Woman in Science — Women in Mathematics, Part 2

In the year following the publication of Agnesi's _Instituzioni Analitiche_ was recorded the premature and tragic death of the distinguished French mathematician, the Marquise Emilie du Chatelet.

She has been described as a "thinker and scientist, precieuse and pedant, but not the less a coquette--in short, a woman of contradictions."

[121] To most readers she is better known by reason of her liaison with Voltaire, of whom she is regarded as a mere satellite, than for her work in science.

But she was far more than a satellite that shone by the light received from the sage of Ferney.

For there can be no doubt that she was a highly gifted woman who, besides having a thorough knowledge of several languages, including Latin, possessed a special talent for mathematics.

It was said of her that "she read Virgil, Pope and algebra as others read novels," and that she was able "to multiply nine figures by nine others in her head."

No less an authority than the illustrious Ampere declared her to be "a genius in geometry."

Among her teachers in mathematics were Clairaut, Koenig, Maupertuis, Pere Jaquier and Jean Bernouilli, the immediate predecessors of such distinguished mathematicians as Monge, Lagrange, d'Alembert and Laplace.

At her Chateau of Cirey, where she and Voltaire spent many years together, she was visited by learned men from various parts of Europe.

Among these was the Italian scholar, Francisco Algarotti, who was the author of a work entitled _Newtonism for Women_.

And as Mme.

du Chatelet was an ardent admirer of Newton, the author of the _Principia_ soon became a strong bond of union between her and the brilliant Italian.

She called the savants who frequented her chateau at Cirey the _Emiliens_ and purposed writing memoirs to be entitled _Emiliana_--a design, however, which she was never able to execute.

The first work of importance from the pen of the Marquise was entitled _Institutions de Physique_.

In it she gave an exposition of the philosophy of Leibnitz and dissertations on space, time and force.

In the discussion of the last topic she seems to have anticipated some of the later conclusions of science respecting the nature of energy.

Her most noted achievement, however, was her translation of Newton's _Principia_, the first translation into French of this epoch-making work.

To translate this masterpiece from its original Latin, it was necessary that the Marquise, in order to make it intelligible to others, should have a thorough understanding of it herself.

To the translation she added a commentary, which shows that Mme.

du Chatelet had a mathematical mind of undoubted power.

She labored assiduously on this great undertaking for many years and completed it only shortly before her death; but it was not published until ten years after her demise.

In his _Elogie Historique_ on the Marquise's translation of the _Principia_, Voltaire, in his usual flamboyant style, declares "Two wonders have been performed: one that Newton was able to write this work, the other that a woman could translate and explain it."

In an effort to express in a single sentence all his admiration for his talented friend he does not hesitate to state: "Never was woman so learned as she, and never did anyone less deserve that people should say of her, 'She is a learned woman.'

" Again he refers to her with characteristic Frenchiness as "a woman who has translated and explained Newton, in one word a very great man--_en un mot un tres grand homme_."

[122] But, although the extent of her attainments and her ability as a mathematician were unquestionable, she fell far short of her great contemporary, Gaetana Agnesi, both in the depth and breadth of her scholarship and in her power of infinitesimal analysis.

As to her moral character, she was infinitely inferior to the saintly savante of Milan.

She was by inclination and profession an Epicurean and an avowed sensualist.

In her little treatise, _Reflexions sur le Bonheur_--Reflections on Happiness--she unblushingly asserts "that we have nothing to do in this world except procure for ourselves agreeable sensations."

Considering her profligate life, bordering at times on utter _abandon_, we are not surprised that one of her countrymen has characterized her as "_Femme sans foi, sans moeurs, sans pudeur_,"--a woman without faith, without morals, without shame.

[123] Anna Barbara Reinhardt of Winterthur in Switzerland was another woman of exceptional mathematical talent.

She is remarkable for having extended and improved the solution of a difficult problem that specially engaged the attention of Maupertuis.

According to so competent an authority as Jean Bernouilli, she was the superior, as a mathematician, of the Marquise de Chatelet.

