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vocation to be an authoress, to write stitution des anneaux de Saturn." A novels, and to this end it was indispen-third, "Sur la réduction d'une certaine sable that she should "study life." classe d'intégrales abéliennes du troiShe was supplied with exceptionally sième degré à des intégrales ellipample material for this study, inasmuch tiques." So admirable was the quality as she was destined to be in Paris dur- of her work, that the faculty of the ing its siege by the Prussians, and university conferred on her the rare during the horrors of the Commune. distinction of a degree granted in abAs soon as it was possible to obtain sentia, and without further examinaaccess to the city, Sophie hurried tion. thither under the protection of her husband, to discover her sister's fate. Anna had plunged into the thick of the intrigues and conspiracies of the Commune, and had "formed a connection!' (knutit en förbindelse) with a young Frenchman and Communist. Unable to induce Anna to leave Paris, or to be of much service to her there, Sophie and Vladimir, after a short stay and some stirring experiences, returned to Berlin. But after the fall of the Commune, the former received an urgent letter from Anna to the effect that M. J was in prison and condemned to death. Anna was now prepared to implore her father's forgiveness and his help in these terrible circumstances.

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It was a strange party that now assembled at Palibino in the long winter nights in the "Salon with the red damask furniture, whilst the samovar hissed on the tea-table, and the hungry wolves howled in the lonely park." Sophie was suffering from reaction after the severe mental strain she had endured. She was worn out, and for the time incapable of further effort; she passed her time in reading novels and playing cards. Anna's life-studies," too, it must be admitted, had been of an exhausting nature; she asked for no more experiences of the kind, no more such violent sensations. Moreoveralas that it should have to be recorded! she was terribly, even jealously, in love with her husband! She, the rigid Suffering keenly under the fresh Anna of the earlier years, with the blow to every cherished sentiment in- lofty scorn of all such "vulgar sentiflicted on him by his eldest daughter, ments," to this complexion had she General Kroukovsky hastened to Paris. come at last. We are told that to Former friendly relations with M. Sophie it was a source of much pleasThiers seem to have enabled him to ure to observe the change that had snatch M. J from the impending taken place in her father's character. fusillade, and to hurry him and Anna It had become much modified under out of France to the safe seclusion of the undoubtedly" severe training" to Palibino. Such were the circumstances which his daughter had subjected him; under which "Aniouta "returned to the so that in these days he tolerated on shelter of her old home. A little later the one hand the revolutionary and the family circle was completed by the socialistic sentiments of his Communist arrival of Sophie and Vladimir. The son-in-law, who with a "somewhat former had obtained the degree of doc- cynical expression on his face, regarded tor from the University of Göttingen, his surroundings from the depths of his to which by the advice of Weierstrasse, red easy-chair," and on the other hand she had sent three papers, all of which the materialistic tendencies of the scihe pronounced to be of great scientific entific pair. Poor Ivan Sergeievitch! value. One of these ("Zur Theorie it is impossible not to feel very sorry der partiellen Differentialgleichungen," for him, and one almost welcomes the Crelles Journal, Bd. 80) ranks as one intelligence that his education — at of the most important of her pro- least in this stage of his existence — ductions. Another valuable paper was was carried no further. He died sudentitled, "Additions avec remarques denly of heart disease. Probably his aux recherches de Laplace sur la con- character was not the only thing that

was

" modified" by the severity of the | been induced to commit a more fatal tasks set him. His death was the sig- mistake than the rash monetary vennal for the dispersion of the family.tures of his later days, and who, in a There were to be no more long winter position beset with difficulties, had, evenings spent at Palibino. upon the whole, borne himself well.

Sophie felt her father's loss keenly. Between her mother and herself there had never from earliest childhood been any deep sympathy. Anna turned for consolation to her husband, to whom she was devoted. To Sophie, at this moment, the loneliness of her existence seemed too terrible to be longer borne. She resolved to bear it no longer, and she proposed to her husband that they should relinquish the attempt - which now seemed to her more painfully unnatural than ever- to base their life on "fiction."

