# Hippolyte Stupuy's Obituary of Sophie Germain

Jean-Léon-Hippolyte Stupuy (1832-1900), a poet, playwright, literary man and polemicist, wrote the "Notice sur Sophie Germain" which was published in the Oeuvres philosophique de Sophie Germain (1879). We give below an English translation in which we have tried (not very successfully!) to preserve the character of the original charming French. We note that in many ways it is a strange obituary, for Stupuy takes the opportunity to fill it with his personal opinions, and produces really hard hitting attacks on academies, Napoleon and many other things. It is, therefore, interesting not only for presenting Sophie Germain's contributions, but also for illustrating the intellectual landscape of the second half of 19th century France.

Notice sur Sophie Germain, by Hippolyte Stupuy.

You have to painfully admit it. While so many women have found fame in frivolous writings, the only French woman who has succeeded in serious work, esteemed by mathematicians, from whom a whole aspect of her genius escapes, is hardly known to the public. Fontenelle, praising a learned anatomist, remarks that his works were, during a long career, as if buried in silence, and he explains: "He has put nothing of his into his reputation except his deserves, and commonly it is far from enough." Sophie Germain's inconspicuous reputation offers the same character. Her work, however, is one of which science and philosophy have benefited and honoured, and her name, which the future will know better, belongs to the history of the progress of the human mind.

Mademoiselle Germain (Marie-Sophie), was born in Paris, Rue Saint-Denis - the birth certificate bears no number - on 1 April 1776, to Ambroise-François Germain and Marie-Madeleine Gruguelu.

Details are lacking concerning her family; we know, however, that her father belonged to that liberal and educated bourgeoisie which, after having applauded Turgot's reformist attempts, awoke to a more extended desire to end the slavery in which, since Louis XIV, France had diminished and was reducing. Was M Germain a supporter, if not a friend, of philosophers and economists? Sympathetic to new ideas, was he noticed and appreciated in the struggles which preceded the events of 1789? The documents testify in favour of the affirmative. Deputy of the Third Estate for the city of Paris, we see M Germain joining the resolutions which transformed the Estates General into a Constituent Assembly; as a constituent, we meet him at the tribune, and two speeches made by him, one on 8 October 1790, the other on 5 May 1791, sufficiently indicate the nature of his ideas on economic matters.

The first speech, about a project concerning the Caisse d'escompte, is one in which M Germain, on behalf of the traders, "fights the bankers and all those gentlemen who are called traders." It begins as follows: "I am a merchant; I live in rue Saint-Denis." The speaker, in his second speech, said that he "has always made a public profession to regard trading as a state crime." This modest title of merchant with which he is honoured, this hatred of stock-trading which he boasts of, these are clues, not only of the personal character of M Germain, but also of the collective thought of the class of which he was the agent: the bourgeoisie had not yet imagined erecting wealth, well or badly acquired, into a social ideal.

After the Constituent Assembly, the name of M Germain no longer appears in any political assembly; the presumption is that the events had gone beyond the scope of his opinions. It has been alleged that he himself, despite his protests against the speculation, later became involved in speculation; it has also been said that his poor health kept him away from public affairs: he was for a time one of the directors of the Bank.

Thus, born the very year of Turgot's dismissal, that is to say on the threshold of the Revolution, Sophie Germain received from her earliest childhood, in the conversations she heard from her father, the influence of intellectual vigour which the eighteenth century then manifested; that if a natural inclination led her to mathematical studies, the scientific philosophy from which she saw the blossoming left an indelible imprint on her mind. We will see later how, by her method of reasoning, she relates to the school of Diderot and Condorcet.

The way in which she became aware of her mathematical vocation deserves to be reported.

It was in 1789. Revolutionary agitation broke out on all sides and, already, at the age of thirteen, with the wisdom of which she was to give so much proof later, Sophie Germain understood and, it has been said, predicted the extent and duration of a movement in which many wanted to see only a passing turmoil. Eager to choose an occupation serious enough to distract her fears, she spent long hours in her father's library. One day, by chance, she opens the Histoire des Mathématiques by Montucla, and, in this book full of erudition, finds the eloquent account of Archimedes' death: this great man, busy thinking about a geometric figure, eyes and thoughts entirely on this meditation, perceives neither the taking of Syracuse, nor the noise of the victors who sack the city, nor of the sword raised above him, and he falls without deigning to respond to the brutal injunctions of his assassin. The choice of the young girl is immediately made. This geometrical science so endearing that nothing can distract from it, not even a threat of death, this science of which she hardly knows the name, this is the one that suits her; and, on the spot, she takes the heroic resolution to give it her all.

Heroic resolve, I said. The word is not excessive. Indeed, unwittingly justifying this saying of Fontenelle, that most of those who have excelled in some way have had no masters; without any guide other than Bezout; alone, devoid of advice, she begins to study everything she has at hand, penetrates, guesses, is interested, is passionate: it is labour day and night, it is such ardour that her family is terrified. At first they tried to interfere with her choice. What could geometry do for a person of her sex? No doubt her response was more respectful than that of Galileo; however, by seeking to erect an obstacle to her desire, they only succeed in increasing it. So, to force her to take the necessary rest, the fire, the clothes, the light are removed from her room. She pretends to resign herself; but, when the family is asleep, she gets up, wraps herself in blankets and, in a cold such that ink freezes in her writing-desk, indulges in her beloved studies. Several times she was surprised like this in the morning, frozen with cold without noticing it. In front of such an extraordinary will for her age, her parents had the wisdom to let the young Sophie dispose of her time and her genius as she pleased, and they did well: like the geometer of Syracuse, she would have died rather than abandon the sketched problem.

Despite the strength of mind that she shows, how painful the young girl's first efforts must have been! Regardless, her progress was rapid, and soon she found herself able to study Cousin's differential calculus fruitfully. The time for ungrateful preparation had passed, and the obstinate worker was enjoying the joy that comes from the certainty of reaching the goal, a joy no doubt very keenly felt since towards the end of her life, the testimony of people who had known her, Mlle Germain still spoke with animation of the happiness she felt at the moment when she finally understood the language of analysis. But then, and precisely because of her progress, a new difficulty arose; it became essential for her to know and to study in depth works of science written in Latin, and she did not understand this language; in this again Mlle Germain took no assistance from anyone and, alone, she made herself capable of reading Euler and Newton. Will we believe it? So much care was not enough for his activity. Imbued with the generalising spirit which is revealed in the Encyclopaedia, she began at the same time to explore the whole domain of knowledge and, by a sort of instinct, thus encountered the necessary conditions for the work which, forty years later, was to rank her among the founders of real psychology. It was while absorbed in these works that she went through the phases of the Revolution: the one, so luminous, where great perspectives were opened up by emancipated knowledge; the other, so dark, where the axe of the deist rhetorician, as stupid as the iron of the Roman soldier, inflicted on the Academy of Sciences the death of Bochart de Saron, of Condorcet, and of Lavoisier.

