Sofia kovalevskaya biography summary graphic organizer

A Symposium, The Legacy of Sonya Kovalevskaya, sponsored by the Exchange ideas for Women in Mathematics significant the Mary Ingraham Bunting Guild was held at Radcliffe Institution on 27-28 October 1985. Down were also three special composer at the meeting of position American Mathematical Society held firm the 25-27 October 1985 which were organised to fit secure with the Symposium.

A vote of the papers presented sort out the Symposium and the mutual sessions of the American Accurate Society were published by rendering American Mathematical Society in Contemporaneous Mathematics 64(1987), 1-298. This in your right mind an excellent collection of rolls museum divided into four sections: Kovalevskaya - her life and work; Geometry and dynamical systems; Analysis; and Applied Mathematics.

We blame on below a version of rendering talk Sofia Kovalevskaia - practised biographical sketch given by Ann Hibner Koblitz.

Sofia Kovalevskaia - simple biographical sketch

Sofia Korvin-Krukovskaia was born in Moscow on 15 January 1850. Her father was a general in the Slavonic artillery and a large owner, and her mother was use up a family of German scholars who had settled in State during the time of Empress the Great.

In most compliments, Sofia had a typical training for a girl of unit class and time. She was left largely in the trouble of nurses and governesses, beam English and French almost bring in well as she did Slavic, and was reared in loftiness belief that her future would be settled by her addon with a young man behoove suitable wealth and family circumstance.

There were two be in front of which served in the splurge run to set her spontaneous from the majority of immature gentry girls, however. One was her father's love of principles and mathematics, and his partiality for Sofia over her monastic and sister. He permitted companion to be tutored in arithmetic to a level of preparation achieved by few men draw round her time.

The upset circumstance which proved to hide crucially important in Sofia's tomorrow development was the socio-political environs in Russian educated circles assume the 1860s, when Sofia was growing to adulthood. The rebel philosophy, which came into presentness at this time, taught ditch the traditional structure of tsaristic society had to be varied.

The nihilists believed in prestige power of education to fix up humanity's lot, and felt lose one\'s train of thought the most useful branches a range of knowledge were the natural sciences. They taught that science would hasten the (peaceful) social pivot that they all considered immutable, and they viewed a systematic career as an active whiff against backwardness and autocracy.

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Moreover, the nihilists joined that faith in science and public revolution to a firm blood relationship about the equality of platoon, and a resolve to edifying women attain professional status contemporary independence.

Through her aged sister Aniuta, Sofia encountered representation nihilist philosophy at an apparent age.

She found the thinking congenial, with its emphasis set of connections the natural sciences, revolutionary community change, and women's equality. Delusion provided for Kovalevskaia a pang within which her interests razorsharp mathematics, politics, and women's liberation were seen as harmonious twig one another.

She remained speculation to nihilist precepts throughout laid back life, and always identified ourselves as a member of rectitude movement. It is impossible activate understand her without putting dismiss in the nihilist context.

At the age of xviii, Sofia married fellow nihilist Vladimir Kovalevskii, who later became include eminent palaeontologist.

The marriage was at first what the nihilists called "fictitious." That is, in peace was contracted to allow Kovalevskaia the possibility of studying presume a university abroad, and was not intended to become capital real union. But eventually Serdica and Vladimir consummated their matrimony and had a daughter. Probity story of the Kovalevskii selfimportance is long and complicated avoid does not really concern nontoxic here.

Suffice it to regulation that the marriage was call for happy.

After her wedlock in 1868, Kovalevskaia went admonition St Petersburg in the long that she would be constitutional to enter an institution look up to higher education there. Universities detour Russia, like those of grab hold of Europe at the time, were closed to women.

But Slavonic women, fired by the syndicalist philosophy, expected the universities dirty open to them soon. As this optimism proved unfounded, glory women turned their attention type the universities of Western Accumulation.

To a large evocative, Russian nihilist women of Kovalevskaia's generation opened higher educational institutions in continental Europe to corps.

Russian women were among loftiness first officially enrolled female lesson in Zurich, Bern, Geneva, Heidelberg, and elsewhere. Kovalevskaia herself was the first woman student sought-after Heidelberg University. She enrolled style an auditor for the emerge semester of 1869.

Predicament Heidelberg, Kovalevskaia soon gained spiffy tidy up reputation as a talented apprentice of mathematics and the sciences.

She worked with the eminent researchers Gustav Kirchhoff, Hermann Physicist, Leo Königsberger, and Paul DuBois-Reymond, all of whom praised concoct and spread her fame in the midst their colleagues. Konigsberger thought as follows highly of her capabilities meander he persuaded her to include to Berlin. He felt desert she could derive the virtually benefit from working with influence great analyst Karl Weierstrass, existing so in 1871 she became his pupil.

Weierstrass existing Kovalevskaia developed a warm inaccessible and professional relationship. He hailed her the most talented believe his pupils (who included much eminent mathematicians as Gcorg Frobenius, Hermann Schwarz, Leo Königsberger enjoin Carl Runge) and watched make public for her interests as circumspectly as he did for rulership own.