The shock of this unlooked-for event, and the bitterness of her self-reproach, cost Sophie a long and painful nervous illness, out of which she struggled, saddened and worn, and suddenly become years older. It was well for her that work was henceforth to be not merely a distraction, or a congenial occupation, but a necessity, a means by which she was to win daily bread for herself and her child. In her moments of deep depression she was wont to turn to mathematics, and to rejoice that there existed a world "from which the 'I' was entirely excluded."

He had been much impressed by her great abilities and by the extent of her scientific knowledge, and was very anxious to secure her services for the benefit of his native city. He proposed, therefore, that she should come to Stockholm, and associate herself with him in teaching as his "Docent." Madame Kovalevsky gladly accepted his offer, and came to Stockholm in the winter of the year 1883-84. The course of lectures which she delivered during this winter season were, therefore, of an unofficial and private character, but so noteworthy were they in all respects that they sufficed to establish her reputation as a teacher.

A new chapter in M. Kovalevsky's During one of the recent years spent life had commenced which opened in St. Petersburg Madame Kovalevsky hopefully, even brilliantly; but it, too, had made the acquaintance of the was destined to become overshadowed | Swedish Professor Mittag-Leffler, like and to end in catastrophe. The next herself a former pupil of Weierstrasse. few years were passed by M. and Mme. Kovalevsky in St. Petersburg, where the latter found herself a centre of attraction and admiration, amid its scientific and social circles. Unhappily they were soon overtaken by serious pecuniary embarrassments brought about by the failure of rash speculations, into which M. Kovalevsky had been tempted to enter. Mere material loss appears to have had few terrors for his wife, who in this crisis stood loyally by his side, and endeavored to lighten the burden of discouragement which pressed on him as he realized that he had reduced his wife and child to poverty. (Madame Kovalevsky's only child was born in St. Petersburg in 1878). But the Not only did they manifest the exrelations between this strange pair be- tent and profundity of her knowledge, came once more strained, and this time but they proved that she possessed, in it was the wife who, with tears and re- an unusual degree, the power of improaches, fled precipitately from her parting it to others. As a lecturer she home, resolved to earn a livelihood for displayed an almost unique power of herself and her little daughter in a for- interesting and stimulating her heareign land. In Paris she received not ers, of taking possession of her audilong after the intelligence of her hus-ence and carrying it along with her, of band's death. Life had become too infusing into it some portion of her painful and complicated an affair for own enthusiasm. "To those among the simple-hearted and unfortunate Vladimir, who in his early youth had

her pupils," says M. Mittag-Leffler, "who possessed the power and the

will to follow her, she delighted to relief the marked dualism of her nacommunicate the extraordinary wealth ture, this was the precise moment of her knowledge and the profound chosen by Destiny to place her face to insight of her penetrating genius." face with a momentous crisis affecting This course of lectures gained for her her whole inner life; to provide each the appointment to the chair of higher side of her twofold nature with its apmathematics at the University of propriate stimulus, aud to leave the Stockholm. All opposition fell away opposing tendencies to a bitter conflict. before this incontestable evidence of In a word, in the maturity of her superiority, and in July, 1884, she was womanhood, and in the full swing of appointed to the position, which she her intellectual activity, Madame Kooccupied until her death. valevsky met the man who alone had the power to awake within her a deep and passionate love.

In the autumn of the same year (1884) she completed a valuable work, begun some time before, on "The He was a Russian, and apparently a Refraction of Light in a Crystalline man of worth and merit. He, on his Medium" (Ljusetts brytning i ett kris- side, was strongly attracted by his distalliniskt medium), which was at once tinguished country woman, and asked translated into German, and was re- her to become his wife. But, rightly ceived with warm admiration by her or wrongly, she believed that his feelold friend and master, Weierstrasse. ing for her was not the same as that In a lively letter to a friend in Berlin, with which she regarded him, that it dated April, 1885, she describes her was admiration for the scientist rather life in Stockholm at this period-her than love for her as a woman; and this three lectures a week in Swedish, her she could not brook. Hers was not a contributions to a mathematical jour- nature that could content itself with nal, the quantity of work she had half measures, least of all where undertaken together with Professor the affections were concerned. She Mittag-Leffler, and her lessons in skat- struggled "with all her soul's energy" ing and in riding (in neither of which to win from him the same love that she exercises does she seem to have ex- had bestowed on him; and she could celled); but she expressed at this time never feel that she had succeeded. It a strong desire to make up for her lost was her nature to love exactingly and youth, to which she looked back with tyrannically, to demand an absolute deregret, as having been passed without votion; yet she was conscious that she young girl's customary joys and was unable to make a corresponding pleasures. sacrifice of herself, of her gifts, her work, her position. She felt it an imperious necessity to belong to herself,