Of a more original and profound mathematical mind was Sophie Germain, a countrywoman of the Marquise du Chatelet.

Hers was the glory of being one of the founders of mathematical physics.

A pupil of Lagrange and a co-worker with Biot, Legendre, Poisson and Lagrange, she has justly been called by De Prony "the Hypatia of the nineteenth century."

Her success, however, was not achieved without overcoming many and great difficulties.

In the first place, she had to overcome the opposition of her family, who were decidedly averse to her studying mathematics.

"Of what use," they asked, "was geometry to a girl?"

But in trying to extinguish her ardor for mathematics they but augmented it.

Alone and unaided she read every work on mathematics she could find.

The study of this science had such a fascination for her that it became a passion.

It occupied her mind day and night.

Finally her parents, becoming alarmed about her health and resolved to force her to take the necessary repose, left her bedroom without fire or light, and even removed from it her clothing after she had gone to bed.

She feigned to be resigned; but when all were asleep, she arose and, wrapping herself in quilts and blankets, she devoted herself to her favorite studies, even when the cold was so intense that the ink was frozen in her ink-horn.

Not infrequently she was found in the morning chilled through, having been so engrossed in her studies that she was not aware of her condition.

Before such a determined will, so extraordinary for one of her age, the family of the young Sophie had the wisdom to permit her to dispose of her time and genius according to her own pleasure.

And they did well.

Like the great geometer of Syracuse, Archimedes, who had ever been her inspiration in the study of mathematics, she would have died rather than abandon a problem which, for the time being, engaged her attention.

She first attracted the attention of savants by her mathematical theory of Chladni's figures.

By the order of Napoleon, the Academy of Science had offered a prize for the one who would "Give the mathematical theory of the vibration of elastic surfaces and compare it with the results of experiment."

Lagrange declared the problem insoluble without a new system of analysis, which was yet to be invented.

The consequence was that no one attempted its solution except one who, until then, was almost unknown in the mathematical world; and this one was Sophie Germain.

Great was the surprise of the savants of Europe when they learned that the winner of the _grand prix_ of the Academy was a woman.

She became at once the recipient of congratulations from the most noted mathematicians of the world.

This eventually brought her into scientific relations with such eminent men as Delambre, Fourier, Cauchy, Ampere, Navier, Gauss[124] and others already mentioned.

It was in 1816, after eight years of work on the problem, that her last memoir on vibrating surfaces was crowned in a public seance of the _Institut de France_.

After this event Mlle.

Germain was treated as an equal by the great mathematicians of France.

She shared their labors and was invited to attend the sessions of the _Institut_, which was the highest honor that this famous body had ever conferred on a woman.

The noted mathematician, M. Navier, was so impressed with the extraordinary powers of analysis evinced by one of Mlle.

Germain's memoirs on vibrating surfaces that he did not hesitate to declare that "it is a work which few men are able to read and which only one woman was able to write."

Biot, in the _Journal de Savants_, March, 1817, writes that Mlle.

Germain is probably the one of her sex who has most deeply penetrated the science of mathematics, not excepting Mme.

du Chatelet, _for here there was no Clairaut_.

[125] Like Maria Gaetana Agnesi, Mlle.

Germain was endowed with a profoundly philosophical mind as well as with a remarkable talent for mathematics.

This is attested by her interesting work entitled _Considerations Generales sur l'Etat des Sciences et des Lettres aux Differentes Epoques de Leur Culture_.

All things considered, she was probably the most profoundly intellectual woman that France has yet produced.

And yet, strange as it may seem, when the state official came to make out the death certificate of this eminent associate and co-worker of the most illustrious members of the French Academy of Sciences he designated her as a _rentiere_--_annuitant_--not as a _mathematicienne_.

Nor is this all.

When the Eiffel tower was erected, in which the engineers were obliged to give special attention to the elasticity of the materials used, there were inscribed on this lofty structure the names of seventy-two savants.

But one will not find in this list the name of that daughter of genius, whose researches contributed so much toward establishing the theory of the elasticity of metals,--Sophie Germain.