However, after the fall of the declaimers, the floor was returned to the scholars. Fourcroy climbs to the Tribunal of the Convention: "The enlightenment," he says, "began the French Revolution, the enlightenment made the French people march from triumph to triumph; it is up to them to overcome all obstacles, to prepare for all successes, to support the French Republic to the height to which it has risen." He denounces the conspiracy of the disciples of Rousseau against the progress of human reason, progress which, in fact, is inseparable from the advent and development of the exact sciences: "Persuade the people that enlightenment is dangerous, and that it only serves to deceive them; to seize every opportunity to declaim vaguely, and in their constant manner, against the sciences and the arts; to accuse even the gift of nature and proscribe the spirit; to dry up all sources of public education, to lose in a few months the fruit of more than a century of painful efforts; proposing the destruction of books, debasing the productions of genius, mutilating masterpieces of the arts, under pretexts cleverly presented to those of good faith; place Omar's torch near all the treasures of arts and letters to set them on fire at the first signal; stop constantly with frivolous objections the draft instruction proposed in this forum; present an education plan that could not be carried out in the circumstances of the Republic, so that there would be no education; destroy all public establishments at the same time, without putting anything in their place; in a word, to annihilate all things and all men useful for instruction: here is a tiny sketch of the vast conspiracy hatched, with the most dangerous and the most treacherous skill, by the last conspirators." And he proposed the establishment of this École centrale des travaux publics which, a year later, took the title of École Polytechnic. The École, immediately organised, had as its first professors, among others, Lagrange, Prony, Monge, Fourcroy, Vauquelin, Berthollet, Chaptal, Guyton de Morveau, a whole host of senior men.

Sophie Germain was then eighteen years old. Struck by the usefulness of a teaching that her sex forbade her to follow in person, and wishing at least to profit from it, she obtained the lessons of various professors, especially the notebooks of Fourcroy's chemistry, those of the analysis of Lagrange. She did more. A habit had become established among the pupils of presenting to the teachers, at the end of the lessons, observations in writing; under the supposed name of a pupil of the School - Le Blanc, a pseudonym which she used for some time, - she sent hers to Lagrange. The latter noticed them, praised them publicly, inquired about the real author and, having got to know her, became the adviser and supporter of the young mathematician.

The original circumstances of her appearance, the approval of the illustrious author of Mécanique analytique, the age of the new geometer, some details about her beginnings which transpired, all this made noise, aroused curiosity, aroused sympathy; we were surprised, we were interested, and immediately Mlle Germain found herself in contact, either directly or by letter, with all the known scholars of the time. Everyone asked for the honour of being presented to her: these communicated their works to her, these addressed their works to her, people came to talk to her. And immediately those who approached her recognised that "this learned woman" escaped the sarcasm of Molière to justify this word from La Bruyère: "If science and wisdom are united in the same subject, I no longer inquire about the sex, I admire." Now if, moreover, Mlle Germain made her entry into the world with the favourable murmur of a good reputation, after an existence entirely of work and reserve, she left the same, leaving an imperishable work and not a flashy glory.

So many marks of sympathy, so many illustrious friendships, far from being for her who was worthy of them an occasion of vanity or of distraction, became for her a new stimulus. For several years, we find her drawing on familiar conversations, in which she herself excelled, food for her mind, and, incessant labour at a time when biological science consisted of an infinite variety of efforts, found herself keeping abreast of courses, books and discoveries, already obsessed perhaps with the thought of a possible analogy between all intellectual operations - thought which she will realise in her maturity - reading poets and cultivating the arts, but preoccupied especially to improve in mathematics.

Legendre having published the Théorie des nombres in 1798, she devoted herself with her usual ardour to the study of this theory, a study that we will see her continue for a long time; hence, between them, a correspondence which, during the academic competition on elastic surfaces to which the name of Sophie Germain remains gloriously attached, will almost take on the character of a collaboration. Later, in 1801, Gauss's Disquisitiones arithmeticae appeared; Mlle Germain's thoughts immediately turns to this subject: she does a lot of research on this kind of analysis, applies the method to several special cases, generalises what is particularised in the book, tries a new proof for prime numbers in Fermat's famous formula and, putting everything under cover, still under the pseudonym of Le Blanc, addressed her essays to the famous professor of Göttingen, convinced, she writes, that he would not disdain to enlighten her with his opinions being "an enthusiastic amateur" in the science he cultivates with such brilliant success. M Le Blanc was far from being a mere "amateur", and Gauss saw this clearly; therefore his answer, which reached the unknown mathematician through M Silvestre de Sacy, was most honourable. A friendly trade ensued.

These friendly relations had lasted for several years without Gauss knowing the sex and the name of his correspondent, when, in 1806, a circumstance made him discover the pseudonym. The anecdote is curious and shows that, even in women, the habit of right thinking does not detract from benevolent impulses. During the Jena campaign, the French, victorious, occupied the town of Brunswick where the learned mathematician then resided. Mlle Germain remembers Archimedes, is alarmed and, in warm terms, writes to a friend of her family, General Pernety, Chief of the Artillery Staff of the Army of Germany. Her letter finds the general in front of Breslau, where he directs the siege. The adjuration was undoubtedly very lively since, without delay, an officer was sent to Brunswick to inquire on behalf of the general and Mlle Germain. The officer rushes in, arrives, finds Gauss who, warmly recommended and invited to dine with the governor, declares that he knows neither the general nor Mademoiselle Sophie Germain: the latter, in her eagerness, had forgotten that M Le Blanc's intervention alone would have been understandable. However on the report that the envoy returned of his mission, explanations were exchanged and Gauss, knowing to whom to address the expression of his gratitude, acquitted himself of it in terms so touching for the friend - it is the word which he will henceforth employ - who is flattering the mathematician. How much has the philosophy of the last century, expanding sociability and calling men to science, tolerance, and peaceful customs, would have saved humanity years of pain without the sophist and the fighter to whom, by the bad luck of events, the dictatorship fell! This passage from General Pernety's response to Mlle Germain also proves it well: "Here I am conducting a siege, hearing and making roars or thunders, burning houses, churches, for steeples are the sights of bombs, finally doing by reflection all the harm I can to those who have never done harm to me, whom I do not know; but that's the job. I am being overwhelmed with cannon balls and shells and bombs, and all is well." The immortal author of the Tactique would have written such words; but are they not singularly significant from the pen of a soldier, even though the bloodthirsty mania for conquest troubled so many brains?

