Books about Sofia Kovalevskaya

1. Beatrice Stillman (ed.), Sofya Kovalevskaya. A Russian Childhood (1978).
1.1. From the Preface.

In the year 1889 Sofya Vasilievna Kovalevskaya, Professor of Mathematics at the University of Stockholm, published her recollections of growing up in mid-nineteenth century Russia. Professor Kovalevskaya was already an international celebrity, and partly for the wrong reasons: less as the distinguished mathematician she actually was than as a "mathematical lady" - a bizarre but fascinating phenomenon.

Her book was an immediate success. She had written it in Russian, but its first publication was a translation into Swedish, the language of her adopted homeland, where it appeared thinly disguised as a novel under the title From Russian Life: the Rajevski Sisters (Sonja Kovalevsky, 1889).

In the following year the book came out in Russia in two instalments of the journal Vestnik Evropy (Messenger of Europe), in the autobiographical form and the language in which it had been written. It was called Memories of Childhood. The editor of another journal, Russkaya starina, one Mikhail Ivanovich Semevsky, went so far as to maintain that Kovalevskaya's work was worthy of standing side by side with Tolstoy's Childhood: an exaggerated but understandable tribute to a native daughter from a public figure who, twenty-seven years before, had presumed to propose marriage to her elder sister Anyuta and been rejected by their father as a penniless upstart.

The success of her book in her native land was to be one of the last sources of pleasure in Kovalevskaya's life, for within six months, in February of 1891, at the age of forty-one, she was dead of pneumonia. Within the next few years the book was translated into French, German, Dutch, Danish, Polish, Czech and Japanese. Two English translations (riddled with errors of the type made notorious in the parodies of Vladimir Nabokov) appeared in 1895: one in London, the other in New York.

For the contemporary reader Kovalevskaya's memoir still retains its original freshness as a personal document. At the same time it vividly recreates a segment of the social history of the period in its portrait of a wealthy landowning gentry family, struggling to preserve its stability against the erosions of an era which witnessed the emancipation of serfs from their masters, the rebellion of children against their fathers, and the rise of radical political groups armed with limitless faith in the power of science to bring about a just social order.

The English version presented here was translated from the 1974 Russian edition of Yospominaniya detstva contained in S V Kovalevskaya, Vospominaniya i povesti, Nauka, Moscow, 1974 (the most complete collection to date of Kovalevskaya's fictional and critical writing), with a few corrections of minor errors discovered in comparing the 1974 text with the editions of 1951 and 1961 edited by S Ya Shtraikh. It includes the first translation into English of the chapter "Palibino" from Kovalevskaya's own text. The early Russian editions did not include this chapter, and the Shtraikh editions (published before Kovalevskaya's original manuscript of the chapter was discovered in the archives of the USSR Academy of Sciences) had utilised a translation from Swedish into Russian done by Kovalevskaya's daughter, Sofya Vladimirovna.

Certain other revisions should be mentioned as well. In the first Russian editions some of the chapters were left untitled, and Shtraikh supplied his own titles for these. The translator has substituted titles more appropriate to the content of the chapters. The chapter called "Palibino," which had been inserted by Shtraikh as Chapter Seven, now stands as Chapter Four, where it seems to fit best chronologically. The present translation also names the family 's Polish tutor, who remained nameless in Kovalevskaya's manuscript for reasons described in the notes. In a few instances, sentences or paragraphs which appeared in the Swedish edition, but not in the Russian, have been included in the translation. These insertions are indicated wherever they occur. Finally, the book's title itself was changed to A Russian Childhood, in the hope of evoking some more concrete association in the minds of English-speaking readers than is called forth by the name of Kovalevskaya, which by now is almost unknown outside of mathematical circles (where she has been cited as "the most important woman mathematician prior to the 20th century").

Kovalevskaya's memoir comes to a close with the Dostoevsky episode, when she was fifteen years old and only just beginning to have some intimation of the possibilities of adult life opening up before her. In order to fill out the picture, therefore, supplementary material has been provided. This includes Kovalevskaya's own Autobiographical Sketch, an account of the highlights of her scientific career published posthumously in Russkaya starina and prepared for publication by her brother Fyodor.

Academician P Y Polubarinova-Kochina, of the Institute for Problems in Mechanics of the USSR Academy of Sciences, has contributed an article explaining the significance of Kovalevskaya's mathematics.

Finally, the translator has supplied a biographical introduction which attempts to set Kovalevskaya's memoir into a broader social and historical context. It first appeared, in briefer and somewhat different form, in Russian Literature Triquarterly ("Sofya Kovalevskaya: Growing Up in the Sixties," No. 9, Spring, 1974, 276-302).

Many people have contributed valuable help and suggestions in the preparation of this book; none of them bears responsibility for its deficiencies. I would like first of all to acknowledge my indebtedness to those scholars who contributed articles and commentary to the various Soviet editions of Yospominaniya detstva: most particularly to S Ya Shtraikh, through whose work I first became acquainted with the complex and fascinating interaction of the Korvin-Krukovsky and Kovalevsky families with the larger society they inhabited.

My gratitude is due to Dr Neal Koblitz of the Mathematics Department of Harvard University and now a fellow-researcher in Moscow, for the graciousness with which he undertook to translate Academician Kochina's article into English. Special thanks go to Joan Thatcher (Zhannochka Tetcher) and to Sharon Miles, for aid and comfort when it was most needed. As ever, I am in debt to Rose Raskin of Columbia University: valued reader, stern critic and priceless friend. To Michael Stillman, who is at the centre of my life, there is no adequate way to acknowledge or measure my gratitude.

1.2. Review by: Franklin A Walker.
Canadian Slavonic Papers 22 (1) (1979), 132.

Kovalevskaya's sensitive and detailed account of her childhood happily is now available to the English-speaking reader who will be entranced with the intimate picture it conveys of family life among the aristocracy in a remote estate in mid-nineteenth century Russia. There are other reasons for welcoming Stillman's text. The author, a distinguished mathematician, was a brilliant example of the "emancipated" Russian female; she was a writer so gifted she might have ranked among the great novelists had she chosen that career; her vivid recollections of childish emotions are unusual contributions to the study of child psychology. The historian may study the effect of the new ideas of the 'sixties on a patriarchal household while everyone will be intrigued with her account of conversations with Dostoevsky.

The editor has collected and collated disparate sets of memoirs to provide a text more complete than some of the earlier Russian versions. The title is not unique but it is understandable why it has been used again. The book includes a chapter by P Y Polubarinova-Kochina of the USSR Academy of Sciences "On the Scientific Work of Sofya Kovalevskaya." It is unfortunate that Stillman did not include from Kovalevskaya's 1893 Literaturnyia sochineniia her recollections of George Eliot, but those memories did not come from her childhood.

It was not an easy task to render into literary English the extraordinarily beautiful prose of the original. Here Stillman has been successful. She is accurate without being mechanical but it is to be regretted that a number of misprints have survived proof-reading. A useful account of the author's life opens the volume, although the reader might prefer to peruse this after he has read the memoirs. Even an abridged bibliography of the relevant Russian books would have been helpful, but for this we must await Stillman's hoped-for full biography.

1.3. Review by: Mary F Zirin.
The Slavic and East European Journal 24 (3) (1980), 310-311.

This translation of Sofja Kovalevskaja's memoirs, the first in English since 1895, was published by a scientific and technical press; in the college libraries I use it has been shelved under mathematics or general biography. But Kovalevskaja's reminiscences of childhood are, first and foremost, a document in Russian cultural history and a gem in the great tradition of memoirs by Russian women from Natalja Dolgorukaja to Nadezda Mandelstam. ... Kovalevskaja's careless conversational style is difficult and Stillman has dealt creditably with it. My one major criticism is that Stillman's change of Kovalevskaja's running present tense to the English past in chapter five (devoted to Miss Smith's iron regime) destroys the parallel to the first chapter where both Kovalevskaja and Stillman use the present tense to depict the routine in Nanny's nursery.

I have more serious reservations about the choice of materials. I do not understand why Kovalevskaja's memoir of the Polish uprising of 1863, published separately in Swedish in 1891 but ignored in Russia until 1974, is not included. Paragraphs from Kovalevskaja's manuscript transmitting her memories of the stories Dostoevsky told the fascinated sisters might well have been inserted also. Teachers in courses ranging from Russian literature and culture to women's studies may want to use this text; a bibliography of the rich literature in Russian and European languages about Kovalevskaja would have been helpful to them. The Springer-Verlag edition also includes an article on Kovalevskaja's science and a brief autobiography published in Russkaja starina in 1891. Stillman teases us with her sketch of Kovalevskaja's crowded and eventful adult life; we can only wish for a speedy completion of the full-length biography on which she is now at work.