Was she excluded from this list for the same reason that Agnesi was ineligible to membership in the French Academy--because she was a woman?

It would seem so.

If such, indeed, was the case, more is the shame for those who were responsible for such ingratitude toward one who had deserved so well of science, and who by her achievements had won an enviable place in the hall of fame.

[126] Four years after the birth of Sophie Germain was born in Jedburgh, Scotland, one whom an English writer has declared was "the most remarkable scientific woman our country has produced."

She was the daughter of a naval officer, Sir William Fairfax; but is best known as Mary Somerville.

Her life has been well described as an "unobtrusive record of what can be done by the steady culture of good natural powers and the pursuit of a high standard of excellence in order to win for a woman a distinguished place in the sphere naturally reserved for men, without parting with any of those characteristics of mind, or character, or demeanor which have ever been taken to form the grace and the glory of womanhood."

[127] The surroundings of her youth were not conducive to scientific pursuits.

On the contrary, they were entirely unfavorable to her manifest inclinations in that direction.

Having scarcely any of the advantages of a school education, she was obliged to depend almost entirely on her own unaided efforts for the knowledge she actually acquired.

She, like Sophie Germain, was essentially a self-made woman; and her success was achieved only after long labor and suffering and in spite of the persistent opposition of family and friends.

When she was about fifteen years old, the future Mrs. Somerville received her first introduction to mathematics; and then, strange to say, it was through a fashion magazine.

At the end of a page of this magazine, "I read," writes Mrs. Somerville, "what appeared to me to be simply an arithmetical question; but in turning the page I was surprised to see strange-looking lines mixed with letters, chiefly X's and Y's, and asked 'What is that?'

" She was told it was a kind of arithmetic, called algebra.

Her interest was at once aroused; and she resolved forthwith to seek information regarding the curious lines and letters which had so excited her curiosity.

"Unfortunately," she tells us, "none of our acquaintances or relatives knew anything of science or natural history; nor, had they done so, should I have had courage to ask of them a question, for I should have been laughed at."

Finally she was able to secure a copy of a work on algebra and a Euclid.

Although without a teacher she immediately applied herself to master the contents of these two works, but she had to do so by stealth in bed after she had retired for the night.

When her father learned of what was going on, he said to the girl's mother, "Peg, we must put a stop to this, or we shall have Mary in a straightjacket one of these days."

The mother, who had no more sympathy with her daughter's scientific pursuits than had the father, and, fully convinced, like the great majority of her sex, that woman's duties should be confined to the affairs of the household, strove to divert her daughter's mind from her "unladylike" pursuits.

But her efforts were ineffectual.

The young woman, in spite of all obstacles and opposition, contrived to continue her cherished studies; and, through her uncle, the Rev. Dr. Somerville, afterward her father-in-law, she was able to become proficient in both Latin and Greek.

When she was thirty-three years of age she became the happy possessor of a small library of mathematical works.

"I had now," she writes, "the means, and pursued my studies with increased assiduity;

concealment was no longer necessary, nor was it attempted.

I was considered eccentric and foolish, and my conduct was highly disapproved of by many, especially by some members of my own family."

[128] In March, 1827, Mrs. Somerville received a letter from Lord Brougham, who had heard of her remarkable acquirements, begging her to prepare for English readers a popular exposition of Laplace's great work--_Mecanique Celeste_.

She was overwhelmed with astonishment at this request, for her modesty made her diffident of her powers; and she felt that her self-acquired knowledge of science was so far inferior to that of university men that it would be sheer presumption for her to undertake the task proposed to her.

She was, however, finally persuaded to make the attempt, with the proviso that her manuscript should be consigned to the flames unless it fulfilled the expectations of those who urged its production.

In less than a year her work, to which she gave the name of _The Mechanism of the Heavens_, was ready for the press.

But it was far more than a translation and epitome, as originally intended by its projector, Lord Brougham; for, in addition to the views of Laplace, it contained the independent opinions of the translator respecting the propositions of the illustrious French savant.

No sooner was the work published than Mrs. Somerville found herself famous.

