Popular Science Monthly/Volume 75/September 1909/Henri Poincare and the French Academy

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THE Académie Française is primarily a literary organization, and its special work is the preparation of a dictionary. But even in this enterprise it is desirable, as M. Masson points out in the document of which I propose to translate a part, to have expert assistance at hand in the matter of the meaning and use of scientific terms. It is probably for this reason that Henri Poincaré, already a member of thirty-five academies, was this year called to membership in the most celebrated of all academies. The great mathematician entered the august body with a eulogy of his predecessor, the poet Sully-Prudhomme—which task was not as strange to him as might seem at first glance, since Sully-Prudhomme was educated for a scientist and all of his work shows a scientific turn—and was received, with the customary biographical welcome, by the historian Frédéric Masson. A study by a layman and for the ears of laymen, M. Masson's address is a thoroughly popular effort; but it has a great deal that is pleasing, and not a little that is suggestive. I quote, with considerable abbreviation, from the part which deals most directly with the new academician's life and work.

You were born, a little more than half a century ago, in that dear and glorious Lorraine which has furnished this body so many men remarkable in lines of activity so diverse; so soon after we have been cruelly touched by the death of Theuriet, of Gebhart and of Cardinal Mathieu, you appear, attesting, by the exercise of a totally different genius, the inexhaustible fecundity of your native province. You come of an old race long established at Neufchâteau, and located at Nancy for a century. Of your name—Pontcaré (square bridge), rather than Poincaré (square point), for, as you have said, one might conceive a square bridge, but scarcely a square point—there have been magistrates, savants, lawyers, soldiers like the Commandant Poincaré, your great-uncle, whose tenderness for his wife and whose sad adventures M. Chuquet has narrated—like that other Poincaré, also an officer, who died for the republic in the year IX., whose son the first consul himself recommended to the ministry of war for a place in their offices, since, a corporal in the Seventh Hussars, "he had lost a leg and a thigh in one of the last battles which adorned the last campaign on the Rhine." Your grandfather was a pharmacist; it was at Nancy, in his house, opposite the ducal palace, that you came into the world; and this house, solid, massive and without ornament, is entered through an almost monumental portal whose worm-eaten posts support a broken pediment bearing the semblance of a boiling pot. Some found a bit of symbolism: the portal is poetry; the house is prose; it gives an impression of bourgeois simplicity and of settled living which is by no means trivial. Your father, a physician, was a conscientious student, a distinguished practitioner; and the faculty of Nancy, where he took his course, considered him a master of whom they were justly proud, at the same time that the working population saluted in him their benefactor. He was one of those men who, having been led by a noble curiosity into the most emotional and uncertain of professions, practise it with admirable disinterestedness and hold themselves amply repaid if they are so fortunate as to save a human life now and then. For the honor of the nation, there are many of the sort in France; but few have been able, like Dr. Poincaré, to discharge the duties of so absorbing a profession, to work in the laboratory, to teach assiduously, and at the same time to travel extensively over Europe.

Your mother was one of those alert, active women, always in motion and always busy, whose spirit of order, organization and command rules a household. She also was a native of Lorraine, of an old local family, home-loving, attached and riveted to the soil; the boys, no matter how brilliantly they had begun life, were never easy till they had returned to the home-nest to live, hunting on their estates or supervising their cultivation; two of your great-uncles joined to their rural tastes an inclination for geometry. Your mother wasted no time on such matters, finding enough to busy her in those occupations which are duties, and which, cheerfully accepted as such, become pleasures. Ah! what admirable sources of vital energy are these Frenchwomen, honest and shrewd, economical and judicious, sovereign in their own domain and disdainful of the other conquests, constantly busy at reforming the national virtue and transmitting intelligent patriotism to their children!. . . In your home you found an uncle recently graduated from the École Polytechnique. What a prestige surrounds these young men who, by a mental effort which is sometimes excessive, succeed in obtaining the first places in their generation, and to how many mistaken choices of vocation does their example lead! But with you, sir, the vocation had nothing to do with example; you were predestined to mathematics! This aptitude, in your paternal and maternal family, is transmitted in collateral lines like the throne in the House of Osman, and yourself twice heir of avuncular gifts, I am told that you have selected one of your own nephews for the precious succession.