Nowadays, to go down into the arena where opinions are discussed, formed, and argued, one only has to find the opportunity - and the opportunity is blind. In the time of Sophie Germain, one respected others enough and oneself, one placed the scope and value of the work well above personal impatience, to make available to the public one's work only after being laboriously prepared; therefore, at the age of thirty, she had not yet published anything. What was her surprise when, one day, Greek verses composed in her honour were given to her! A distinguished Hellenist, d'Ansse de Villoison, had echoed the admiration she inspired in a few superior men, and, in a poem intended to celebrate the day of the birth of the astronomer Lalande, rendered tribute to her talents. Mlle Germain became angry, and, even after the Greek verses had been burned by their author, held fast to the indiscretion so that he had some difficulty in returning to grace. Such was the modesty of this remarkable woman. It is true that Villoison, though having had to give "his word of honour" not to speak of her in any writing, and to keep his muse "dumb and chained," began again some time later, this time in Latin. Like Horace glorifying his friend Lollius,
Non ego te meis
Chartis inornatum silebo
Totve tuos patiar labores
Impune, Lolli, carpere lividas
Obliviones, [$\text{trans}$]
the versifier did not want the labours of the young scholar to fall prey to envious oblivion. But let's notice the difference. While Lollius only lives in the verses of the poet of Tibur, Sophie Germain exists in a work which is personal to her and the verses of Villoison are forgotten.

This was in 1802. A few more years, and the genius of Sophie Germain was finally going to assert itself publicly. This is how she began her life as an author.

Chladni, already famous in Germany, by curious experiments on the vibrations of elastic surfaces, came in 1808 to repeat his experiments in Paris; they tended to show that the influence of vibrations on bodies is subject to constant mathematical laws. His method, simple and ingenious, consisted of sprinkling fine sand or dust on plates whose vibrations were reflected in the eyes by the figures they drew. It was a new field open to acoustics; the learned world was stirred, a commission was set up to rule on the results obtained, and a favourable report ensued. Napoleon, before whom the experiments had taken place, then had an extraordinary prize proposed to the Institute for them to be submitted for calculation, and Mlle Germain resolved to take part in the competition.

But, to put the reader in a position to fully appreciate the importance of the work she undertook in this regard, it is necessary to take a quick history of the question. History, in all things, provides valuable clarity.

Although the study of the propagation of sound and the nature of harmony goes back a long way, acoustics can be considered a somewhat modern science; it was, in fact, only towards the middle of the seventeenth century that the theory of sound was freed from anti-scientific assumptions. In ancient times, Pythagoras, Aristoxenus, Aristotle, understood that harmony consists in the perception of the relations of sounds - which differentiates it from actual noises, in which the sensations produced are not exactly comparable to each other - but they did not know how to appreciate these relationships, nor to fix their limits. For a long time, first theology, then metaphysics, veiled the true conditions of research with their chimerical expedients; and it is necessary to arrive at Bacon and Galileo to meet the real bases of the scientific conception of the production and transmission of sound vibrations, a conception which required prior knowledge of the mechanical properties of the atmosphere.

Diderot writes in his Principes d'acoustique,
Air is the vehicle of sound. If you pluck an instrument string, you will notice a movement that causes it to come and go with speed, beyond and below its state of rest; and this movement will be the more sensitive the heavier the string. - By virtue of the vibrations of the body making the sound, the surrounding air acquires and exerts similar ones on the nearest particles; these on other contiguous ones, and so on, with the only difference that the action of the particles on each other is greater the smaller the distance to the body making the sound.
This is the phenomenon. It should be added that the movement is spreading, not only in the direction of the original disturbance, but also in all directions. This natural phenomenon, it was necessary to observe it, to discover its general laws, to determine its particular cases, and to do that by observation, experience and calculation. However, the elasticity and the gravity of the air being demonstrated, the discoveries, like a chain whose rings are unrolled, followed one another quickly. Gassendi was the first to explain the sharpness and severity of sounds. Otto de Guéricke, who had the idea of the pneumatic machine, showed that sound cannot be propagated in a vacuum. Kircher made known the causes of the echo phenomenon. Newton showed, by calculation, that the transmission of sound is due to the elasticity of air, and by that very fact indicated the direct relationship of acoustics with abstract mechanics.

The immortal author [Auguste Comte] of the Cours de Philosophie positive writes:
Considered from the most general point of view, sound phenomena are obviously linked to the fundamental theory of very small oscillations of any system of molecules around a stable equilibrium situation. Because, for sound to occur, there must first be an abrupt disturbance in the molecular equilibrium, by virtue of an instantaneous shock; and it is equally essential that this temporary disturbance be followed by a sufficiently prompt return to the original state. The more or less perceptible and continuously decreasing oscillations thus effected by the system below and beyond its resting figure, are by their nature appreciably isochronous, since the elastic reaction by virtue of which each molecule tends to resume its initial position is all the more energetic the greater the spacing, as in the case of the pendulum. As long as these vibrations are not too slow, the result is always an appreciable sound. Once produced in the directly shaken body, they can be transmitted at great distances, with the aid of any medium provided it is sufficiently elastic, and principally by the atmosphere, by exciting there a gradual succession of alternating dilations and contractions, that their obvious analogy with the waves formed on the surface of a liquid has rightly qualified as sound undulations. In air, in particular, because of its perfect elasticity, the agitation must propagate, not only in the direction of the original agitation, but also in all directions to the same degree. Finally, the vibrations transmitted are always necessarily isochronous to the original vibrations, although their amplitude may be very different. - The most elementary analysis of the general phenomenon of sound vibrations was therefore sufficient to conceive this study, almost from its origin, as immediately subordinate to the fundamental laws of rational mechanics.
Even during Newton's lifetime, Joseph Sauveur, with whom the demonstrative explorations began, discovered the nodes and troughs of vibration. Finally, Brook Taylor, in the Memoirs he presented to the Royal Society of London, then Daniel Bernouilli, Euler and d'Alembert submitted the vibrating string theory to analysis; but, until then, such a delicate analysis had only been able to provide mathematicians with very imperfect solutions; a new calculation was needed, that of partial differences: d'Alembert had the honour and, in 1747, applying it to sound vibrations, gave the solution of the linear case; however the glory of having discovered the fundamental principles belongs to Bernouilli.