1.4. Review by: E Cohen.
Revue d'histoire des sciences 34 (3/4) (1981), 376.

A reissue that was needed. The French translation (1895) of Sophie Kowalevsky's childhood memories was long out of print. The English edition offered here corrects several errors in earlier English editions and additionally contains a new chapter, the manuscript of which was recently discovered. It opens with an introduction giving interesting details about Russian social life at the time. Several notes clarify points in the text, and an essay on the mathematical work of Kowalevsky has been attached. The work itself has kept all its simplicity and freshness. It is a pleasure to reread this literary work. Perhaps one could have added the biography written with love and in the same spirit by Mrs Mittag-Leffler, and which takes up the life of Kowalevsky, where "a Russian Childhood" ends.

1.5. Review by: Willard Parker.
Mathematical Reviews MR0524890 (80h:01033).

A Russian childhood is an account of the first fifteen years of the life of Sofja Kovalevskaja (1850-1891). It begins with her earliest memories and concludes with the story of Dostoevsky's courtship of Sofja's older sister. The work contains no record of Sofja's interest in mathematics, but does provide insight into Russian social history of the mid-nineteenth century and into the development of Sofja's personality.

This work, which was first published in Swedish in 1889 and in Russian the next year, was an immediate literary success. The present translation is based on the 1974 Russian edition of Kovalevskaja's works; it corrects many errors in previous English translations and translates one of the chapters for the first time into English.

This edition is supplemented by a biographical introduction by the translator, Kovalevskaja's own An autobiographical sketch and an article by Academician P Y Polubarinova-Kocina explaining the significance of Kovalevskaja's mathematics. The biographical introduction (45 pages) "attempts to set Kovalevskaja's memoir into a broader social and historical context'' and provides an account of the major events of her life.

An autobiographical sketch (16 pages) is a record of Kovalevskaja's mathematical development and works. Beginning with her first interest in mathematics, it relates her early education at home, her formal education in Germany and her first publications, her return to Russia and scientific inactivity, her return to Europe in 1882, followed by her appointment to Stockholm University, and her life, work and achievements while there.

The 18-page article "On the scientific work of Sofya Kovalevskaya'' by P Y Polubarinova-Kocina (translated by Neal Koblitz) discusses the ten mathematics and physics publications of Kovalevskaja. The article explains the mathematical content and significance of the Cauchy-Kovalevskaja theorem in partial differential equations and of Kovalevskaja's work on the problem of the motion of a heavy rigid body near a fixed point, the work for which she won the Bordin prize in 1888.

1.6. Review by: Mary Ann Rygiel.
Biography 10 (3) (1987), 208-224.

When Kovalevskaya's autobiography was first published, it was well received by critics. One Russian reviewer, Semevsky, compared it favourably with Tolstoy's Childhood (Stillman, x), and a London reviewer compared it with Turgenev's novel, Fathers and Sons (Koblitz, p. 266). By the 1890s, it had been translated and published in eight languages in addition to Swedish and Russian. Afterwards, however, the book fell into obscurity outside Russia and outside mathematical circles (Stillman, xi). Given the compelling life of Kovalevskaya, and the literary quality of her autobiography, we must ask why her autobiography is not widely known. Three related reasons have rendered her work un known to American readers. The first is Kovalevskaya's adult occupation as professor of mathematics. People outside the physical sciences tend to think of mathematics as a seamless and completed web, without regard to its history of thinkers building upon, extending, and correcting previous thinkers' results, results which were the received, "correct," textbook mathematics in their day. ...

The second reason for the obscurity of A Russian Childhood resides in the virtual unavailability of Kovalevskaya to English-speaking readers, at least in America. Leo Wiener's standard two volume English translation Anthology of Russian Literature, which was first published in 1902 and later reissued in 1967, contains no selection from Kovalevskaya nor any reference to her. For the intrepid who wanted to venture beyond stock anthologised material, two earlier book-length translations of Kovalevskaya's autobiography were available, but the circumstances of these translations did little to assure a work of quality which would gain a lasting readership. The third reason for the unfamiliarity of Kovalevskaya's autobiography lies in the response to it by some of the readers within scientific circles.
That Kovalevskaya was not inimical to some sketch of herself as a scientist is indicated by the brief sketch she produced in 1890. The sketch is remarkable for its compression, simplicity, and omissions. Kovalevskaya's way of handling personal life is to blandly and lightly touch on it or to omit reference to it altogether. Had Kovalevskaya lived longer, I believe she might have produced a fuller, more penetrating account of her adult life. What we do have of Kovalevskaya's autobiography is a reflection on a childhood past by a mature mathematician. The work succeeds in eliciting our compassion and under standing and in enlarging our sympathies. It presents us a child who later becomes a mathematician. The author knew it and we know it, but the child did not. Hence, we see a scientist, not as a god or a monster-maker, but as a scientist with a human face.
2. Pelageya Ya Kochina, Sofya Vasilevna Kovalevskaya 1850-1891 (Russian) (1981).
2.1. From the Preface.

The famous Russian woman mathematician Sofya Vasilevna Kovalevskaya is so significant, multifaceted and interesting that the great Norwegian author Henrik Ibsen said that to write Kovalevskaya's biography is to create a poem about her. I have not set myself such a goal here. My task is a more modest one: to present in compact form the basic facts of the numerous available materials on the life of our compatriot. The first to collect the extensive correspondence of Kovalevskaya and the people close to her - her husband Vladimir Onufrievich and his brother Aleksandr Onufrievich - was S Ya Shtra-kh. He wrote books of a biographical nature: 'S V Kovalevskaya', 'Sestry Korvin-Krukovskie', and 'Semya Kovalevskikh', and prepared for publication the book 'S V Kovalevskaya Vospominaniya, pisma'. They give rich factual material for a biography of Kovalevskaya.

After the Second World War the Academy of Sciences of the USSR obtained photocopies of Kovalevskaya's correspondence which were placed at my disposal by the Academy President S I Vavilov. I have gradually published individual parts of this correspondence, shedding light on the years of Kovalevskaya's scientific work. This includes letters to her from Russian scholars and a number of prominent foreign scholars. The letters of C Hermite and K Weierstrass have been published separately. I am currently working on an edition of Kovalevskaya's correspondence with G Mittag-Leffler, which is the most extensive in the archives. After the letters were analyzed and edited, I used them in my three brief sketches of the life and activity of Kovalevskaya and in commemorative papers. L A Vorontsova used all of these sources to write a literary biography of Kovalevskaya.

In this book I wanted to bring together the most significant and interesting of all the materials known to me. I have given considerable attention to the discussion of mathematical questions.

Kovalevskaya's biographies have given a detailed picture of her personal life. Despite this, there are those who think of her as a 'bluestocking'. No, she was no bluestocking, but a woman striving intensely for happiness. She experienced all the joys and sorrows which can fall to the lot of a woman, and her life was guided by a lofty striving to open up a wide road for the many-sided activity of women. She played this role with honour, gaining fame as a mathematician and popularity by her literary productions. I cannot devote much space in this book to her personal experiences, but I cannot avoid mentioning them completely, since both the life and activity of this first woman professor of the past century are of interest to all her devotees.

I have made ample use here of materials from the Mittag-Leffler archives. In Appendix 6, I list all letters from this archive that still await publication.''
3. Ann Hibner Koblitz, A Convergence of Lives. Sofia Kovalevskaia : Scientist, Writer, Revolutionary (1983).
3.1. From the publisher.

The second half of the nineteenth century was an exciting time in European intellectual and social history. The period saw the growth of revolutionary activism, the rise of Darwinian evolutionary biology, the emergence of women's rights movements, and other challenges to established ways of thinking. Progress and change were the key words of the day, and most members of the educated classes felt confident that the future would be bright. In Russia especially, the "intelligentsia" (an amorphous, peculiarly Russian class of professors, writers, and thinkers) had the feeling that they were on the threshold of a great new age. Russia's ignominious defeat in the Crimean War in 1856 signalled to many that wide-ranging political and social reforms were urgently needed. Most of the intelligentsia hoped that the defeat would be followed by the emancipation of the serfs, modernisation of education, moves toward the equality of women, and other reforms. It was in this period that the Russian intelligentsia developed into an influential social group that concerned itself with much more than just cogitation and empty philosophising. During the second half of the nineteenth century, Russian intellectuals increasingly assumed burdens that their counterparts in other European countries considered outside their province. The intelligentsia became the source of most political and social activism in Russia, the social conscience and often the sole voice of protest against autocratic and reactionary policies.