You did not wait long to reveal your vocation, and you are justly cited as the most precocious of infant prodigies. You were nine months old when you first saw the sky at night. You saw a star come out. You obstinately pointed out the shining spot to your mother, who was also your nurse. You discovered a second, with the same astonishment. You greeted the third, the fourth, with the same cry of joy and the same enthusiasm; it was necessary to put you to bed, you were so excited by your new occupation of star-finding. That evening brought your first contact with infinity and your first lesson in astronomy; you were the youngest professor known.

I have been told that you were a delicate, alert, charming child, spoiled and adored by your parents; a terrible illness suffered at the age of five years, as a result of which it was feared that you would never be able to speak again, left you more delicate, timid and somewhat awkward, so that you were afraid of the noisy games of the boys and preferred the society of your little sister. I do not imagine that violent sports ever tempted you, or that you ever became skilful in them. Nevertheless, you learned to hunt very large game. As soon as you learned to read, your curiosity was excited by those books of popular science which have replaced fairy stories in realistic schemes of education. You found extreme pleasure in them, and you experienced a grandiose horror in witnessing cosmic upheavals and battling with antediluvian animals. It was formerly the fashion to run after Prince Charming and awaken Sleeping Beauties. Now the child is no longer expected to make the acquaintance of those trivial personages; he must content himself with those whose skeletons have been discovered. Let me ask you: Between creatures which have really lived and of which we know nothing and never shall know anything, except that they lived, and beings which have lived only in the dreams of humanity, but which in the course of the ages have gratified us with so much beauty, grace and poetry, which are the more real, which bring more of light, of consolation, of joy? But you were not made to sit in the arm-chair of Charles Perrault.

It was in your father's house that you received from a retired teacher, a friend of your family, your first notions of things; he did not require written exercises from you; he conversed with you, talking of everything at haphazard; this encyclopedic instruction was so appropriate to your nature that when you entered the collège you at once took the first place; but this sort of work would be injurious to children of different endowment. Your memory was and still is more auditory than visual. Pronounced words engrave themselves on it. When you come back from a journey, no matter how long, you can recite the names of all the stations you have passed, if you heard them cried before your car. More than this—a character presents itself to your mind like a sound. In the evening, you can recite the numbers of all the coaches you have met in the course of the day, but you hear them, you do not see the figures. This is one of the most remarkable peculiarities of your brain, and I venture to note it because I have the unanimous testimony for it of those who know you most intimately. At the lycée of Nancy, you were superior to your comrades in every branch, and you seemed so well endowed for literary studies that one of your teachers, who is one of our best historians, would have been glad to attract you to our speciality; but when, in the fourth grade, you opened a text on geometry, the work was done. Your astonished teacher rushed to your mother and said to her: "Madam, your son will be a mathematician." And she was not particularly frightened. Mathematics, as soon as you made her acquaintance, seized you and held you. She is a tenacious mistress, with this peculiarity, that she fires all her lovers with the same impulse: the mathematician is a peripatetic. Pedestrian exercise seems necessary to him in order to stimulate thought, and, as he walks, certain mechanical gestures with which he occupies his fingers seem the indispensable auxiliaries of an intellectual labor that leaves him indifferent to the exterior world and even unconscious of it. One day, when promenading, you suddenly discovered that you were carrying in your hand a wicker cage. You were prodigiously surprised. When, where, how had your hand plucked this cage, which was new and fortunately empty? You had no idea, and retracing your steps, you walked until you found on the sidewalk the stock of a basket-maker whom you had innocently despoiled. Such phenomena are very common with you; they will become, if they are not already so, as celebrated as those attributed to Lagrange, to Kant, to Ampere. You might be in worse company.