She had, as Sir John Herschel expressed it, "written for posterity," and her book placed her at once among the leading scientific writers and thinkers of the day.

She was elected an honorary member of the Royal Astronomical Society at the same time as Caroline Herschel, they being the first two women thus honored.

Her bust, by Chantry, was placed in the great hall of the Royal Society, and she was made a member of many other scientific societies in Europe and America.

In recognition of her services to science she was granted by the government a pension of L200 a year--a sum which was shortly afterward increased to L300.

In addition to all this, Mrs. Somerville had the satisfaction of learning that her work was so highly esteemed by Dr. Whewell, the great master of Trinity, that it was, chiefly on his recommendation, introduced as a textbook in the University of Cambridge and prescribed as "an essential work to those students who aspire to the highest places in the examinations."

What Mme.

du Chatelet had done for Newton, Mrs. Somerville did for Laplace.

Among other books from the pen of this highly gifted woman is her _Connection of the Physical Sciences_ and a work entitled _Physical Geography_, which, together with the _Mechanism of the Heavens_, was the object of the "profound admiration" of Humboldt.

Then there is a number of very abstruse monographs on mathematical subjects, one of which is a treatise of two hundred and forty-six pages _On Curves and Surfaces of Higher Orders_, which, she tells us, she "wrote _con amore_ to fill up her morning hours while spending the winter in Southern Italy."

Her last work was a treatise _On Molecular and Microscopic Science_ embodying the most recondite investigations on the subject.

This book, begun after she had passed her eightieth birthday, occupied her for many years and was not ready for publication until she was close upon her ninetieth year.

Her last occupations, continued until the day of her death at the advanced age of ninety-two, were the reading of a book on _Quaternions_ and the review and completion of a volume _On the Theory of Differences_.

Like her illustrious friend, the great Humboldt, Mary Somerville was possessed of extraordinary physical vigor, and, like him, she retained her mental powers unimpaired until the last.

And like her great rival in mathematics, Maria Gaetana Agnesi, she was always "beautifully womanly."

Her scientific and literary occupations did not cause her to neglect the duties of her household or to disregard "the graceful and artistic accomplishments of an elegant woman of the world."

Her daughter Martha writes of her: "It would be almost incredible were I to describe how much my mother contrived to do in the course of the day.

When my sister and I were small children, although busily engaged in writing for the press, she used to teach us for three hours in the morning, besides managing her house carefully, reading the newspapers--for she was always a keen and, I must add, a liberal politician--and the most important new books on all subjects, grave and gay.

In addition to this, she freely visited and received her friends....

Gay and cheerful company was a pleasant relaxation after a hard day's work."

[129] The life of Mary Somerville, like that of Gaetana Agnesi, proves that the pursuit of science is not, as so often asserted, incompatible with domestic and social duties.

It also disposes of the fallacy, so generally entertained, that intellectual labor is detrimental to the health of women and antagonistic to longevity.

The truth is that it is yet to be demonstrated that intellectual work, even of the severest kind, is, _per se_, more deleterious to women than to those of the stronger sex.

Scarcely less remarkable as a mathematician was Mrs. Somerville's distinguished contemporary, Janet Taylor, who was known as the "Mrs. Somerville of the Marine World."

She was the author of numerous works on navigation and nautical astronomy which in their day were highly prized by seafaring men.

In recognition of her valuable services to the marine world she was placed on the civil list of the British government.

As an eminent mathematician as well as a "representative of the highest intellectual accomplishments to which women have attained," Sonya Kovalevsky will ever occupy an honored place among the votaries of science.

In many respects this richly endowed daughter of Holy Russia was _par excellence_ the woman of genius of the latter half of the nineteenth century.

She was born in Moscow in 1850, but although her career was brief it was one of meteoric splendor.

At an early age she exhibited an unusual talent for mathematics and an unquenchable thirst for knowledge.

Not being able to obtain in her own country the educational advantages she desired, she resolved at the age of eighteen to go to Germany with a view of pursuing her studies there under more favorable auspices.

She first matriculated in the University of Heidelberg, where she spent two years in studying mathematics under the most eminent professors of that famous old institution.