A "long and glorious" struggle, says Condorcet, took place on this subject:
M d'Alembert had solved, in 1747, the problem of vibrating strings, by giving the first integral equations, in their true form, for this problem: this solution had all the generality possible given the nature of the question. M Euler, shortly afterwards, gave a solution, founded on the same principles, and in which he is led to the same results by a similar method. These two great geometers differed only in the manner of subjecting to the law of continuity the arbitrary functions that calculus introduced into the integrals. M Bernouilli claimed that Taylor's method, which had first solved the problem of vibrating strings, but with a particular hypothesis, was by its nature as general as the new method, and thereby reduced the merit of the solution that it gives to that of having known how to use a completely new analysis then, that of partial difference equations.
Few mathematicians, adds the hapless secretary of the Académie des Sciences, shared Bernouilli's view on the generality of the methods themselves.

During Chladni's experiments, the mathematical theory of vibratory movement along a single dimension was therefore the only one complete. What was needed to take a new step? It was about considering a case which was more difficult and closer to reality: the vibration of surfaces. Therein lies the importance of the work of Sophie Germain; because, Auguste Comte does her this justice, it is "the memorable impulse given to science, in this respect," by her genius, which incited mathematicians to this new study.

The Institute's competition therefore opened, and the question was asked:
Give the mathematical theory of elastic surfaces and compare it to experiment.
Lagrange having asserted that this question would not be resolved without a new kind of analysis, all geometers bowed to this imposing authority and, it seems, abstained. Only Sophie Germain did not despair of success, observed and studied the phenomena for a long time and, on 21 September 1811, sent to the Institute an anonymous memoir which gave an equation for elastic surfaces.

No doubt, in the course of her research, she had helped herself with the advice or at least taken the opinion of her learned friends, since we have a letter from Legendre, addressed to her, in which, raising objections and indicating difficulties, he says that he has not thought enough about these kinds of questions and that he prefers "to give Mlle Sophie a won case, than to fight with her on a subject that she has pondered a lot." Lagrange did not follow this reservation and communicated a note to the commissioners responsible for examining the Memoir, a note in which he pointed out the inaccuracy of the proposed equation and declared "that the way in which one seeks to deduce it from that of an elastic strip while passing from a line to a surface seems to him improper." The prize was not given. The truth is that Sophie Germain, working almost instinctively and never having taken a regular course in analysis, had not completely resolved the question; but her Memoir, the wisdom of which was noticed, opened the way so well that Lagrange found the exact equation. Legendre (4 December 1811) warns the author, tells her that M Biot also believes he has found the true equation of the vibrating elastic surface, which equation is not the same as that found by Lagrange according to the hypothesis of the Memoir, and he adds: "I imagine that the question will be proposed with a new deadline; so benevolence is not lost: on the contrary, it is more than ever necessary to think of winning the award."

A second competition was, in fact, opened. Mlle Germain returned to her studies and on 23 September 1813 sent a second Memoir. Here again we see the author's sagacity deceived by the imperfection of her initial education, and Legendre, whom she consults (4 December 1813), does not hide it from her:
I do not understand at all,the analysis you are sending me, there is certainly an error either in the writing or in the reasoning; and I am inclined to believe that you do not have a very clear idea of the operations that are done on double integrals in the calculus of variations.
And further:
It seems recognised, however, that your equation is really that of the vibrating surface. Putting the analysis aside, the rest can be good, as far as the explanation of the phenomena is concerned. If the Institute's commission were of this opinion, you could be mentioned honourably; but I am afraid that the failed analysis will seriously harm the Memoir, despite the good that it may contain.
Legendre was not mistaken: Mlle Germain only obtained an honourable mention.

A third competition took place in 1816. This time, it was Poisson that Mlle Germain consulted on the Memoir sent by her, and Poisson (15 January 1816) replied:
The criticism that the commission made against her (briefly) is less about the hypothesis you are making and more about how you applied the calculus to that hypothesis. The result to which this calculation led you does not agree with mine except in the sole case where the surface deviates infinitely little from a plane, either in the state of equilibrium, or in the state of movement.
More self-confident, Mlle Germain had, for this new competition, renounced anonymity. The Academy handed down a judgment which resulted in the memoir being finally awarded the prize, although the equation had not yet been rigorously demonstrated.

The public sitting where the prize was announced took place on 8 January 1816. Reserved here, as in everything, Sophie Germain refrained from appearing there.

This is what the Journal des Débats of the time notes in these terms:
The class of mathematical and physical sciences of the Institute held its public session today, at 8 o'clock, in front of a very large assembly which had undoubtedly been attracted by the desire to see a virtuoso of a completely new kind, Mlle Sophie Germain, to whom the prize of the elastic undulations was to be given. The public's expectations were deceived: the latter did not come to receive a prize that her sex had not yet been able to collect in France.
The motto of the Award Winning Memoir was borrowed from Virgil (Georgics, Book II):
Felix qui potuit rerum cognoscere causas.
[Happy is he who has been able to learn the causes of things.]

So many important men were led to deepen and revive a question posed by her; this is a fact which fully justifies the epithet of "memorable" which has been characterised as the impetus given to science by our mathematician. And then, this intellectual brotherhood that they show to their valiant emulator, the advice they give her, the encouragement they give her, finally this solemn justice that they render her, isn't all this touching? Happy times, when love of the truth inspired such disinterestedness! Noble spectacle, which shows us united in the same men great intelligence and impersonal feelings!

Certainly, the discovery of the equations which express the vibrations of elastic surfaces was an important event; important not only from the special point of view of sound phenomena, the scientific character of which was thus established in its entire purity, but also, from the point of view of the improvement of relating notions either to inorganic bodies or to animate beings. The double importance attached to this part of knowledge, the legislator of science [Auguste Comte] observes with his usual certainty: "On the one hand, the examination of sound vibrations constitutes our most rational and efficient means, if it is not the only one to explore, up to a certain point, the mechanical constitution of natural bodies, the influence of which must above all be manifested in the modifications which the vibratory movements of their molecules undergo. - On the other hand, acoustics obviously provide physiology with an indispensable point of support for the exact analysis of the two most important elementary functions in the establishment of social relations: hearing and producing sound."

If it is true, however, that despite the more recent experiments of Savart, the analytical theory of vibratory movement in three dimensions remains still ignored, the efforts of Sophie Germain have, nonetheless, marked progress which deserves attention and recognition.