You were, nevertheless, at times, a child who liked pleasure and games, but you invented your own amusements. You played at railroad or diligence with a map or a guide in reach, and thus you learned geography. You put history into dramas and comedies; at sixteen years you had written a five-act tragedy in verse, and you would not have been a son of Lorraine if the heroine had not been Joan of Arc. Even charades had a charm for you. Are they not problems? The war interrupted these games. You were sixteen years old; your age and your health prevented your mingling with the combatants, but you tried to make yourself useful; every day you accompanied your father to the hospital and served as his secretary; you were so eager to learn the news that, in order to read them in the only papers that were accessible to you, you learned German. The war must have matured you; it certainly left its trace upon you; but it did not change your life. To the men of the generation preceding yours, it brought a definite conversion with introspection. You have read Sully-Prudhomme's verses entitled "Repentance." In them he confesses the error into which the generosity of his heart had drawn him and in which the fallacious discourses of the rhetoricians had maintained him; in order to carry out designs which were unworthy and shameful, these gentry resort to sonorous words to lull a careless people to security; and when the nation awakens and finds herself rolling into the abyss, she cries out treason but is unable to distinguish the traitors. So Sully-Prudhomme had detested war and shown himself rather disdainful of soldiers. Then he learned from his own experience that any one who chooses can not be a soldier, that it is one thing to deliver philosophic harangues and another to submit one's physical and moral being to monotonous regulations and entire self-effacement; he learned—and the lesson cost him dear—that in order to possess the right to think, one must have conquered first the right to live; that it is folly which would be ridiculous if it did not bring such despair to profess humanitarianism when all of Europe is under arms; and that, however inelegant the solution may appear, there is but one, if a people intends to maintain its nationality, guard its independence, continue its race, possess its territory, speak its language—and the solution is to be strong enough to defend them.

You lived your life, sir, under the yoke of the victorious enemy. It was in a city occupied by the Germans that you resumed and continued your studies. You were thoroughly successful in them; but the joy was doubled for you by the fact that your public success coincided with the evacuation of Nancy. As our dear late colleague Émile Gebhart has told us, it was in a hall filled with the joy of deliverance that you received your last scholastic honors. You held the first rank, a native of the city and ten times a prize-winner. You carried off the prize in mathematics from all your rivals, from Paris and the departments; it depended on you alone to enter the School of Forestry second on the list of appointees; this would have been another glory for Nancy, but you refused to go further with the school than to leave your visiting-card; you were distrustful of the fallacious dryads who delight in troubling the absent-minded.

The next year you presented yourself as a candidate at the École Polytechnique and at the same time at the École Normale; for the latter you stood number five, for the former number one. Which of the two great schools would you choose? That which decided your choice, more even than the familiar memories, than the temptation of the uniform and the glory of the sergeant-major's chevrons, was it not, tell us, the groaning of the mutilated fatherland? But you never reached the point of entering upon a military career. Your scientific bent showed itself so brilliantly at the school that there was no question of another sort of glory; your residence there is a matter of piously transmitted tradition. It is related that you attended your classes, at least in mathematics, without taking a note, without reading or even collecting the mimeographed sheets which reproduce the professor's lecture. Your method was to classify the results established, to study their connections, with no care for the demonstrations, sure of finding others, if you happened to forget the ones which they had employed; at the time of your entrance examination, did you not find a new solution for a problem which had been set you? When you worked, you did not remain in your room, but gave your brain a promenade through the corridors, and in place of a pen, a pencil or a piece of chalk, your hand was busy with a bunch of keys—your opener of ideas.