3.2. Review by: Susan Purves McCaffray.
The Historian 48 (1) (1985), 118-119.

Sofia Vasilevna Kovalevskaia (1850-1891) was a Russian mathematician of international stature, who overcame what was at the time the great liability of being female in order to receive a doctorate and a university chair, and whose acquaintances included the likes of Dostoevsky, Chernyshevskii, and Lavrov. Her eventful life is the subject of Ann Hibner Koblitz's meticulous biography.

Drawing on her dissertation research, the author has crafted Kovalevskaia's life story primarily from private papers held by the Royal Swedish Academy of Sciences as well as from the Soviet Archive of Literature and Art and the Soviet Academy of Sciences. Koblitz also relies heavily on published Soviet collections of Kovalevskaia's works and on other published sources in five languages.

The study undertakes three main tasks. First, it illuminates Kovalevskaia's contributions to mathematics. Unable to pursue advanced study in Russia because of her sex, she eventually became the student of the eminent German mathematician Karl Weierstrass. At the age of twenty-four, she completed her work on partial differential equations, giving final form to the Cauchy-Kovalevskaia Theorem. Kovalevskaia later received the French Prix Bordin for her work on the revolution of a solid body about a fixed point. Koblitz demonstrates convincingly that charges Weierstrass was responsible for his favorite student's results are unfounded, and that Kovalevskaia served as a conduit through which other Russian mathematicians came to know and be known by their western European counterparts.

Koblitz also offers Kovalevskaia as an example of the young Russians of the 1860s who called themselves nihilists. Although one finds more nuanced considerations of nihilism elsewhere, Kovalevskaia's life story does bring into focus those idealists who "felt that the only way for an honest, right-thinking person to live honourably in a country with the unjust social order of Russia was to devote oneself to science, trusting science and education to make everything right eventually".

The book is most successful in its portrayal of the kind of unorthodox and complicated lives embraced by women who sought admission to male professions. At the age of eighteen Kovalevskaia entered into a fictitious marriage in order to study abroad. This unwieldy arrangement ensured Kovalevskaia a strained personal life which culminated in her husband's suicide. Professionally, she had to settle for private lessons from Weierstrass, but in time he persuaded Göttingen University to grant her a doctorate in absentia, after she had completed the equivalent of three dissertations. ...

It is as a female pioneer in the academic professions, then, that Kovalevskaia is most interesting, and Koblitz has told admirably the story of this "extremely gifted but in some ways perfectly ordinary woman who fought against the prejudices of her time and sometimes won."

3.3. Review by: Alexander Vucinich.
The American Historical Review 90 (3) (1985), 737-738.

Sofia Kovalevskaia was a true child of the age of nihilism. She wrote a drama, a novel, and exciting biographical sketches, all of which portrayed an increasing struggle between the high ideals of nihilism and the stark realities of the day.

Koblitz's work will appeal to historians of mathematics, to persons interested in the intellectual history of Russia, and to serious students of the struggle of modern women for freer access to academic positions. The book is readable, adequately documented, and skilfully put together, an exceedingly difficult task when dealing with a person possessing disparate talents. A more general and systematic analysis of Kovalevskaia's mathematical papers would have made this study more complete and meaningful. This reviewer would have welcomed a more critical examination of Kovalevskaia's literary works. Despite these limitations, the book is the best single study of Kovalevskaia's life and work. It is both a warm tribute to a grand person and a successful scholarly endeavour.

3.4. Review by: Stuart S Antman.
Amer. Math. Monthly 93 (2) (1986), 139-144.

Ann Hibner Koblitz presents Kovalevskaia's fascinating biography in a style that is generally lively and graceful. The author is at her best in capturing the social and cultural milieu in which Kovalevskaia moved: Kovalevskaia was on familiar terms with many of the premier mathematicians of the time, her husband and his brother were distinguished scientists, and her path crossed those of Dostoevsky, Chekhov, George Eliot, and Darwin. Koblitz's treatment of Dostoevsky's association with Kovalevskaia's family is particularly noteworthy.

Throughout her life Kovalevskaia was supremely conscious of her pioneering role as a woman scientist, the foremost of her century. Though endowed with her share of human frailties, she conducted her scientific life with a combination of daring, perseverance, and tactful circumspection. Koblitz carefully documents Kovalevskaia's sympathies for liberalism and for what was then deemed revolutionary. But the hyperbole of the book's title notwithstanding, the author admits," [Kovalevskaia] was not a revolutionary herself." Koblitz points out that scarcely any of the obstacles Kovalevskaia encountered on account of her sex were erected by mathematicians. Indeed, Königsberger, Hermite, Weierstrass, and especially Mittag-Leffler took great pains to combat the reactionaries opposing her rise to her rightful position. Most American mathematicians know of Kovalevskaia's life through Bell's [X] superficial portrait, which lacks any bibliographical citation. In contrast, Koblitz's full-scale biography is based upon examination of Russian and Swedish archives and is written with an outward adherence to the norms of historiography.
Koblitz's book gives a very readable account of Kovalevskaia's life. It was a life filled with personal drama. The author has uncovered much new material about Kovalevskaia. But the author's admiration for her subject and her lack f expertise in mathematics have led her to colour many episodes of Kovalevskaia's mathematical life and assessments of her work in ways more favourable to Kovalevskaia and less favourable to her ostensible opponents than a sober evaluation of the evidence and its context warrants. Kovalevskaia did not require assistance. She was the author of influential papers and was respected by the mathematical community for mathematical abilities beyond those reflected in her research. She was recognised for her literary efforts. But perhaps her greatest legacy is that today there are many female mathematicians whose mathematical accomplishments have surpassed hers.

3.5. Review by: Paul Avrich.
The Journal of Modern History 59 (4) (1987), 892-893.

Ann Hibner Koblitz tells the story of Kovalevskaia's life with sympathy and understanding. Using archival sources in both the Soviet Union and Sweden, as well as a broad range of printed materials, her book is detailed and scholarly yet accessible to the general reader. A compelling narrative, engagingly written, it deserves a wide audience. Yet in one important area Kovalevskaia's contribution to mathematics it seems deficient. For all Kovalevskaia's talents, so well conveyed by Koblitz, her scholarly reputation rests on a slender body of writing. She published only ten papers during her lifetime, two of which are French and Swedish editions of the same work. None of these, moreover neither her paper on the revolution of a solid body about a fixed point nor even her proof in the field of partial differential equations known as the Cauchy-Kovalevskaia theorem broke entirely new ground. From Koblitz's account, which to a layman appears sketchy and inadequate, her achievements seem far from being of the first rank. Why, then, to quote Koblitz's appraisal, was she the "greatest woman scientist before the twentieth century"?

It would be unfair, however, to conclude on a negative note. Koblitz has been assiduous in locating pertinent source material. She writes, on the whole, with clarity and intelligence. Despite its limitations, she has produced an absorbing biography, a welcome contribution to the history of Russian women and Russian science.

3.6. Review by: D Bushaw.
The College Mathematics Journal 16 (3) (1985), 240-242.

As the subtitle of this new book suggests, Sofia Vasilevna Kovalevskaia (1850-1891) was a scientist, a writer, and, if not precisely a revolutionary, then certainly a sympathiser with revolutionaries. She was, more specifically, a prize-winning mathematician, a dramatist, a writer of mainly autobiographical prose, a poet, a supporter of socialist causes, and a fighter for women's rights. She was also a teacher, a wife and mother, and a member of the 1880s counterpart of the European jet set. Numerous chronological and other superlatives have been applied to her: for example, she is said to have been the first female European university professor after the Italian Renaissance, and the greatest female scientist (a fortiori the greatest female mathematician) before the twentieth century. On top of everything else, she was a warm and charming human being. In short, she was a phenomenon.

This biography draws not only on the published Kovalevskaia literature, of which there is already a good deal, but also on archives in the USSR and, most importantly, on archives of the Institut Mittag-Leffler in Sweden. The documentary base alone would make Koblitz's book an excellent foundation for further Kovalevskaia studies; but the book's thorough scholarship does not prevent it from being also a vivid and enjoyable account of an entrancing subject. It clearly has been written to be accessible to non-specialists, and requires of the reader no specific historical or scientific background; it could be recommended without malice to a serious undergraduate. There are reproductions of some interesting photographs and a rich, though admittedly incomplete, bibliography.