Although the question deserves serious consideration, the nature of this Study does not allow me to dwell on the connections of acoustics and the hierarchically higher sciences. One will find in the Éléments de Physiologie of the eminent professor Charles Robin, besides a complete account of what concerns the transmission of sound from the physiological point of view, the table of the observations and the experiments made in this respect by Müller, Wollaston, Colladon, among others, and a history of theories of the voice, from that of Aristotle and Galen, to that of Liscovius.

Sophie Germain had therefore valiantly conquered her place among scholars. But she was not one of those weak souls that a first success annihilates. More laborious than ever, we then see her attending sessions of the Academy of Sciences, continuing her work, paying attention to that of others and, even, finding the time to work for her friends. Here she is, for example, helping Fourier, the illustrious geometer to whom the Cours de Philosophie positive is dedicated, to obtain from the votes of her colleagues the post of perpetual secretary of the Academy of Sciences: "The people you love and whom you protect do not have to be unhappy. - A vote that I owe you has even more value in my eyes. Finally, the gods will decide. But what is independent of the gods are my feelings of gratitude." These passages from a letter addressed to her by the candidate testify that Mlle Germain did not believe herself to be exempt because of the integral calculus, from the active kindness of which the fabulist [Jean de La Fontaine] will seek example from Monomotapa.

In 1821, having reviewed and coordinated all of her previous mathematical work, she sent the Academy a Memoir entitled: Recherches sur la théorie des surfaces élastiques, in which she outlined the foundations of her analysis. Fourier gave her an account of the presentation of her work:
Last Monday, M Cuvier was responsible for reading the correspondence. I have asked him to present your Memoir and I have indicated the purpose. After the reading, MM Laplace, Prony and Poisson, will be named commissioners. I will insist as much as is necessary for them to make the report you desire. If M Poisson intends to oppose the results of your research in any way, he cannot help yielding to the authority of experience, which no one knows better how to consult than you. As far as I have been able to understand the discussion with which you were concerned, it seemed to me that you illuminate the influence of the theoretical hypothesis from which he wanted to deduce the 4th order equation that you have found.
This Memoir was published, at the instigation of Fourier and Legendre, in 1824. However, Sophie Germain was constantly studying, reviewing and correcting. In 1826, she put in bookstores a new memoir: Remarques sur la nature, les bornes et l'étendue de la question des surfaces élastiques. The academicians had not yet made their report on the first Memoir: here, she comments on it, amends it, develops it, produces new confirmations of the doctrine that she has exposed, multiplies its applications and gives this equation of vibrating elastic surfaces:
$N^2 \left[\Large\frac{d^4 \rho}{ds^4}\normalsize + 2\Large\frac{d^4 \rho}{ds^2 d{s^\prime}^2}\normalsize -\Large\frac 4 S\left(\frac{d^2 \rho}{ds^2}\normalsize +\Large\frac {d^2 \rho}{d{s^\prime}^2} \right)\right]\normalsize + \Large\frac{d^2 \rho}{dl^2}\normalsize=0$
which, she says, is generated, and belongs to the curved-elastic-vibrating surface; so that the different values that can be attributed to the radius $S$ of average curvature make it applicable to all possible curvatures. I cannot resist the pleasure of reproducing the preamble to these Remarks; in addition to clarifying and clearly circumscribing the question, it shows in the author this knowledge of herself, in her strengths as in her weaknesses, which is the mark of true superiority:
When, for the first time, I was concerned with looking for the expression of elastic forces in relation to surfaces, I was working, so to speak, under the dictation of experience. The question was new then; perhaps it would have been difficult to set the limits.

The only known phenomena belonged to the movement of vibrating plates; and yet the way I had envisaged elastic force already gave me hope that a similar hypothesis would be applicable to curved surfaces.

None of the observed facts related to the case where the thickness varied from one point to another on the surface; however, theory, which had formed without regard to such variability, was found to explain its effects.

The direction which should be attributed to the movement of the different points of the vibrating surface had not been sufficiently determined; and in this respect there were models rather than doctrines. In the linear case, mathematicians have assumed that the entire movement takes place in a direction perpendicular to the plane of the lamina at rest: I admit the same thing with respect to flat surfaces. Guided then by analogy alone, I thought I could assume that the motion of the various points of a curved surface runs entirely in directions perpendicular to the planes tangent to each of the same points, considered on the surface at rest. I have since recognised that this supposition, far from constituting a particular simplification in certain cases of the movement of surfaces, expressed, on the contrary, an essential condition for this kind of movement.

Finally, it always seemed certain to me that simplifications analogous to those used to establish the vibrating plate equation would lead to finding, for curved surfaces, an equation of the same order; I even tried to realise this idea by taking the cylindrical surface as an example; and I had no doubt about the correctness of the formulas which I had published: but I nevertheless recognised that an embarrassed and faulty analysis deprived these formulas of the evidentiary character which they needed. I still had some difficulty in doing better, when the legitimacy of the simplifications, which had only a more or less well established analogy in their favour, appeared to me as a necessary consequence of the very nature of the question."
Doesn't this preamble, so masterfully written, have the value of a character trait?

She worked.

Working on the theorems that Fermat had left without proof, she herself finds remarkable numerical theorems, so remarkable that Legendre will insert them in a supplement to the second edition of his Théorie des nombres. At the same time, she contributes to various periodical collections. In the first, in the Annales de Physique et de Chimie, there is an examination of the principles which can lead to understanding of the laws of equilibrium and of motion of elastic solids; this examination is an obvious answer, although it is not named there, to a Memoir of Poisson in which there is the supposition that it is enough to consider the molecular actions as unspecified forces, decreasing rapidly with distance. Mlle Germain, for her part, seeks to establish that the hypotheses on the intimate constitution of bodies are useless and even harmful in the question of elastic bodies, and that it suffices, in order to resolve problems of this kind, to start from the general fact that the elastic bodies have a tendency to re-establish themselves in the form which an external cause may have caused them to lose; whereupon Navier, in his turn, writes: "Some esteem has generally been given to the efforts which have resulted in establishing the principles and analytical forms by means of which a particular class of phenomena was, for the first time, subjected to the world of calculation. As for the observations of M Poisson, after which it would not be permissible to represent the forces resulting from molecular actions by definite integrals, we do not share this opinion." Then, in the Annales of Crelle, in Berlin, there is a Memoir on the curvature of surfaces. Finally, in these same Annales, there is a note on how the $y$ and $z$ values are composed in the equation
$4\Large\frac{x^p - 1}{x - 1}\normalsize = y^{2} ± pz^{2}$,
and those of $Y'$ and $Z'$ in the equation
$4\Large\frac{x^{p^2} - 1}{x - 1}\normalsize = Y^{\prime 2} ± Z^{\prime 2}$.
We know that, taking refuge in her study during the first reforming crisis, she composed these last two works to the sound of the cannon of July 1830.