Your superiority in mathematics was so decided that, in spite of your inaptitude for anything practical—manipulations, linear design, imitative design—you were, at the closing examination, placed second, and admitted to the School of Mines. There you found life pleasant for more than one reason. In the first place, in the Latin Quarter, you lodged with one of your cousins, who was taking a literary and law course. . . . With him, in the practise of peripatetism—which was, perhaps, less a philosophical school than a physical peculiarity of philosophers and mathematicians—you followed those studious rounds in the course of which you discussed philosophic themes, already indissolubly associated in your mind, as in those of the ancients, with mathematical theories.

In 1880, the Academy of Sciences had set as the subject of the mathematical great prize, the theory of differential equations. When the illustrious M. Hermite presented his report, he mentioned a discussion bearing the motto: Non inultus premor, whose anonymous author he invited to persevere in a work which promised to produce results. The motto was that of Nancy; you were the author; but your paper was only a first sketch; you presented at that time only the results which you were soon to obtain and which, in the month of February, 1881, burst forth—it is the only exact phrase, says one of your admirers—in the report of the Academy of Sciences. From week to week, with the notes which you sent out regularly, your discovery increased in precision and amplitude for a period of nearly two years. Your contribution was the "the crowning of the work of Cauchy and Riemann, the representation of the coordinates of any algebraic curve in uniform functions, the integration of linear differential equations with algebraic coefficients—it was a new and immense perspective opened to view."

This discovery was a great victory for French science. For some years the German geometers had been roving about the house without finding the door. You located it and opened it.

From there I need not follow you in your career: Professor in the University of Paris and the École Polytechnique, your lessons have had an unequaled vogue; and if, among your auditors, many were not able to follow you, all agreed in proclaiming your astonishing superiority; at thirty-two years you were elected a member of the Academy of Sciences, you have been called into the majority of the scientific societies of two hemispheres; you have received all the honors that a legitimate ambition could crave. Your name, going out beyond the narrow circle where your work can be appreciated, has become illustrious and added to a nation's glory, and this fame you owe only to yourself; it is the gift of no one, you have followed no master, you belong to no school, you are yourself—and that is enough.

Similarly, when you undertake a criticism of science, you make it a personal matter, and without adopting any tradition, without bowing to any formula, you walk on in your independence and because you choose to. You run indeed, and so fast, with such bounds, that in order to follow you it is necessary to leap ditches and fill in gaps; but you are built so. Original in mathematics, you remain so in this branch of philosophy; you apply to it, at the same time, a highly-developed interest in psychology, a rare aptitude for observing physiological phenomena in your own person, and that mathematical habit which organizes precision and with refined subtlety binds arguments together with chains that seem impossible to break. Restrained by nothing which you place confidence in or accept a priori, you build up your doubt against official science and sound its nothingness. So your work is double: in mathematics you erect to scientific truth a temple accessible only to the few initiates; and with your philosophic artillery you hurl into the air the chapels about which throng the crowds of rationalists and freethinkers who by a common school certificate have acquired the right to believe in nothing which is not proved to them, to celebrate the mysteries of a pretended religion of science. Ah, sir, what havoc you are making in these demonstrations! Nothing would survive the rudeness of the blows you are dealing if you did not stop from time to time to banter your victims, or if^ seized with a sort of remorse, you did not amuse yourself by gluing together again the members you have broken. The axioms which seemed established by the wisdom of the ages are no longer more than definitions when you have passed; the laws become hypotheses; and at the same time that you prove the essential role of these hypotheses, you show their merely temporary utility—you make it evident that these definitions are convenient but ephemeral. What remains? Nothing, or little more than nothing, and the most precious idols of primary religion go to join the dead stars in the depopulated heavens.

Does this mean, sir, that you doubt science more than truth? Neither the one nor the other; but the latter gives way constantly before the advance of the former, and, as man proceeds one step farther, the space he must cross withdraws before him; beyond the steppe whose extent his eye embraces, others await him, and still others, for he only is assured of reaching the end who stopped with the rudiments—and learned them by heart. . . .

  1. Translated, with an introduction, by Professor Roy Temple House.