3.7. Review by: Barbara Engel.
The Russian Review 44 (3) (1985), 303-304.

Koblitz's Kovalevskaia ... is a radical. Exposed to progressive thought in early adolescence, she embraced eagerly the ideas of the 'sixties, made no secret of her socialist sympathies even when they harmed her professionally, and while she never committed herself directly, she envied her radical friends their involvement in active political work, gave them her passport, accepted coded letters, and helped them out in small ways that entailed some risk. ... Although she does not ignore Kovalevskaia's romantic attachments, Koblitz downplays their significance. [She emphasises] Kovalevskaia's brilliance and her position at the frontiers of mathematical research; she concludes Kovalevskaia is about to have a second period of recognition in her field. .... And while I suspect that Koblitz tends to downplay Kovalevskaia's flaws, as she downplays some of her personal problems, she nevertheless presents the reader with a nuanced portrait of a sometimes difficult and demanding woman, strong-willed and selfish, but also warm, generous, devoted to her friends, and easily approachable even at the height of her fame. Koblitz's book makes a substantial contribution to Russian history, women's history and the history of science, and it is likely to become the definitive biography of Kovalevskaia.

3.8. Review by: Beatrice Farnsworth.
Slavic Review 44 (3) (1985), 541-542.

Much has been written about Sofia Kovalevskaia, the first woman in the nineteenth century to receive her doctorate in mathematics and to hold a university appointment. Why then a new biography? Koblitz rejects previous works as "unreliable." The best known of them, by Anna Leffler, she dismisses as a "fictionalised account." Seeking to avoid the "distorting haze" of biographies written by close friends like Leffler, Koblitz utilised memoirs, unpublished letters and diaries, Swedish and Russian archives, and a multitude of English and Russian sources. The result is well researched and even-handed. Yet despite its scholarly merit, this book does not convey a real sense of Kovalevskaia the woman: her intensity is lost. Perhaps Koblitz's determination to be objective caused her caution in probing the personal. But if Leffler is "melodramatic" and untrustworthy, what then was the full story of Kovalevskaia's unhappy attempts to resolve the private and the professional in her life? Koblitz does not really tell us. Nothing in her book seriously revises the image of Kovalevskaia drawn by Leffler. Instead, we have a pale copy. Indeed, although Koblitz dismisses Leffler's study in her bibliography, she draws on it freely in her text.

Koblitz is more successful in discussing Kovalevskaia's formative years. To Kovalevskaia's own reminiscences Koblitz adds important information. Presumably because her memoir was a tribute to her recently deceased sister, Kovalevskaia did not indicate that she, Sofia, was her father's favourite. Writing of the special relationship between father and daughter, Koblitz contributes to our understanding of factors influencing the development of outstanding women. Kovalevskaia is another example of the achieving woman who in childhood identified closely not with her mother but with her father. Marie Curie, Emmy Noether, Elizabeth Cady Stanton, and Aleksandra Kollontai are other such women.

The real strength of this biography, carrying it significantly beyond its predecessors, is its re-creation of a mathematical community. Koblitz, a historian of science, provides a valuable picture of a female scientific intelligentsia in the late nineteenth century. Russian women studying abroad showed remarkable mutual devotion, but we also see tensions within their women's communes. Here in microcosm is the "knowledge versus revolution" debate which troubled the Russian radical movement. Kovalevskaia was among those who decided, not without guilt, to put education before political activism. As a result, Kovalevskaia and her friends Elizaveta Litvinova, Iulia Lermontova, and Nadezhda Suslova were among the first Russian women in modern times to receive advanced degrees in Europe.

Focusing on women mathematicians, Koblitz provides us with another perspective from which to view the female intelligentsia. Together with Richard Stites and Barbara Engel, she contributes significantly to our knowledge of nineteenth-century Russian women who rejected traditional female roles. Scholars of the history of science and of Russian and women's history will welcome her book.

3.9. Review by: Beate Fieseler.
Jahrbücher für Geschichte Osteuropas, Neue Folge 43 (3) (1995), 441-442.

Although Koblitz rightly puts the mathematician Kovalevskaia at the centre of her biographical study, fortunately she does not succumb to the temptation to overestimate her professional achievements. According to Koblitz, it was not Kovalevskaia's main merit to break new ground in mathematical thinking or to found his own "school". Rather, for many years she had acted as an important link between Western European and Russian scientific tradition and culture, the "princess of the natural sciences", soon glorified, soon mocked, has probably been thoroughly freed of old and new ideological ballast for the time being, but the private person Kovalevskaia remains, although the ups and downs of her personal life are roughly outlined by the author, a largely unknown being even after reading this biography.

3.10. Review by: Judith V Grabiner.
Isis 76 (4) (1985), 645-646.

This successful biography draws on many sources, especially in manuscript, not previously exploited. Its only real weakness stems from its chief virtue. The social history is at centre stage, while Kovalevskaia's mathematics is discussed only briefly, and neither its mathematical antecedents nor its influence is explained in detail. Thus I would suggest reading Roger Cooke's new book The Mathematics of Sonya Kovalevskaya (Springer-Verlag, 1985) together with the present volume in order to get a full picture of "the greatest known woman scientist before the 20th century". Nevertheless, I highly recommend Koblitz's biography. It is carefully researched, judiciously reasoned, beautifully written, and eminently readable.

3.11. Review by: Maita Levine.
The Mathematics Teacher 86 (9) (1993), 785.

Koblitz's biography of the first woman in modern Europe to receive a doctorate in mathematics analyses the many facets of Sofia Kovalevskaia's life and accomplishments - professional mathematician; writer of plays, novels, and essays; political activist; wife; mother; sister; hostess; and friend. Although the book discusses the significance of Kovalevskaia's contributions to the theory of partial differential equations and to the study of the revolution of a solid body about a fixed point, the emphasis is on Kovalevskaia's life rather than on her mathematical achievements.

Included is an extensive description of the nihilist movement of the Russian intelligentsia in the 1860s and a detailed account of the women's movement in Russia in the latter part of the nineteenth century, not unlike the recent women's movement in the United States. The reader also becomes acquainted with many famous mentors, colleagues, and friends of Kovalevskaia, including Weierstrass, Mittag-Leffler, and Dostoevsky. The historical facts were carefully researched, as evidenced by a lengthy bibliography and footnotes on almost every page.

A Convergence of Lives is an informative, easily read account of a talented mathematician who led a brief but fascinating life.

3.12. Review by: D J Struik.
Mathematical Reviews MR0729126 (85j:01028).

This is a biography that does full justice to its subject: a careful study of her life as a mathematician, author, political radical, wife and mother, succeeding in an academic career despite the enormous difficulties a woman scientist had to face in her days (and later). It is based on a study not only of the written sources (among them the writings, between 1897 and 1950, of P Ya Polubarinova-Kochina) but also of the material in the archives of the Akademiya Nauk in Leningrad and the Institut Mittag-Leffler near Stockholm. The picture emerges of a woman of many talents and great vitality, and of greater mathematical standing than has usually been accorded to her.

Sofia (Sonia) was born in 1850, the daughter of the landowner-colonel (later general) Vasilii Korvin-Krukovskii, passed her youth mostly on the family estate near Pskov, found that entrance as student into a Russian university was impossible for a woman and therefore, in order to be able to study abroad, entered into a nominal marriage (it later became actual) with the publisher-scientist Vladimir Kovalevskii (1842-83), later a well-known palaeontologist. In Germany she studied with Weierstrass (privatim, since even in Berlin she could not enter the university as a student) and received her doctorate at Göttingen in 1874 on three papers, one of them containing the theorem now called after her and Cauchy. For some years she lived a life of social activity, Weierstrass worrying that she had abandoned mathematics, then returned to her research and was rewarded, in 1888, with the Prix Bordin of the Academie des Sciences. By that time she had, at last, through the efforts of G Mittag-Leffler , received a position at the new Stockholm University, where in 1889 she received a lifetime professoriate, the first European woman in modern times to be so honoured. She died rather suddenly in 1891, at the height of her career and fame.