Such is the succinct summary of the mathematical works of Sophie Germain.

Here we are now in front of the work which assures our geometer a place among the truly modern thinkers, I mean those who have ceased to philosophise outside of real knowledge. Because, if it is true, as Navier thought, that his geometrical writings are such that "very few men can read and that only one woman could do", we must add with Auguste Comte that her posthumous discourse on the state of science and letters at the different periods of their culture, indicates in it "a very lofty philosophy, both wise and energetic, of which very few superior minds today have a feeling so clear and so deep." The word "today" after more than half a century is not to be removed.

When did Sophie Germain start to deal with this philosophical discourse? When did she write it? Is it true, as an opinion placed at the head of the first edition asserts, that it was drafted at the time when the sharp pains to which she succumbed did not allow her to indulge in the mathematical sciences? Is it especially true that it was not intended for printing? Despite the authority which attaches to the affirmation of a man [Amant-Jacques Lherbette] united to Mlle Germain "even more by the bonds of affection than by those of a close kinship," it is without temerity to suppose that, imperfect as it still was, as to the execution, when death tore the quill from the hands of the writer, a work of such great significance had been conceived long before, at length thought through, often revised and retouched. The clues abound. First of all, here is the manuscript, which bears corrections which leave certain sentences unfinished or doubtful, then here is this word found in the Pensées detached from the author: "If the men who have advanced the sciences through their work, if those to whom it has been given to enlighten the world, want to return to the path they have taken, they will see that the most beautiful ideas, the greatest , are the ideas of their youth matured by time and experience. They are enclosed in their first trials like the fruits in the spring buds." Is it not plausible that the whole history of the posthumous discourse is to be found in this beautiful thought, a thought of which our scholar, whom we did not know, shares the honour with a poet [Alfred de Vigny]? It is also a curious thing, which should be noted, that the contemporaries of Mlle Germain, her friends and her parents themselves, will have known and appreciated her only as a mathematician; Libri does not even quote her philosophical pamphlet in the Obituary [Notice nécrologique, by Guglielmo Libri], so esteemed by the way, that he gave it to the Journal des Débats, a year after the death of his friend; M Lherbette having found it, this pamphlet, in his aunt's papers, declares that he publishes it "to fulfil a pious duty towards her memory" and seems to doubt the reception which will be given to it: the theory of sound and indeterminate analysis were, for both of them, the only titles of this woman raising her memory for posterity. We will see how unjust posterity would show itself in restricting its homage in this way.

Fontenelle, recounting that the learned Bourdelin had, at the age of sixteen, translated all Pindar and all Lycophron and could hear without help the great work of La Hire on conical sections, exclaims: "There is a great distance from the Greek poets to the conic sections!" For his part, Condorcet, noting to what extent the poets of his time were indignant at being judged by a geometer, wrote: "The dryness of mathematics seemed to them to have extinguished the imagination and they were no doubt unaware that Archimedes and Euler have put as much into their works as Homer and Ariosto have shown in their poems." Both Condorcet and Fontenelle were well versed in science and literature, and therefore recognised the importance of neither this one nor that one; where does this difference of opinion come from between them, one not hesitating to identify these two branches of human genius, the other eager to differentiate them? The question is more interesting than it first appears.

I do not know whether Sophie Germain, struck by the new insight of Condorcet, had kept it in her memory as one preserves a precious germ to use it in due time; what I know is that her philosophical work has the precise object of bringing down, under the weight of a contrary demonstration, the fictitious barriers that we had hitherto enjoyed, presumably between imagination and reason. Showing reason in aesthetics and imagination in science, I was mistaken in attributing to Sophie Germain the merit of having understood that such a subject could not be usefully approached before mental operations had returned to the experimental method? No, since we see her, although preoccupied with the problem, remain silent for a long time and, witnessing, so to speak, the blossoming of biology, keeping abreast of all that is discovered and written in this regard; no, because when she picks up the pen she begins with these firm words: "The human mind obeys laws; they are those of its own existence."

But, before examining the author's demonstration, let's get to the heart of the matter.

In the first place, if it is true that science results from the systematisation of observed facts, it is also true that all scientific systematisation applies, not to facts surrounded by their concrete complication, but to simplified forms that we obtain by means of abstraction. Abstraction, what is this? It is a process - an artifice if you will - by which one confines oneself to presenting sufficient approximations to supply the absolute reality which one would not otherwise be able to embrace as a whole. Now, to design by abstraction objects that are simpler than real objects, then to coordinate these objects by means of a design the aim of which is to make it easier to grasp the whole, such is the double role of the imagination in science. The atomic system, that of Leibniz in mathematics, that of Laplace in astronomy, that of Jussieu and Blainville in biology, offer examples: these are ingenious designs that currently meet the needs of science, more simply and better than any other; what we must beware of, while giving them a legitimate preference, is to give them an objective reality. The error of theologians and, subsequently, of metaphysicians, is to objectify their conceptions.

In the second place, if it is obvious that art consists of an ideal representation which involves the exaggeration of images, which, according to the judicious remark of Auguste Comte, "must go beyond reality, in order to push us to the improvement," it is also clear that the creative genius, under pain of aberration, is subject to the need to subordinate its idealisation to the natural order. What is idealisation? Like abstraction, it is a process by virtue of which, the main features taking on importance, the representation becomes more faithful in the sense that it is then freed from the empirical mixture which altered it. Now, to regularise utopias by subjecting them to real order, then to make intelligible the communication of the interior type imagined, simplified, modified, such is the double role of reason in aesthetics. All the masterpieces whose brilliance has not waned over time bear witness to this: they are ideal combinations that reason brings back to an indispensable and sufficient reality. The flaw in works without duration, whatever the passing vogue, is to make subjective inspirations prevail over objective notions, or the latter over those.

Dr Segond, in his Programme de Morphologie, has shown very well, on the one hand, how the best-supported studies cannot exempt the artist, at the time of execution, from the presence of a model who must always, to a certain degree, "put obstacles in the way of idealisation;" on the other hand, to what extent the scientist trained in analysis in the study of nature needs the synthetic eye, without which he would see "his theoretical faculties fail, in great coordination."