Thence she went to Berlin.

She could not enter the University there, as its doors were closed to female students;

but she was fortunate enough to prevail on the illustrious Professor Weierstrass, regarded by many as the father of mathematical analysis, to give her private lessons.

He soon discovered to his astonishment that this child-woman had "the gift of intuitive genius to a degree he had seldom found among even his older and more developed students."

Under this eminent mathematician Sonya spent about three years, at the end of which period she was able to present to the University of Goettingen three theses which she had written under the direction of her professor.

The merit of her work and the testimonials which she was able to present from Weierstrass, Kirchhoff and others were of such supreme excellence that she was exempted from an oral examination and was enabled, by a very special privilege, to receive her doctorate without appearing in person.

Not long after receiving her doctor's degree--one of the first to be granted to a woman by a German university--she was offered the chair of higher mathematics in the University of Stockholm.

She was the first woman in Europe, outside of Italy, to be thus honored.

But her appointment had to be made in the face of great opposition.

No other university, it was urged by the conservatives, had yet offered a professor's chair to a woman.

Strindberg, one of the leaders of modern Swedish literature, wrote an article in which he proved, "as decidedly as that two and two make four, what a monstrosity is a woman who is a professor of mathematics, and how unnecessary, injurious and out of place she is."

[130] The fame that came to Sonya through her achievements in the German and Swedish universities was immensely enhanced when, on Christmas eve, 1888, "at a solemn session of the French Academy of Sciences, she received in person the _Prix Bordin_--the greatest scientific honor which any woman had ever gained; one of the greatest honors, indeed, to which any one can aspire."

She became at once the heroine of the hour and was thenceforth "a European celebrity with a place in history."

She was feted by men of science whithersoever she went and hailed by the women of the world as the glory of her sex and as the most brilliant type of intellectual womanhood.

Mme.

Kovalevsky's printed mathematical works embrace only a few memoirs including those which she presented for her doctorate and for the _Prix Bordin_.

But brief as they are, all of these memoirs are regarded by mathematicians as being of special value.

This is particularly true of the memoirs, which secured for her the _Prix Bordin_; for it contains the solution of a problem that long had baffled the genius of the greatest mathematicians.

The prize had been opened to the competition of the mathematicians of the world, and the astonishment of the committee of the French Academy was beyond expression when it was found that the successful contestant was a woman.

[131] Everyone admired her varied and profound knowledge, but, above all, her amazing powers of analysis.

A German mathematician, Kronecker, did not hesitate to declare that "the history of mathematics will speak of her as one of the rarest investigators."

[132] Shortly before her premature death, she had planned a great work on mathematics.

All who are interested in the intellectual capacities and achievements of woman must regret that she was unable to complete what would undoubtedly have been the noblest monument of woman's scientific genius.

She was then in the prime of life and perfectly equipped for the work she had in mind.

Considering the extraordinary receptive and productive power of this richly dowered woman, there can be little doubt, had she lived a few years longer, that she would have produced a work that would have caused her to be ranked among the greatest mathematicians of the nineteenth century.

It is pleasant to record that this woman of masculine mind, masculine energy and masculine genius, far from being mannish or unwomanly, was, on the contrary, a woman of a truly feminine heart; and that, although a giantess in intellectual attainments, she was in grace and charm and delicacy of sentiment one of the noblest types of beautiful womanhood.

She could with the greatest ease turn from a lecture on _Abel's Functions_ or a research on Saturn's rings to the writing of verse in French or of a novel in Russian or to collaborating with her friend, the Duchess of Cajanello, on a drama in Swedish, or to making a lace collar for her little daughter, Fouzi, to whom she was most tenderly attached.

[133] Little more than a quarter of a century has elapsed since Strindberg, expressing the sentiment of the great majority of the men of his time, declared that a woman professor of mathematics is a monstrosity.

But during this short period what a change has been effected in the attitude of the world toward women who devote themselves to the study and the teaching of science!

Women mathematicians are found to-day in all civilized countries, and no sane person now considers it any more "unwomanly" or more "monstrous" for them to study or teach mathematics than for them to teach music or needlework.