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It was, however, during the two following years (1886-88) that Madame Kovalevsky undertook the crowning to be mistress of herself, of her time, scientific labor of her life. She re- of her actions; but that the man she solved to enter the lists as a competitor loved should recognize these claims of for the Bordin prize, to be bestowed, genius, and, bowing to them, should in the year 1888, by the French Acad- withdraw his own, plunged her into emy of Science for the best treatise on the bitterness of despair. the following subject: "To perfect It was under such conditions, and in one important point the theory of with her intellectual powers strained to the movement of a solid body round an the utmost, that she labored day and immovable point." The contest for night during several months previous this prize once entered on, the winning to the completion and sending in of her of it became, says her biographer, "a work to the French Academy. In July necessity " for her, inasmuch as all her of the year 1888 the commission apmathematical friends knew of her de- pointed to report on the Bordin prize termination to compete. And as if announced that it had unanimously dewith the view of bringing into sharp cided to award this prize to the Thesis

bearing the Number 2.
. . . of this remarkable
the report, "has not been content with
adding a result of the highest interest
to those which have been transmitted
to us on this subject by Euler and La-
grange; he has made an exhaustive
study of the discovery which we owe
to him, in which are employed the
entire resources of the modern theory
of functions."

"The author | triumph was not confined to Paris. It work," says was hailed with pride at St. Petersburg, Berlin, and Stockholm. She had won a position amid the ranks of the foremost scientists of the Continent, and, in the eyes of the world, she seemed to occupy a position as enviable as it was unique. But the world was mistaken. Before a month had passed (in January, 1889) she writes thus from Paris to M. Mittag-Leffler :

The sealed note attached to this

paper was opened, and was found to contain the name of Sophie Kovalevsky. On the following 24th of December the prizes were delivered at a public meeting held for that purpose, when the president said: "Among the crowns which we are about to bestow, one of the most important and most difficult to obtain will be placed on a woman's brow. The grand prize in

I have just received your friendly letter. How thankful I am for your friendship. It seems to me that it is the only really good thing which life has left me... From all sides I receive letters of congratulation, and, by a strange irony of fate, I was never in my life so wretched as I am now. Miserable as a dog! No! I hope for the dogs' sake that they cannot be so miserable as men, and above all as women can be. But I shall become more reasonable in time; at any rate I will try to be so. mathematical science will be carried . . I return to my rooms at night only to off this year by Mme. Kovalevsky. pace up and down. I have neither appeOur colleagues of the Section of Geom-tite nor sleep, and my nervous system is in etry have recognized in this work the a frightful state. Adieu. Preserve your proofs, not only of extensive and pro- friendship for me; I assure you I greatly found learning, but also of great powers need it. of original research."

It was announced that, in recognition of the extraordinary merits of the paper, the judges had decided to raise the amount of the prize from three thousand to five thousand francs. This was the crowning moment in the scientific career of the distinguished author of Treatise No. 2.

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A few months later she writes to

Mme. Edgren-Leffler :

I work because I must, but I neither You can hope nor desire anything more. scarcely conceive to what a degree I feel indifferent to everything.