Sonia is often seen as an exceptional figure, almost an oddity, like M G Agnesi or Hypatia, a lonely woman in a world of men. Against this the author argues that Sonia was a typical representative of a movement, that of the so-called nihilists in the Russia of the 1860s and 1870s after the humiliation in the Crimean war. Many young people sought to improve social conditions, not least by studying the natural sciences. This movement encompassed women as well as men (here is a parallel with abolitionism in the USA) and brought, against much Tsarist opposition, Russian science into the modern orbit. Sonia was only an exception insofar as she was one of the few mathematicians, and the most talented one, among several Russian woman scientists. More details can be found in the author's article in "Science for the People'', July/August 1982.

The author also points out that Sonia's merits as a mathematician have often been underestimated. The Russian and Swedish archives contain many documents to show how highly the leading mathematicians such as Chebyshev, Mittag-Leffler, Weierstrass and Hermite thought of her work, and how much the early flowering of the Acta Mathematica owes to her editorial activity. Moreover, modern research has found inspiration in a renewed study of her papers.

In several chapters, notably the one called "Mathematics in abeyance'', we learn much about Sonia's many social and literary contacts, with Dostoevsky, Turgenev, George Eliot and others, including Anna Carlotta Leffler who wrote a (not too reliable) account of Sonia's life. Among the socialists of her acquaintance we find Lavrov, Volmar and Branting, but she does not seem to have been an activist like her beloved sister Aniuta (1843-87), who participated in the Paris Commune, married the communard V Jaclard and was acquainted with Marx.

The book deserves comparison with the equally readable biography of Sonia by D H Kennedy [Little sparrow: a portrait of Sophia Kovalevsky (1983)]. That book, however, suffers from the fact that its author possessed neither the archival information of the present author nor her understanding of the scientific aspects of Sonia's work. Incidentally, Sonia can hardly be characterised in her creative years as "little'' or as a "sparrow'', and the equally enigmatic title of the present book refers, as the author tells me, to the convergence, in Sonia's person, of the lives of a scientific, a literary and a political figure.
4. Don H Kennedy, Little sparrow: a portrait of Sophia Kovalevsky (1983).
4.1. From the Publisher.

Little Sparrow is the first complete biography in any language of Sophia Kovalevsky, the nineteenth-century Russian mathematical genius, champion of equal education for women, and first woman professor of higher mathematics. She pushed the development of analytical mathematics - such as ultraelliptical functions - beyond that of anybody before her. From the French Academy of Science she won an award as important as the later Nobel prize.

Sophia Kovalevsky was born January 15, 1850, into the Russian nobility, daughter of a general, descendant on the paternal side from a Hungarian king and on the maternal side from German astronomers. She joined the nihilist movement at age 16. At age 18, in order to escape Russia and study abroad, she obtained parental permission to enter a marriage, which for five years remained platonic.

Though a woman, she obtained special permission to study at Heidelberg. When rejected for higher study at Berlin University, she was accepted as a special pupil by the foremost mathematics teacher of the age, Professor Karl Theodore William Weierstrass. After receiving a Gottingen doctorate magna cum laude, in abstentia, she returned to Russia to enter the intellectual life of St. Petersburg, to consummate her marriage, and to bear a daughter.

She was a friend of Dostoevsky, Turgenev, George Eliot, and other literary lights of the period, and she wrote an account of her Russian childhood that was considered on a par with Tolstoy's book on his youth.

Kennedy's work focuses less on the professional mathematician than on the unusual woman whose life reflects the plight of the female intellectual and scientist in Russia and Europe late in the century.

4.2. Review by: Barbara Engel.
The Russian Review 44 (3) (1985), 303-304.

... despite her participation in the nihilist subculture, Kennedy's heroine remains above all an aristocrat who definitely opposed revolution; an elitist who believed that a worthwhile society needs an elite intellectual class. ... Kennedy tends to emphasise a Kovalevskaia who displayed a very feminine helplessness in many things (p. 234), who longed for a husband to love and sustain and comfort her (p. 244) after Vladimir's death. He dwells on her romantic attachments. ... Finally, Kennedy accepts the prevalent view that all of Kovalevskaia's mathematical work was derivative; he concludes that the passage of a century has inevitably dimmed the importance of her scientific contribution.

4.3. Review by: Marie Boas Hall.
The British Journal for the History of Science 17 (2) (1984), 238.

The Kovalevsky family occupies seven pages of the Dictionary of Scientific Biography: Alexander was a distinguished embryologist, Vladimir a notable palaeontologist and the latter's wife, Sonya (born Korvin-Krukovsky in 1850) the greatest female mathematician of the 19th century. This book contains less on their scientific contributions than does the DSB but, based (often literally) on Sonya's own recollections (there is a 1978 English version with an analysis of her mathematical contributions not cited here) as well as those of her close friends and on her extensive correspondence, gives an incredibly detailed account of her aristocratic Russian childhood, her 'nihilistic' marriage at 18 in order to escape to a European education (she succeeded in becoming a pupil of Weierstrass, who adored her), her friends and relations, her life in Sweden as professor of mathematics. Hers was a tempestuous personality, demanding in friendship and marriage. As a gloss on Russian novels this is to be highly recommended; for historians of science there is too much detail and too little mathematics.

4.4. Review by: D J Struik.
Mathematical Reviews MR0773666 (86h:01078).

Although Sonya Kovalevskaya is best known as a mathematician, she was a woman of many parts - a novelist, a fighter for women's education, a representative of the younger "nihilist'' generation in the Russia of the 1860s and 1870s, a vivacious conversationalist who in her extensive travels met many outstanding persons, including Dostoevsky, Turgenev, Hermite, Poincaré, Huxley, George Eliot, Lavrov, Branting, Chebyshev, not to speak of her closest friends and protectors, Weierstrass and Mittag-Leffler. This rich life is material for a good story, and this book by a former California newspaperman and aerospace design engineer is proof that it can be written. It is a pleasure to read this work about Kovalevskaya's ups and downs, with the ups at the end prematurely cut short by her death in 1891 at the age of 41. But there is not very much in it for the mathematician; in the author's words: "The biography is not about a mathematician as such, but about an unusual woman who happens to have a secure place in the history of science as she does in Russian literature''. For those interested in Kovalevskaya's mathematics, the author recommends the article by P Y Polubarinova-Kochina, appended in English to B Stillman's translation of Kovalevskaya's book, A Russian childhood [Springer, Berlin, 1978]. We can add the recent book by A H Koblitz [A convergence of lives (1983)], written by a mathematician and also using archival material in Russian and Swedish not used by the author. R Cooke's recent book [The mathematics of Sonya Kovalevskaya (1984)] is also of interest.
5. Roger L Cooke, The mathematics of Sonya Kovalevskaya (1984).
5.1. From the Preface.

This book is the result of a decision taken in 1980 to begin studying the history of mathematics in the nineteenth century. I hoped by doing it to learn something of value about Kovalevskaya herself and about the mathematical world she inhabited. Having been trained as a mathematician, I also hoped to learn something about the proper approach to the history of the subject. The decision to begin the study with Kovalevskaya, apart from the intrinsic interest of Kovalevskaya herself, was primarily based upon the fact that the writing on her in English had been done by people who were interested in sociological and psychological aspects of her life. None of these writings discussed her mathematical work in much detail. This omission seemed to me a serious one in biographical studies of a woman whose primary significance was her mathematical work. In regard to both the content of nineteenth century mathematics and the nature of the history of mathematics I learned a great deal from writing this book. The attempt to put Kovalevskaya's work in historical context involved reading dozens of significant papers by great mathematicians. In many cases, I fear, the purport of these papers is better known to many of my readers than to me. If I persevered despite misgivings, my excuse is that this book is, after all, primarily about Kovalevskaya. If specialists in Euler, Cauchy, etc., find omissions or misinterpretations in my handling of the works of these authors, I can only plead that the background of a painting never has the same clarity as the foreground. In reading secondary sources I found noticeable differences between the accounts written by mathematicians and those written by historians. Among other differences, the former devote much more space to the technical details of how a result was obtained, while the latter tend to emphasise the influence of one idea or school upon another. As a newcomer to the field, I considered it my place to learn as much as I could from both mathematicians and historians. Naturally, the present work is written in the "mathematician's" style, though I have tried to make it as accessible as possible to nonspecialists.