The analogy of the cerebral operations which preside over the knowledge of truth and the production of beauty is established, we can easily understand, first, how we form the hypotheses which we feel are useful to link our observations, then how, not knowing or forgetting that these same hypotheses have come out entirely from our brain, we represent them as having an objective existence: the gods, the entities, the religions are in this case, and their historical raison d'être is of having been functions of time. From this point of view where all human conceptions emanate from the same background, that is to say from the brain making approximations and idealisations closer and closer to reality depending on whether it is better informed about observable facts, the march of humanity through the ages appears as a series of logically linked phases: fictions lead to truth, the past prepares for the future. Who does not recognise here the positive philosophy?

Does this mean that Sophie Germain had, in this way of considering the intellectual development of humanity, the power and the correctness of the founder of sociology? Point: she does not distinguish between the logical processes which are specific to each category of knowledge; she does not indicate, while noting the organic similarity of aesthetic genius and scientific genius, the different destination of art and science, and her work is not exempt from all metaphysics. However, if it is linked to the old schools by a tendency to unite under the same law the physical order and the moral order, there is, however, in it more general conformity with the doctrines of Auguste Comte than with those of the philosophers in search of the absolute. I take as proof the way the question is asked by her:
If it were given to us to penetrate the nature of things; if the observations, the reflections, the theories which make up our intellectual wealth were not of man, we would choose with certainty between these two propositions: either the type which we find in ourselves and in the external objects which reveal to us the conditions of being; or this type, belonging to us alone, only attests to the way in which we can understand the possible. - This high knowledge is forever forbidden to us. But, by limiting ourselves to investigating how a deep feeling of order and proportion becomes for us the character of truth in all things, we will be able to come to see that, in the various genres, our studies, turned towards the same goal, employ procedures which are always the same.
I underlined the word "how": to seek the how and no longer the why, this is, in fact, what marks the philosophical progress outlined by the school of Diderot.

As for the demonstration, despite a few metaphysical reminiscences that stain, it is peremptory. What does it consist of? In the particular sense, to follow in the poet and in the scientist the cerebral elaboration and the realisation of a mother idea in the general sense, to go through the history of the human spirit to put before us how in all things, "even in its deviations, and by virtue of the laws of its being, all its efforts have been directed towards order, simplicity and unity of conception." The grace of style, the depth of thought, the elegance which the most severe deductions assume, the in some way mathematical precision of the argumentation, an extensive competence in matters of science, a perfect feeling in matters of taste, I do not know what hope of a rebirth where the imagination is mastered by truth as it was by error, a hope which, piercing everywhere, everywhere corrects the correctness of the mind by the abundance of the heart, she uses all this to move and to convince. It convinces and it moves.

What makes this work of Sophie Germain so alive even today is something more than the intuition of a new harmony between our thoughts and feelings; at the same time that it indicates to the scientist, to the poet, to the artist what relations unite them, artificial relations at the time when more or less happy hypotheses formed all their intellectual richness, one feels that she is conscious of working to establish the true relationships which will make, as she says herself, stand out in all its light, the identity between the module of each science, of each art, and the various parts of this science or this art. And, of course, this is not a pipe dream. Still poetry worthy of the name, I mean that which is not limited to expression, has rested on some philosophy; always the artists of the good times have been the affected interpreters of a fundamental doctrine common to the greatest number: it is in their work that humanity, under the multiple aspects of its previous existence, truly survives. This is so true that, even on bad days when aesthetic pride imprints the seal of genius on individual whims, the supposedly inspired people who believe themselves to be the most independent give us the spectacle of a sickly inconsistency, when they do not borrow their inspirations from outstanding systems; I am not talking about those who, strangers to both imagination and reason, limit themselves to imitation, the name of artists not belonging to them. There is more. Do we examine the aptitudes and the work of the men who have left indelible traces in the intellectual world? It is easy to recognise that, driven by circumstances or the impulses of the environment towards the special genre which they have cultivated, they would have equally succeeded in science or in art: Leonardo da Vinci and Goethe, to a large extent, are they not scholars? Buffon and Diderot, in various capacities, are they not artists? Let us therefore conclude with Sophie Germain that if the creative faculty has disappeared from aesthetics with the credit of fictions, this faculty can and must be reborn with the credit of incontestable truths. That this rebirth is possible, everything announces it. But shouldn't we first set aside the vain theories which suppose the incompatibility of imagination and reason, show the current inanity of the notions that are being abandoned, justify those that are substituted for them? This is what the pen of the author of the Considérations has set out to do, doing a great service, not only for the study of the question itself, but also for the importance of the social results that it brings. What advantage would it not be for the politician, still reduced to the contingency of empirical data, to be able to appeal to the certainty of natural laws? I imagine he would carry out our business better. Especially if at the same time he was imbued with that practical truth expressed in the praise of the Tsar-Academician [Peter the Great], namely that it takes vigour to bind a nation to useful novelties.

Sophie Germain's disconnected Pensées, to be sure, were not written for the public, they are mere notes thrown down on paper during her studies and work; however, it suffices to read them to realise that they were, for the most part, inspired by an in-depth reading of Tycho Brahé, Newton and Laplace.

None are dated, they appear without apparent connection, no plan, no order: here it is only a feature, there are the developments of a special point barely indicated; here is the moralist's glance, here is the poet's flap of the wing, and whoever read this somewhat confused mixture without knowing the philosophical work of the mathematician could very well see only the whims, brilliant, but without tomorrow, with a curious and active mind. Have we read the Considérations? Everything is explained and everything is linked. In a way, we surprise the brain of the mathematician in the act of synthetic preoccupations; this intimate collection then takes on a singular interest, because, without a doubt, it contains the germs, and sometimes the flowers, of a conception which will bear fruit, and, not without charm, we think soon, to apply to it this word of Diderot, "The disconnected Pensées are so many brass nails, which sink into the soul and which one does not tear out."

We must distinguish, however. Some of these Pensées, although true, are of a particular, contemporary, fleeting truth. This, for example:
It is there (in the academies) that the human spirit resides: it is alive there in a number of united men, it renders oracles there through their organ and in this human form, animated by the passions of the utility and glory, it is unique like the individual and enduring like the species.
Just recently, this opinion of Sophie Germain could no longer be accepted without reservation.

Auguste Comte treated this question with the breadth and authority of genius; limiting myself to touching on it, I refer the reader to the chapter full of firmness and power which he devoted to it in Cours de Philosophie positive. But I will not leave the subject without pointing out that Sophie Germain's philosophical work is, in itself, a protest against the independence of facts of a psychological and biological order, of which, more than any other, the Académie des sciences morales et politiques is dedicated. Thought, in whatever form it manifests, religion, art, literature, science, history, morality, is inseparable from the organism which conceals it and, consequently, is subject like it to the laws of evolution; I mean, not an indefinite evolution, but the appreciable conditions under which a previous state passes into a new state, retaining its fundamental characteristics. There is a whole series of relationships there, a whole adequate set that it is no longer permissible to split up if you will, I will not say solving the questions, but only asking them well. Let us dare to admit it, if most of our official scientists are individually men of value and conscience, their conscience and their value come to lose their growth in a fragmentary institution which calls for a serious reform.