When, in the following September, she returned to Stockholm, her friends found her much changed. Her old bright look was gone, and her eyes had lost their fire. "To outsiders she endeavored to appear cheerful; but to us who stood near her," says her friend, “the alteration was very marked. She had lost her old pleasure in society, not only for that of strangers, but also for ours. She took up her lectures as a matter of duty, but without any interest in them." It was rather to literary work, to the writing of romances, that she turned as a distraction from painful reflections. It was a welcome relief to her thus to describe her own inner history. "Vae Victis" was the title of the novel with which she busied herself

Seated in the midst of one of the most noteworthy scientific assemblies in Europe the centre of observation, the object of unstinted admiration and congratulations — we would fain believe that there was crowded into that hour of triumph a reward, in some degree, adequate to her previous toils and sorrows. During the last days of the year 1888 and the opening ones of 1889, she was the heroine of the learned circles of Paris, and her time was passed in the midst of a veritable whirlpool of excitement. She went from fête to fête, listened to speeches in which her health was proposed and returned thanks for the compliment, received "interviewers" and visitors all day long. Her at this period. VOL. VI. 304

LIVING AGE.

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Few women have won so much fame, so | from defeat, and success which is but much success; yet in this book it is the another name for failure. There was story of the "Vanquished" that she seeks never a period in Sophie Kovalevsky's to tell. She felt herself, in spite of all her intellectual career, in which her magtriumphs, to be one of the "Vanquished,' nificent gifts and her indomitable will for she had failed in the "Struggle for failed to carry her triumphantly to the Happiness," ,"1 and her sympathy was always with them that go under, never with the goal she wished to attain; nor a period in which the friend, who stood nearest to her, failed to catch the sorrowful words: "Thou would'st not think how ill all's here about my heart."

fortunate.

A deep sympathy with suffering was one of her characteristic traits; not the Christian idea of compassion for suffering, but sympathy (medlidande) in the literal meaning of the word. She felt the sorrows of others as her own, but not with any idea of seeking to console them, rather with despair over life's misery.

Taking the direction of her life into her own hands, and choosing for herself one of the steepest paths to fame, she traversed it with swift and steady steps, only to find, when she had In the last year of her life (1890) she reached the summit, that at her feet entertained great hopes of being elected there was a chasm which she could not a member of the Academy of St. Peters-cross, and that whilst glory was on this burg, not only because it was the great- side happiness lay on the other; the est honor that Russia could bestow "heart's happiness," the happiness of on an eminent scientist, but because the emoluments of the position would enable her to live, and would free her from the necessity, now become intolerable to her, of continuing her work in Stockholm.

But, in truth, for her the need for work of any kind was destined soon to cease. In February, 1891, she was attacked by an illness, the gravity of which was perhaps scarcely recognized by herself or those about her, and with which her state of deep mental depression fitted her but badly to contend. It ended fatally after three or four days. In a foreign land, alone, save for the presence of the "Elizabeth Sister," who was watching her, the end

came.

It was Madame Kovalevsky's oftenexpressed wish that the story of her life should be written by her friend. Possessed by a strong presentiment that she herself would die young, and that her friend would outlive her, she exacted from the latter a promise that she would write her biography. It is impossible to lay down the book in which Madame Edgren-Leffler has fulfilled her task, without a sense of sadness and a feeling akin to dismay. Here is victory not to be distinguished

1 The title of another of her manuscripts.

being loved and cherished, which was the lot of so many "ordinary women, who are the first, the best beloved in their own little circle," and it was this, not glory, that she "wanted most.”

Neither Madame Kovalevsky nor her biographer seeks to deny or to ignore this truth. Both of them, we imagine, must be classed as eminent examples of the type of woman, who, with a fine sense of discrimination, describes herself as "new;" but they occupied too high an intellectual standpoint to be merely the blind partisans of a preconceived theory, or to refuse to recognize "the inexorable logic of facts." Nature, whilst endowing Sophie Kovalevsky with a masculine intellect, left her essentially, unalterably, and before all else, a woman. Here, as every page of her history abundantly proves, lay the secret of her inharmonious and sorrowful life. It is only too probable that many other women, without possessing her genius, will repeat her sad experience. Not because she is inferior to man, rather because she is in this respect his superior, is it true that, for a woman, love, not glory, is the supreme good.

Man's love is of man's life a thing apart, 'Tis woman's whole existence.

ELLIS WARREN CARTER.

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