Yet more.

They are now frequent contributors to mathematical magazines and to the official bulletins of learned societies, and not infrequently they are on the editorial staffs of publications devoted exclusively to mathematics.

They are also found as computers in some of the largest astronomical observatories, where the speed and accuracy of their work have evoked the most favorable comment.

Of women in America, who have distinguished themselves by their work in the higher mathematics, it suffices to mention the name of Miss Charlotte Angas Scott, recently deceased, who was for years professor of mathematics in the College of Bryn Mawr.

Her writings on various problems of the higher mathematics show that she faithfully followed in the footsteps of her illustrious predecessors,--Hypatia, Agnesi, du Chatelet, Germain, Somerville and Kovalevsky.

FOOTNOTES:

[108] "Ipse mulieres Philosophas in libris Veterum sexaginta quinque reperi," _Historia Mulierum Philosopharum_, p. 3, Amstelodami, 1692. [109] Plato had inscribed above the entrance of his school, [Greek: Oudeis ageometretos eisito].

Let no one enter here who is not a geometer.

[110] Menagius in referring to this matter, op.

cit.

, p. 37, writes as follows: "Meritrices Graecas plerasque humanioribus literis et mathematicis disciplinis operam dedisse notat Athenaeus."

[111] The sentiment of the Greek epigram is well expressed in the following Latin verses: "Quando intueor te, adoro, et sermones, Virginis domum sideream intuens.

E coelis enim tua sunt opera, Hypatia casta, sermonum venustas, Impollutum astrum sapientis doctrinae."

[112] Among modern works on Hypatia may be mentioned _Hypatia, die Philosophin von Alexandria_, by St. Wolt, Vienna, 1879; _Hypatia von Alexandria_, by W. A.

Meyer, Heidelberg, 1886; _Ipazia Alessandrina_, by D.

Guido Bigoni, Venize, 1887, and _De Hypatia_, by B. Ligier, Dijon, 1879. [113] Ambrosius in his preface to the works of Abelard and Heloise refers to the latter as "Clarum sui sexus sidus et ornamentum," and declares "necnon mathesin, philosophiam et theologiam a viro suo edocta, illo solo minor fuit."

[114] Mazzuchelli says of her in his _Museo_, "Sembra non avervi nella Natura cosa la piu intralciata ed oscura nelle storie, ne finalemente la piu astrusa nelle matematiche e nelle mecchaniche, che a lei conta non sia e palese, e che sfugga la capacita del suo spirito."

_Dizionario Biografico_, Vol. I, p. 122, by Ambrogio Levati, Milano, 1821. [115] _Delle Donne Illustri Italiane del XIII al XIX Secolo_, p. 268, Roma.

[116] The full title of this celebrated discourse is _Oratio qua ostenditur Artium liberalium studia a Faemineo sexu neutiquam abhorere, habita a Maria de Agnesis Rhetoricae Operam Dante, Anno aetatis suae nono nondum exacto, die 18, Augusti, 1727_.

It is found at the end of a work entitled _Discorsi Academici di varj autori Viventi intorno agli Stuj delle Donne in Padova_, 1729. This subject, it may be remarked, frequently engaged the attention of Maria Gaetana as she advanced in years, for we find it among the questions discussed in her _Propositiones Philosophicae_, pp. 2 and 3, Mediolani, 1738. [117] M.

Charles de Brosses, in his _Lettres Familieres ecrites de l'Italie en 1739 et 1740_, speaks of Agnesi in terms that recall the marvelous stories which are related of Admirable Crichton and Pico della Mirandola.

"She appeared to me," he tells us, "something more stupendous--_una cosa piu stupenda_--than the Duomo of Milan."

Having been invited to a _conversazione_ for the purpose of meeting this wonderful woman, the learned Frenchman found her to be a "young lady of about eighteen or twenty."

She was surrounded by "about thirty people many of them from different parts of Europe."

The discussion turned on various questions of mathematics and natural philosophy.