Now if, among a few other inadmissible Pensées, I have chosen that which concerns the scope and effectiveness of scientific direction to show its current inaccuracy, it is because it is important to keep popular instinct on guard against an error which it shares and which opposes, if not defeats, our intellectual forces; namely, the propensity to believe that academies are the repositories of general knowledge. It is not so. And everything that is done outside of them, in spite of them, against them, proves abundantly that it would be expedient to adapt to modern manners and opinions, do what they are by expanding knowledge, something other than the survivals of the ages when knowledge was limited.

Without a doubt, a writer as active as Sophie Germain would have produced again; and how many truths perhaps a spirit of this power, nourished by so many studies, served by so many talents, had, in its maturity, brought to the full light! An untimely death decided otherwise. As early as 1829, Sophie Germain had felt the attacks of the terrible disease - cancer - which was to lead her to the tomb. She knew she was lost. However, during her illness, which was long and cruel, she did not withdraw her attention from people or things, and her mind, accustomed to superiority, remained superior even in suffering, even in the face of the certainty of the inevitable and imminent destruction. In the meantime, gathering her strength, she resumed her working habits, reopened her living room, and chatted calmly. Finally, she died on 27 June 1831, aged 55.

In this relation of a life worthily employed, it is regrettable that biographical details are so scarce; but if, a discreet worker, Sophie Germain did not tire her contemporaries with the noisy concern for her personality, isn't that even one more headline in our estimation? However, when time, too, has done its work and chosen the names which must not perish, a legitimate curiosity attaches itself to the memory of its chosen ones; it is then that we regret that modesty is one of the attributes of true greatness. Fortunately, we have a moral portrait of Sophie Germain left; I borrow it from Libri who had the good fortune to be received in her privacy [Journal des débats, 18 May 1832]:

"Her conversation had a very special character. The strong characters were a sure tact to capture the parent idea instantly, and arrive at the final consequence, crossing the intermediaries; a joke, the graceful and light form of which always veiled a just and deep thought; a habit, which came to her from the variety of her studies, of constant connections between the physical order and the moral order, which she regarded as subject to the same laws. If we add a continual feeling of benevolence, which made her always forget herself and think only of others, you will feel what her charm must have been.
This forgetfulness of herself, she carried it into everything. She carried it into science, which she cultivated with complete personal abnegation, without thinking of the advantages that success procures; even applauding herself to sometimes see her ideas fertilised by other people, who seized upon them; often repeating that it doesn't matter from whom an idea comes, but only how far it can go; and happy, as soon as hers gave their fruits for science, she did not derive any for the reputation, which she scorned and jokingly called the glory of the bourgeoisie, the little place we occupy in the brains of others.

She wore it too, that noble character, in her actions, always marked at the place of virtue, which she loved, she said, as a geometric truth. For she did not conceive that one could love orderly ideas in one genre without loving them in another; and the ideas of justice, of virtue, were, according to her expressions, ideas of order, which the mind should adopt, even when the heart would not cherish them.
Is this peremptory enough? Even a woman can be a philosopher to the point of writing "that Sacred Scripture does not warn posterity with regard to the sciences," and at the same time give the example of disinterestedness and virtue. Sophie Germain's life brings precious clarity to this delicate point, and this is not the slightest service that she has rendered us.

Sophie Germain is buried in the Père-Lachaise cemetery.

Eager to greet her ashes, I made a pious pilgrimage there recently. Sadness awaited me there. At the crossroads where the sumptuous monument of Casimir Périer rises, a paved lane opens up called the Chemin de La Bédoyère; on entering it, on the left, we meet the mausoleum of Élisa Mercœur and, a few metres behind, that of Auguste Comte: fifty paces away, on the right and in the second line, we see the tree that covers Sophie Germain's grave. Initially, it was a somewhat severe garden, but very convenient: a boxwood plant, a stone tombstone, an iron grid surrounding it, nothing more. Today it is an abandoned ruin: the gate is rusty, broken, out of place; the ground, in places, is broken up; the boxwood, which has not been pruned for many years, forms a bushy shrub left to chance; the stone, overturned, rests on its old base and, by removing the brambles which partly hide it, we can read this modest inscription:

HERE RESTS
DEMOISELLE
MARIE-SOPHIE GERMAIN
BORN IN PARIS
APRIL 1, 1776
DECEASED IN THAT TOWN
JUNE 27, 1831

However, a seed, brought no doubt by the wind, produced a magnificent chestnut tree which, sinking its roots in the tomb itself, extends its shadow far away; an ivy climbs its trunk, gains the first branches and, here and there, lets fall melancholically long stems. Nature, not without grace, has remedied the forgetfulness of men.

Have all of Sophie Germain's parents, all of Sophie Germain's friends entered into eternal absence? It's possible. The impossible is that those - and touching signs show that there are many - whose veneration is attached to the tombs of the young muse and the great philosopher, her neighbours of burial and glory, do not care about honour to raise a stone on which time would soon erase a name that may be dear to them in so many ways. Do not poetry and science owe the same tribute to the one who meditated their alliance?

I mentioned earlier one of Sophie Germain's Pensées as being of ephemeral truth; I will indicate another, in closing, which is of immutable truth. "The real opinion of a century is in the minds of the great men it produced." Nineteenth-century opinion, what is it, judging from this view? It is because, divided by the mysterious hypotheses which once brought our ancestors together, and brought closer, on the contrary, by the scientific realities which divided them, we are at one of those decisive times when the need for a new agreement is imperative. Listen and read. It explodes, this opinion, under the pen or on the lips of all our eminent thinkers, and, of course, the name of Sophie Germain will remain as one of the most precious testimonies of the truth expressed by herself.

But, for this opinion of the century to be translated into fact, what must be done? In the words of the poet, videre longius assueto, one must see further than usual and, for that, having risen to those philosophical summits from the top of which Aristotle, Descartes, Auguste Comte announced to men the progress of the human spirit, to salute, as the goal of knowledge, the reconciliation of mind and heart, of imagination and reason, a supreme goal which is still blurred by a distant twilight.

Hippolyte Stupuy.

[Horace]
I won't be silent about unornamented you
in my pages, and I won't let, Lollius,
black oblivion snatch away