Since Kovalevskaya's periods of mathematical activity, first as a student of Weierstrass and later as a mature scholar, were separated by a 6-year period of more or less domestic life, this natural division has been used as the plan for this book. In order to fix the chronology, the chapters discussing her work during these two periods are preceded by chapters of biography. It is very light biography, written to entertain as well as to instruct. It skims lightly over the years, touching down at points that seemed particularly interesting. The reader should by no means infer that the incidents reported here for any given year were necessarily the most important ones for understanding Kovalevskaya's life. For a serious scientific biography of Kovalevskaya the reader should turn to the excellent recent account by Ann Hibner Koblitz (1983). Readers who know Russian will also find much of interest in the book of P Va Kochina (1981). The present book uses the two just mentioned extensively as sources. The primary sources used in Chapters 1, 5, and 9 of the present book are in the archives of the Institut Mittag-Leffler. All letters quoted in this book, unless otherwise cited, come from that source.

The motivation for this book resides in the six chapters of mathematical analysis, in which an attempt is made to place Kovalevskaya's work in context within the history of nineteenth-century analysis. The effect of focusing on, and, so to speak, enlarging Kovalevskaya's papers, is a certain distortion of the picture. To make this book of reasonable length and readability, it was necessary to restrict the discussion of the works of her predecessors to the most significant results relevant to Kovalevskaya's work. Such a restriction makes the history of each topic resemble a ladder on which each successive mathematician moved one rung higher than his predecessors, whereas the reality is more like a tree, with branches sprouting in all directions. With that caveat I trust the reader will be better able to place Kovalevskaya's work in perspective after reading this book than before.

A few words are in order about the text itself, especially the mathematical analysis in Chapters 2-4 and 6-8. These chapters contain too few formulas to constitute a textbook exposition of the subjects they discuss and too many for a popular exposition. My impression after reading older histories of mathematics which discuss the works of great mathematicians in prose has been that such a style conveys no real idea of what the mathematics was. The formulas seem essential to any real communication of ideas. They should be used however as one would use a child's model airplane to explain that invention to someone who had never seen one. One would not expect to fly in a model airplane. For the same reason, one should not take the formulas in this book, even the long strings of formulas, for an attempt at a mathematical proof. The formulas are in the book only as a means of referring to the mathematics.

The six appendices were written for two reasons. The first was to make the book more "user-friendly" to a hypothetical undergraduate reader who has had only a year or two of mathematics. With these appendices, such a reader should be able to understand the gist of what is said in the text. The second reason for the appendices is that in the text it was necessary to touch on two topics (Weierstrass' method of solving partial differential equations of a certain form, and Jacobi's last multiplier method) which are no longer part of the basic courses in differential equations. I thought that mathematicians who, like me, had not seen these topics before, would be interested in a more detailed exposition of them.

Finally I should also explain my system, or rather my lack of system, in transliterating Cyrillic. Since the ending -sky is familiar to Europeans and Americans in such names as Dostoevsky and Tchaikovsky, I see no point in using -skii. In general Russian words are transliterated in a way which will cause the average English-speaking reader to pronounce them in an approximately correct manner. Those who know Russian will recognise these words anyway, and those who do not will suffer no harm from reading a nonstandard transliteration. Knowing that Kovalevskaya's maternal ancestors came from Germany, I refer to them by the name Schubert, rather than Shubert. On the other hand, I have retained the spelling Mendel'son in preference to Mendelssohn, because the woman in question was Polish. In connection with Russian names, many conversations with non-Russian-speaking devotees of Russian literature have convinced me that the invariable sequence of given-name-plus-patronymic is excessively wearisome to most readers. Therefore I make very little use of patronymics, trusting that any Russian-speaking readers will understand that no disrespect is intended. Similarly, in order to avoid confusing my readers with the many diminutives of the name Sophia I consistently use "Sonya" even though Kovalevskaya did not get that nickname until adulthood.

5.2. Review by: Lars Garding.
American Scientist 75 (1) (1987), 88-89.

Recently, some one hundred years after her most active years, Kovalevskaya has become the subject of three books, a biography by Koblitz written from the feminist point of view, a biography in Russian by Kochina, and this book. Cooke combines biography with historical analysis of Kovalevskaya's work. Two of her achievements made history, the Cauchy-Kovalevskaya theorem and her discovery of a new integrable case for the spinning body. Her work on the propagation of light in a doubly refracting crystal was one of the abortive attempts at the time to tackle this knotty problem, first solved in 1919 by the Swedish mathematician Zeilon.

Cooke takes Kovalevskaya's papers one by one, sketches their background, analyses their contents, and proceeds to an evaluation. This process leads him into the labyrinth of 19th-century mathematics, including such topics as elliptic and hyperelliptic functions, the intricacies of the spinning body, and the properties of the aether. Partly due to the format, biography mixed with sketchy mathematics, the mathematical parts suffer from lack of clarity and depth. When it comes to the double refraction, the essential point is missed altogether. But a wealth of background material permits the author to make thoughtful and fair evaluations of Kovalevskaya's work. Cooke has written a very worthwhile book full of interesting details, despite its weak points. It evokes a world of mathematics, once vibrating with life and now surviving only in parts, sometimes transformed and extended beyond recognition.

5.3. Review by: Elliot Cohen.
Revue d'histoire des sciences 40 (2) (1987), 238.

The author thinks precisely that one can only get an idea of a mathematical work, especially as in the present case when a large part of its substance is computational, by having the main formulas in front of your eyes. It is probably true that the form is inseparable from the content here. For each subject, Roger Cooke describes the work of Sonya Kovalevskaya after having placed them between the work accomplished by her predecessors and that of her immediate successors. He also assesses its importance, both for the time and in the more general context of the history of mathematics.

The last chapter (9) is devoted to the opinion expressed on Sonya Kovalevskaya and her work by her contemporaries and by herself. It ends with an appreciation by the author, situating the work of Sonya Kovalevskaya and specifying various points in the history of mathematics that his study has led him to correct.

The work is clearly presented, but the material remains at times difficult to read, despite the appendices and even if we do not try to make up for the missing links in the calculations. This was undoubtedly inevitable from the moment the author had chosen to give mathematical details.

This honest work constitutes a brief but precious guide for all those interested in Sonya Kovalevskaya. They will find here the main biographical elements of her life and the references and bases necessary to deepen particular points of her work.

5.4. Review by: Jesper Lützen.
Mathematical Reviews MR0765377 (86h:01071).

Recently two books have appeared dealing with the first female professional mathematician, Sonya Kovalevskaya. The biography of A H Koblitz [A convergence of lives (1983)] gives an excellent analysis of the life of this complex person. The book under review also tells extracts of this story in two entertaining chapters. The first follows Kovalevskaya's childhood in Russia and her student years in Germany, the second summarises her mature life including her activity as the world's first female professor of mathematics in Stockholm.

However, the principal aim of the book under review is to analyse Kovalevskaya's mathematical works. This enterprise, which has been somewhat neglected in other accounts, is not only important for the evaluation of this outstanding woman but also throws light on interesting aspects of the history of mathematics of the last half of the 19th century, which draws the attention of an increasing number of historians of mathematics.

To be sure, Kovalevskaya was not among the most outstanding mathematicians of her time but at least two of her contributions are important enough to deserve attention for their own sake. These are her contribution to the Cauchy-Kovalevskaya theorem and her ingenious analysis of a rotating rigid body - the so-called Kovalevskaya top. In the six central chapters of the book the author analyses these works as well as Kovalevskaya's works on degenerate abelian integrals, the shape of Saturn's rings, light propagation in crystals and potential theory. He places Kovalevskaya's works in their historical context, both summarising what her predecessors had done and describing the road - often full of obstacles - which led her to the results.

The analysis is based on a careful study of Kovalevskaya's published works as well as her unpublished letters and manuscripts preserved in Stockholm. As for the predecessors, the author is refreshingly honest about his heavy reliance on secondary sources, although it is occasionally surprising to see that he did not even bother to look up published material (for example on p. 25). His readiness to summarise even complicated mathematics has made the account true to the original. It makes hard reading, but generally his illuminating comments lead the reader through.
The book ends with an informative chapter on the highly diverging evaluations of Kovalevskaya by her contemporaries and successors.

A final small critical point concerns the account of the last days of Kovalevskaya's life. She had been on a vacation in Genoa. According to the author, her way back to Stockholm went through Copenhagen where she had to carry her bags in a driving rain, because she had no Danish money to tip a porter. According to Anne-Charlotte Leffler's biography of Sonya Kovalevskaya, however, she took great pains to avoid Copenhagen on this trip, because she was afraid of the smallpox epidemic that was afflicting its population. The tip story took place in Fredericia, a small town on her strenuous route through more remote parts of Denmark. The hardships of this detour broke her health.
6. A P Yushkevich (ed.), The correspondence of S V Kovalevskaya and G Mittag-Leffler (Russian) (1984).
6.1. Review by: Roger L Cooke.
Mathematical Reviews MR0770576 (86d:01018).