"She spoke," writes de Brosses, "wonderfully well on these subjects, though she could not have been prepared beforehand any more than we were.

She is much attached to the philosophy of Newton; and, it is marvelous to see a person of her age so conversant with such abstruse subjects.

Yet, however much I was surprised at the extent and depth of her knowledge, I was still more amazed to hear her speak Latin ...

with such purity, ease and accuracy, that I do not recollect any book in modern Latin written in so classical a style as that in which she pronounced these discourses....

The conversation afterwards became general, everyone speaking in the language of his own country, and she answering in the same language; for, her knowledge of languages is prodigious."

[118] At the conclusion of an elaborate review of Colton's translation of Agnesi's _Instituzioni Analitiche_ in the _Edinburgh Review_ for January, 1804, the writer expresses himself as follows: "We cannot take leave of a work that does so much honor to female genius, without earnestly recommending the perusal of it to those who believe that great talents are bestowed by nature exclusively on man, and who allege that women, even in their highest attainments, are to be compared only to _grown children_, and have, in no instance, given proofs of original and inventive powers, of a capacity for patient research, or for profound investigation.

Let those who hold these opinions endeavor to follow the author of the _Analytical Institutions_ through the long series of demonstrations, which she has contrived with so much skill and explained with such elegance and perspicuity.

If they are able to do so, and to compare her work with others of the same kind, they will probably retract their former opinions, and acknowledge that, in one instance at least, intellectual powers of the highest order have been lodged in the brain of a woman.

"At si gelidus obstiterit circum praecordia sanguis; and if they are unable to attend this illustrious female in her scientific excursions, of course, they will not see the reasons for admiring her genius that others do; but they may at least learn to think modestly of their own."

[119] It is surprising how many legends have obtained respecting the life of Agnesi after the publication of her _Instituzioni Analitiche_.

Thus, the writer of the article in the _Edinburgh Review_, above quoted, declares that "she retired to a convent of _blue nuns_,"--a statement that has frequently been repeated in many of our most noted encyclopedias.

In a _Prospetto Biografico delle Donne Italiane_, written by G. C.

Facchini and published in Venice in 1824, it is stated that Maria Gaetana was selected by the Pope to occupy "the chair of mathematics which had been left vacant by the death of her father," while Cavazza in his work _"Le Scuole dell," Antico Studio Bolognese_, pp. 289-290, published in Milan in 1896, assures us that Gaetana Agnesi taught analytical geometry in the University of Bologna for full forty-eight years.

The facts are that neither the father nor the daughter ever taught even a single hour either in this or in any other university.

Cf.

_Maria Gaetana Agnesi_, p. 273 et seq.

, by Luisa Anzoletti, Milano, 1900. This is far the best life of Milan's illustrious daughter that has yet appeared.

The reader may also consult with profit the _Elogio Storico_ di Maria Gaetana Agnesi, by Antonio Frisi, Milano, 1799, and _Gli Scrittori d'Italia_, of G. Mazzuchelli, Tom.

I, Par.

I, p. 198 et seq.

, Brescia, 1795. [120] M.

Rebiere, in _his Les Femmes dans la Science_, p. 13, Paris, 1897, writes, "Ne pourrait-on aller plus loin et canonizer notre Agnesi?

J'estime, moi profane, que ce serait une sainte qui en vaudrait bien d'autres."

[121] _An Eighteenth Century Marquise, a Study of Emilie du Chatelet_, p. 5, by F. Hamel, New York, 1911. [122] Preface to Mme.

du Chatelet's translation of the _Principia_ of Newton, Paris, 1740. [123] Voltaire's last tribute, "The Divine Emilie," or, as Frederick II was wont to call her, "Venus-Newton," concluded with the following verses: "L'Univers a perdu la sublime Emilie;

Elle aimait les plaisirs, les arts, la verite;

Les dieux, en lui donnant leur ame et genie, N'avaient garde pour eux que l'immortalite."

The universe has lost the sublime Emilie; she loved pleasure, the arts, truth; the gods, in giving her their soul and genius, retained for themselves only immortality.

