the thirty-second proposition of the first book of Euclid. My father asked him what had made him think of looking for that: he said it was because he had found such-and-such another thing; and when my father put the same question to him again, he told him of some further demonstrations he had made; and at last, working backwards and always explaining himself by the names “round” and “bar,” he came to his definitions and his axioms.

My father was so overwhelmed by the greatness and power of this genius that, without saying a word to him, he left him and went to the house of M. Le Pailleur, who was his intimate friend and also a very learned man. When he arrived there he stood motionless, like a man beside himself. M. Le Pailleur, seeing this, and seeing too that he was shedding some tears, was alarmed, and begged him not to hide from him any longer the cause of his distress. My father answered him: “I am not weeping for sorrow, but for joy. You know the pains I have taken to keep the knowledge of geometry from my son, for fear of turning him from his other studies: and yet see what he has done.” Upon this he showed him everything the boy had found, from which one might say that in a manner he had invented mathematics. M. Le Pailleur was no less surprised than my father had been, and told him that he did not think it right to hold this mind captive any longer and to keep this knowledge from it still; that he ought to let him see the books, without restraining him further.

My father, thinking this advisable, gave him Euclid's Elements to read in his hours of recreation. He went through them and understood them entirely by himself, without ever needing any explanation; and while he was going through them he was composing, and advanced so far that he regularly attended the meetings held every week, where all the able men of Paris gathered to bring their own works or to examine those of others. My brother held his own there very well, both in examining and in producing; for he was among those who most often brought new things. There were also often seen at these gatherings propositions sent from Italy, Germany and other foreign countries, and his opinion was sought on everything with as much care as that of any of the others; for his insight was so keen that it sometimes happened that he discovered errors which the others had not noticed. Yet he gave to this study of geometry only his hours of recreation; for he was learning Latin by rules my father had drawn up expressly for him. But as he found in this science the truth he had so ardently sought, he was so satisfied with it that he put his whole mind into it; so that, however little he applied himself, he advanced so far that at the age of sixteen he wrote a treatise on Conics which was held to be so great a feat of intellect that it was said nothing of such power had been seen since Archimedes. The learned were of the opinion that it should be printed at once, for they said that, although it was a work that would always be admirable, yet if it were printed at a time when its inventor was still only sixteen, that circumstance would add much to its beauty: but as my brother never had any passion for reputation, he made no account of this; and so the work has never been printed.

Throughout all this time he went on learning Latin and Greek; and besides this, during and after meals my father would talk with him now of logic, now of physics and the other parts of philosophy; and that is all he ever learned of them, having never been to college, nor had any other masters for these subjects any more than for the rest. My father took such pleasure as may be imagined in the great progress my brother was making in all the sciences, but he did not notice that such great and continual application at so tender an age might seriously affect his health; and in fact it began to be impaired as soon as he reached the age of eighteen. But as the ailments he then felt were not yet very severe, they did not prevent him from continuing his usual occupations; so that it was at that time, at the age of eighteen, that he invented the arithmetical machine by which one can perform not only every kind of calculation without pen or counters, but can even do so without knowing any rule of arithmetic, and with unfailing accuracy.

This work was regarded as something new in nature: to have reduced to a machine a science that resides wholly in the mind, and to have found the means of performing all its operations with complete certainty, without any need of reasoning. This labour tired him greatly, not on account of the idea or the mechanism, which he found without difficulty, but in making the workmen understand all these things. So that he spent two years bringing it to the perfection in which it now stands.

But this fatigue, and the delicate state his health had been in for some years, brought on ailments that never afterwards left him; so that he would sometimes tell us that since the age of eighteen he had not passed a day without pain. Yet as these ailments were not always equally violent, as soon as he had a little rest and respite his mind would turn at once to seeking something new.

It was at that time, at the age of twenty-three, that, having seen Torricelli's experiment, he went on to devise and carry out the other experiments that are called his experiments: those on the vacuum, which proved so clearly that all the effects hitherto attributed to nature's abhorrence of a vacuum are caused by the weight of the air. This was the last occupation in which he applied his mind to the human sciences; and although he discovered the cycloid afterwards, that does not contradict what I say; for he found it without thinking of it, and in a way that shows plainly he gave it no application, as I shall tell in its place.