This work contains Russian translations of the carefully edited correspondence of Mittag-Leffler and Kovalevskaya. It is especially valuable to have all this material within the covers of a single book, since the individual letters are kept in several different files at the Institut Mittag-Leffler and since some of the correspondence is inaccessible to the majority of researchers, being written in Swedish (and nearly illegible Swedish in the case of Mittag-Leffler).

The editor has provided some eighty pages of supplementary material including detailed commentaries on the letters. In a private communication to the reviewer the editor mentioned that the wrong Laurent was described in the notes (p. 298). Despite that one small flaw this book will be most welcome to all who are doing research on the history of late 19th century mathematics.
7. Pelageya Ya Kochina, Love and mathematics: Sofya Kovalevskaya (1985).
7.1. Note.

This biography of Kovalevskaya was translated (and revised) from the 1981 Russian original ["Nauka'' Moscow, 1981].
8. Reinhard Bölling (ed.), Briefwechsel zwischen Karl Weierstrass und Sofja Kowalewskaja
8.1. Review by: C J Scriba.
Mathematical Reviews MR1222198 (94e:01024).

Though it has long been known that the famous German mathematician Karl Weierstrass (1815-1897) entertained an intensive correspondence with his Russian student Sofia (or: Sonia) Kovalevskaya (1850-1891), no satisfying edition of it has been available. (A publication, with Russian translation and brief commentary, by P Ya Kochina-Polubarinova, Moscow 1973, has long been out of print.) The present, superb edition fills this lacuna. It is in every respect worthy of the examples it has taken as model: the editions by Kurt-R Biermann of letters by Alexander von Humboldt and Carl Friedrich Gauss.

The Weierstrass-Kovalevskaya correspondence covers the two decades 1871 to 1890. More than 160 letters must have been sent and are registered in the present edition, although, with one partial exception, the letters by Kovalevskaya are lost (the recipient burnt them after the premature death of his pupil and friend). Weierstrass' letters (preserved in the Mittag-Leffler Institute in Djursholm, Sweden) reflect in many details the state of mathematics towards the end of the 19th century, as well as the chequered life of the unconventional Russian mathematician in Berlin, Paris, and (as professor of mathematics) Stockholm. The editor has spared no pains to elucidate this very informative correspondence: apart from an introductory survey, he has equipped the volume with extensive notes on both the mathematical details and the social, cultural, professional and human aspects touched upon in these letters. As far as possible he also has reconstructed the contents of the lost letters by Kovalevskaya (only one draft, here incorporated in the last minute, has survived [see R Bölling, Historia Math. 20 (2) (1993), 126-150; see the following review]). ...
9. Wilderich Tuschmann and Peter Hawig, Sofya Kovalevskaya. Ein Leben für Mathematik und Emanzipation (1993).
9.1. Review by: Roger L Cooke.
Mathematical Reviews MR1390762 (97a:01066).

Over the past century, and especially over the past two decades, Sofya Kovalevskaya (1850-1891) has been studied from more points of view than one might think possible: as the romantic heroine colourfully described by her friend and collaborator the playwright Anne-Charlotte Leffler, as the radical nihilist who was at the forefront of several revolutionary struggles in the Russia of her day, as a European intellectual and leader of the women's movement, and as one of the prominent mathematicians of the late nineteenth century. She was all these things and more; the seeming plethora of books about her is therefore justified. Is there a need for yet another book, however? The authors address this question in their introduction, pointing out that there is no original German-language biography of Kovalevskaya. (This claim turns out to be not quite accurate. There is such a biography at the Institut Mittag-Leffler, written in German by an apparently Russian author named Romanowa. However, it does not seem to have been published, and so the authors are on solid ground with this claim.) The authors disclaim any research into archival materials; but there is little need at this point for such research, since the archival material has been studied carefully by a number of scholars.

In the current climate of delicate feelings, a number of feminist scholars (though by no means all) resent any attempt by men to interpret or even discuss the life of any woman of the past. The authors - two men - raise this issue in their introduction, but their response to it is the book itself. In the reviewer's opinion they have achieved something that no one else has managed to do in all the many-faceted studies of Kovalevskaya up to now: They have written a lively and interesting book about a fascinating woman, presenting a balance of general biography and a fair representation of all of her many activities. Kovalevskaya was a full-fledged mathematician, but she was also much more than that. The authors, while giving a clear general interpretation of her mathematical work that steers clear of the many legends that grew up about her, do not neglect her journalistic and literary efforts. They have selected, it is true, material likely to be of interest to the general reader, but its interest lies precisely in communicating important facts about Kovalevskaya's personality and achievements to the reader. Although many details given in the book are not intrinsically important, they add greatly to the interest of the book. The reviewer had not known, for example, that Kovalevskaya's great-great grandfather Johann Ernst Schubert had been friends with a man whose son committed suicide, thereby becoming the model for the central character of Goethe's Die Leiden des jungen Werthers.

In summary, mathematicians should not expect from this book the story of "a life in mathematics''. Kovalevskaya was not so confined, and the book is a tribute to the whole woman. ...
10. Michèle Audin, Souvenirs sur Sofia Kovalevskaya (2008).
10.1. Note.

We give the English translation of part of the Introduction in 12. below.

10.2. Review by: Victor V Pambuccian.
Mathematical Reviews MR2574015 (2010k:01009).

This is not just another book on Sofia Kovalevskaya which happens to be written in French, but a very remarkable look at the following aspects, which tend not to be treated in such detail: (1) the actual mathematics involved in the two major papers of Kovalevskaya: the one containing what is now called the Cauchy-Kovalesvkaya Theorem, and the one on rigid body motion in which she introduced what is now known as the "Kowalevski top''; (2) the story of her life; and (3) the wild rumors masquerading as history regarding her life and work. Regarding (1), we are not only given the historical context of the two results, but also, in particular in the case of the Kowalevski top, their legacy, down to the present, showing very eloquently that the mathematics of that Prix Bordin 1888 paper was so deep, that results referring to it in an essential way appeared as recently as 2005. When telling the story of Kovalevskaya's life, the author is very careful to use reliable sources, and lets the reader know, both during the narrative and in two chapters of letters and quotations, how the story was distorted by authors - many of whom were famous mathematicians of the 19th and 20th centuries, Felix Klein for example - who relied on hearsay and a generous amount of prejudice. The author spends more time than a historian would debunking parts of E T Bell's Men of mathematics, as she is interested in Kovalevskaya's image among mathematicians at large and not among genuine historians. This is also an in-depth study of the gradual decline of Kovalevskaya's reputation over time, and of the factors responsible for it. The idea of writing this book was to a great extent influenced by meeting Jean-François-Peyret, the playwright and director of Le Cas de Sophie K.

The one question left unanswered is the one on Russian nihilism and Dostoevsky. As in other books on Kovalevskaya, Russian nihilism is presented here as a harmless version of an anti-establishment progressive youth movement, with its own distinctive dress code. In The Demons, Dostoevsky had an entirely different take on it, and prophesied that it would lead to disaster. Dostoevsky himself is of little help, for he published fiction by Kovaleskaya's sister Aniuta in his journal, and was on friendly terms with both women (in fact he once declared his love to Aniuta), avowed nihilists, before and after having written the novel.
11. Natasha Kolchevaka (tr.), Nihilist Girl, by Sofya Kovalevskaya.
11.1. Review by: Helena Goscilo.
The Women's Review of Books 19 (8) (2002), 7-8.