For further information of this extraordinary woman, see _Lettres de la Mme.

du Chatelet, Reunies pour la premiere fois_, par Eugene Asse, Paris, 1882. [124] At the beginning of her correspondence with Gauss, Legendre and Lagrange Mlle.

Germain concealed her sex under a pseudonym, "in order," as she declared, "to escape the ridicule attached to a woman devoted to science"--_craignant le ridicule attache au titre de femme savante_.

She, too, suffered from the widespread effects of Moliere's _Les Femmes Savantes_, as had many a gifted woman before her time and as have many others of a much later date.

[125] This celebrated mathematician, as is well-known, was a collaborator with Mme.

du Chatelet in her translation of Newton's _Principia_.

[126] For further information respecting this remarkable woman the reader is referred to _Oeuvres Philosophiques de Sophie Germain Suivies de Pensees et de Lettres Inedites et Precedees d'une Etude sur sa Vie et ses Oeuvres_, par.

H.

Stupy, Paris, 1896. One may also consult Todhunter's _History of the Theory of Elasticity and of the Strength of Materials_, Vol. I, pp. 147-160, Cambridge, 1886, in which is given a careful resume of Mlle.

Germain's mathematical memoirs on elastic surfaces.

[127] _Saturday Review_, January 10, 1874. [128] _Personal Recollections, From Early Life to Old Age, of Mary Somerville_, p. 80, Boston, 1874. [129] _Personal Recollections_, ut sup.

, p. 5. [130] _Sonya Kovalevsky, Her Recollections of Childhood, With a Biography_, by Anna Carlotta Leffler, p. 219, New York, 1895. [131] "The prize was doubled to five thousand francs, on account of the 'quite extraordinary service rendered to mathematical physics by this work,' which the Academy of Sciences pronounced 'a remarkable work.'

The competing dissertations were signed with mottoes, not with names, and the jury of the Academy made the award in utter ignorance that the winner was a woman.

Her dissertation was printed, by order of the Academy, in the _Memoires des Savants Etrangers_.

In the following year Mme.

Kovalevsky received a prize of fifteen hundred kroner from the Stockholm Academy for two works connected with the foregoing."

[132] Men of science will realize the capacity of this gifted Russian woman as a mathematician when they learn that she gave in the University of Stockholm courses of lectures on such subjects as the following: Theory of derived partial equations; theory of potential functions;

applications of the theory of elliptic functions; theory of Abelian functions, according to Weierstrass; curves defined by differential equations, according to Poincare; application of analysis to the theory of whole numbers.

How many men are there who give more advanced mathematical courses than these?

[133] To a friend, who expressed surprise at her fluttering to and fro between mathematics and literature, she made a reply which deserves a place here, as it gives a better idea than anything else of the wonderful versatility of this gifted daughter of Russia.

"I understand," she writes, "your surprise at my being able to busy myself simultaneously with literature and mathematics.

Many who have never had an opportunity of knowing any more about mathematics confound it with arithmetic, and consider it an arid science.

In reality, however, it is a science which requires a great amount of imagination, and one of the leading mathematicians of our century states the case quite correctly when he says that it is impossible to be a mathematician without being a poet in soul.

Only, of course, in order to comprehend the accuracy of this definition, one must renounce the ancient prejudice that a poet must invent something which does not exist, that imagination and invention are identical.

It seems to me that the poet has only to perceive that which others do not perceive, to look deeper than others look.

And the mathematician must do the same thing.

As for myself, all my life I have been unable to decide for which I had the greater inclination, mathematics or literature.

As soon as my brain grows wearied of purely abstract speculations it immediately begins to incline to observations on life, to narrative, and _vice versa_, everything in life begins to appear insignificant and uninteresting, and only the eternal, immutable laws of science attract me.

It is very possible that I should have accomplished more in either of these lines, if I had devoted myself exclusively to it; nevertheless, I cannot give up either of them completely."

From Ellen Key's _Biography of the Duchess of Cajanello_, quoted in Anna Leffler's biography of Sonya Kovalevsky, ut sup, pp. 317-318. CHAPTER IV