Kovalevskaya reportedly claimed that mathematics (in her words, "an exalted and mysterious science") required no less imagination than her second passion - writing. In addition to articles for newspapers on scientific and cultural subjects, she penned revealing memoirs and several works of fiction typically centred on female protagonists. Her literary reputation rests on her single completed novella, Nihilist Girl (sometimes cited as Vera Vorontsov), published in Switzerland in 1892, which appeared in Russia fourteen years later. Rich in vivid psychological detail, it recreates the atmosphere of Russia in the 1860s and 1870s, an era of transition and turmoil dominated by the intelligentsia's idealistic commitment to socio-political engagement and personal self-fulfilment through two related causes: woman's emancipation and the equitable integration of the recently liberated serfs into a radically divided society. Inasmuch as Nihilist Girl simultaneously reflects the struggles and convictions of Kovalevskaya and her sister Anyuta, it also personalises a paradigmatic woman's story.
Kovalevskaya's prose lacks the febrile intensity of Dostoevsky's novels and the deceptively seductive authority of Tolstoy's longer works; it is disciplined and, above all, poetic. Curiously, in a story focused primarily on character formation, female psychology and social ferment, the most impassioned sections focus lovingly on details of an expressive landscape that intimates the divine:

11.2. Review by: Christine Johanson.
Canadian Slavonic Papers 44 (3/4) (2002), 325-326

The present translation of Nigilistka, a novella by celebrated mathematician Sofya Kovalevskaya, is indeed welcome. Unlike earlier English-language editions that are abridged under alternative titles, Nihilist Girl follows the original Russian version. Written shortly before Kovalevskaya's death in 1891, the tale of a young woman's struggle to find a purpose in life does more than reflect the literary conventions of Russian realism or document historical events of the author's lifetime. By identifying herself as the narrator, Kovalevskaya not only inserts herself into the course of history depicted here. She also defines in her own terms the reality of Russian women during the reign of Alexander II.

Both the narrator and Vera Barantsova, the heroine of the novella, represent different types of "new women" who appeared in contemporary life and literature. Neither resembles the frightful nigilistka favoured by the conservative press. Nor do they engage in the revolutionary violence of such real-life radicals as Sofya Perovskaya and Vera Figner.
Kovalevskaya's critique of contemporary Russia constitutes the main strength of Nihilist Girl. Satirical thrusts and the occasional comic scene also enliven the narrative. Character development, however, is not always felicitous. Nor is the transition between different stages in Barantsova's life. The substantial introduction, which includes biographical material and literary criticism, enhances the volume.
12. Michèle Audin, Remembering Sofya Kovalevskaya (2011).
12.1. Note.

The French original [M Audin, Souvenirs sur Sofia Kovalevskaya (2008)] is reviewed above.

12.2. From the Introduction.

This is not a history book. Proof: I am not a historian. Nor is it a novel, since I am not a novelist either. And it is not even a mathematics book, although I am a mathematician. It is a personal book and it is a serious book. It deals with serious matters, with the work and life of a woman, of a serious woman, brilliant, professional, tenacious, and with the scientific reputation of this woman. I approach her story, sometimes with humour, often with jubilation, and always with pleasure. And with seriousness.

The first woman? Sofya Kovalevskaya was not the first woman to obtain a doctorate, even in mathematics: before her there was Maria Agnesi, in the 18th century, in Bologna. She is perhaps not even the first woman to obtain a university position; the same Maria Agnesi undoubtedly preceded her (but it seems never took up her position and devoted herself to religion and charity). In this book we will even witness one of the most eminent Swedish mathematicians of our time confirm (although in a rather ambiguous way) that, yes, Sofya Kovalevskaya was indeed the first woman to obtain a professorial position ... in Sweden. She was not the first woman to receive a prize from the Académie des sciences: Sophie Germain, another Sophie, another mathematician, had received one in 1816. She is very likely the first woman to have served on the editorial committee of a scientific journal.

Why Sofya Kovalevskaya? She is without doubt the first woman to have had a professional university career in the way we understand it today: she proves original theorems that earn her the title of doctor, she gives courses, she concerns herself with politics, she believes in the responsibilities of scientists, she travels, she proves more theorems, she participates (without much enthusiasm) in committee meetings, she has a daughter, she is editor of an international journal (Acta Mathematica), she fights for women's rights, she attends and contributes to scientific meetings, she's up for promotion, she writes reports and letters of recommendation, she travels to meet with colleagues at other universities. As was done in the 20th century, as we continue to do in the 21st. It is in this sense that she is close to us and it is why her life, her work and what she said touches us. Especially when we add that she led her professional life under very difficult conditions and in a wide variety of personal situations (married, separated from her husband, widowed, mother and head of the family).

I also want to emphasise the profound unity of the various facets of Sofya Kovalevskaya's personality, brilliantly summarised under the nice title (A convergence of lives) of the biography that Ann Hibner Koblitz dedicated to her. The fact of her being a mathematician and a writer is inseparable from her political convictions. Sofya was a nihilist. Many people think of nihilists as dangerous anarchists (as they were called before the word terrorist was made fashionable by the Nazis). In reality, the nihilists wanted to reform society with the notion that they, men and women equally, should contribute to raising the level of knowledge of society, which, in 19th–century Russia, was no small undertaking. In this regard, I refer the reader to the excellent preface of the book by Ann Hibner Koblitz [1993]. Where did this book come from? My association with Sofya's mathematical work (I explain on page 27 how and why I call her "Sofya") is long-standing, my association with her personality (see chapter XII) much less so: Sofya, her appearance, her life, her romances, her writings, the things she is thought to have experienced, Sofya, with all her facets, entered my life definitively at the end of 2004, for reasons both personal and mathematical, and actually took over my life after I got to know Jean-François Peyret and the cast of the theatre production The Case of Sophie K in the Spring of 2005. It was in order to "go beyond" that I decided to write this book. Its title comes directly from having been present with that "troop", so many times did I hear Jean-François Peyret say that his play displayed "memories of someone who was never known".

12.3. Review by: Peter Giblin.
The Mathematical Gazette 97 (539) (2013), 363-364.

Recently I reviewed for the Gazette a biography of G Mittag-Leffler by Arild Stubhaug in which the subject of the present book, S Kovalevskaya, figured quite prominently. Stubhaug's approach to biography is of the 'beeline' or 'as the crow flies' kind, an almost day by day chronological account from cradle to grave. Audin's book is very different; if it is a biography at all its approach is that of the butterfly, sipping at nectar from first one delectable flower and then another. Readers will certainly learn a lot about Kovalevskaya's life (1850-1891): her childhood in Russia; her 'false marriage' to escape to Europe; her difficulties in attending any lectures; the way in which she impressed Karl Weierstrass, the foremost analyst of his time, enough that he took her on as a private student (1870); her subsequent appointment to positions at the new Stockholm College (this is where Mittag-Leffler comes in); her success in winning a major prize (1888); her parallel literary career; the birth of her daughter (1878) and suicide of her husband (1883); her early death from influenza. These topics are covered, in some cases several times, throughout the book, sometimes through quotations from those who knew Kovalevskaya personally or by reputation, sometimes from modern sources. The author also has a considerable axe to grind about the reputations of women in mathematics during and after their lifetimes, and indeed she has a good point. Several parts I found just too fanciful, and maybe over-indulgent on the part of the author, such as a story about Kovalevskaya and Mittag-Leffler apparently adapted from various sources including Dostoevsky and A S Byatt; as the author says, 'I like to mix things up a bit'. (In the same place the author describes an anachronism occurring in her story, regarding Cantor's creation of set theory, as being 'discrete' which is either a very subtle joke or a misspelling of 'discreet'.) The author is fond of quoting women writers, especially A S Byatt and George Eliot, but maybe Alice Munro's short story Too Much Happiness, based on Kovalevskaya's final journey back to Stockholm, is just too recent for inclusion.

The book contains very thorough and interesting expositions of Kovalevskaya's mathematics, including discussions of her work on the spinning top (where she discovered a new solution now known as the Kovalevskaya Top) and on solutions of partial differential equations. There are some oddities in the exposition, combining on the same page very technical mathematics, where much knowledge is assumed of the reader, and phrases such as 'the solution is what is called an analytic function' which seem to suggest that the reader might not know a basic fact. But without doubt these technical discussions are very useful, and they go back to the original sources.

The book is translated from the French and this may account for some interesting words, such as 'medecine' and 'gayly'; more significantly the lengthy chapter dissecting parts of E T Bell's Men of Mathematics (itself an inflammatory title) is rather over-concerned with flaws in the French translation of that book. All the same the author does make serious points about Bell's condescending treatment of Kovalevskaya as well as his romantic versions of the lives of other mathematicians, never letting the facts get in the way of a good story. The chapter on Bell actually lists all the women occurring in Men of Mathematics.

Altogether this is a very unusual book, by an author who has published widely on the history of mathematics and also in the technical literature on symplectic geometry and integrable systems. If you can be patient with the extreme mix of styles, from the very technical through the usefully informative to the (to my mind) irritatingly informal, then you will learn much about this very interesting 19th century mathematician and, significantly, about her mathematics.

Last Updated January 2021