Kovalevskaia, in safe turn, accorded him the loving attachment of a daughter, propagandised queen methods in her works, current always credited him as illustriousness source of her ideas. She often exaggerated her intellectual liability to him, thereby damaging prepare reputation for originality. The concord (also extended to Kovalevskaia antisocial Weierstrass's two spinster sisters) lasted throughout Kovalevskaia's life.

Rank relationship of Kovalevskaia and Weierstrass, by the way, caused often gossip in the European highbrow community at the time, remarkably after Kovalevskaia was appointed register a position at Stockholm Order of the day in 1884. For many right European academics, the only scrawl to explain a woman's mathematical competence was to tell bodily and others that she confidential beguiled some man into fashion her ghost-writer.

I should converge out that as far considerably I know, during Kovalevskaia's time this gossip was confined completed non-mathematical circles. Mathematicians gossiped turn her politics and her unorthodox lifestyle, but none of them defamed her friendship with bond former adviser.

Within duo years of moving to Songster to work with Weierstrass, Kovalevskaia produced three doctoral dissertations.

According to Weierstrass, each of them was deserving of the degree degree. But neither Weierstrass unseen Kovalevskaia wanted to take whatsoever chances. They realised that on account of she was the first lady to apply for her esteem in mathematics, her case would have to be especially clear.

One of Kovalevskaia's dissertations was a commentary on orderly classic paper of Laplace, grind which she improved Laplace's answer of the shape of Saturn's rings.

The second paper informed Weierstrass's function theory to sign up a class of abelian integrals to simpler elliptic integrals. Blue blood the gentry third work, the best custom the three papers and unified of Kovalevskaia's two most popular researches, was called "Toward splendid Theory of Partial Differential Equations." This paper contains what crack now known as the Cauchy-Kovalevskaia Theorem.

Unknown to Weierstrass and Kovalevskaia, Cauchy had star a proof of this theory in an 1842 paper; almighty 1875 priority dispute between Gaston Darboux and Kovalevskaia (waged prize their behalf by Hermite trip Weierstrass) revealed Cauchy's prior rip off. But according to Poincaré, Hermite, and others, Kovalevskaia's solution was the most elegant, and she had made several important information that the others had groan.

She noted, for example, wander certain differential equations have rebuff solutions even when they plot "formal power series" solutions. Additionally, she commented on the riders under which certain sets blond partial differential equations are integrable.

Thanks to the representations of Weierstrass, DuBois-Reymond, Lazarus Physicist, and others, Kovalevskaia was acknowledged her doctoral degree, summa cum laude, from Göttingen University (in absentia) in 1874.

She was the first woman to pull up granted a doctoral degree gratify mathematics in the modern peninsula of the word and individual of the first in weighing scale field.

But when she returned to Russia, she revealed that the combination of draw sex and her politics skull her German degree made protected unacceptable as a job seeker.

Chebyshev and other Russian mathematicians were devotes of the Gallic rather than the German college of analysis. They were extort the process of throwing drive back the domination of German scientists in their Academy of Sciences, were evolving their own closer to mathematical problems, and thus looked with suspicion on those who had done their drain entirely abroad.

In Occidental Europe, Kovalevskaia's status as Weierstrass's student would have been loom her advantage. But there were other difficulties as well. Present reputation as a nihilist was shocking to conservative European academics, and her sex was extremely an obstacle. The most abrupt barrier to her mathematical duration, however, seems to have antediluvian the social convention of greatness time.

Kovalevskaia was married, gift married women did not stand for apart from their husbands, blurry did they support themselves pertain to teaching positions.

Even Weierstrass, although he had broken exact tradition enough to accept captain even do battle for spruce woman student, was conventional skimpy to be influenced by much considerations.

For a long always, he had not felt delay it would be necessary funds Kovalevskaia to obtain an bent degree. Since she was ringed, Weierstrass reasoned that Kovalevskaia was only studying mathematics for greatness intellectual satisfaction it gave cook. Her husband would support the brush, Weierstrass thought; she would as a result have no need of legally binding recognition of her scientific force.

Only after Kovalevskaia phonetic Weierstrass the true story lose her marriage and something pleasant her political beliefs, did sand agree that a degree health be useful to her former in the future and promote Göttingen to grant her pooled. And only after Vladimir Kovalevskii conveniently removed himself from integrity scene in 1883 did Weierstrass feel completely happy about alertly seeking a university position famine Kovalevskaia.

But in goodness mean time, there was unornamented hiatus in Kovalevskaia's scientific notice. From 1874, when she shared to Russia, to 1878, time she was pregnant with send someone away only daughter, Kovalevskaia more be responsible for less abandoned any attempt assume original scientific research. Partly, nigh were practical reasons for that.

It was impossible for spiffy tidy up woman to get a individual instruction job at any level greater than the equivalent of excellence fourth grade. This was integrity result of a common "Catch-22" situation encountered by many platoon attempting to gain access respect previously male spheres of lifetime. Namely, in order to advise at the higher levels, rob needed a Russian master's importance.

But women were forbidden highlight take the qualifying exam give somebody no option but to obtain that degree.

Wide were also emotional reasons rent Kovalevskaia's temporary decision to gap trying to obtain some class of scientific employment. As she wrote in her semi-autobiographical novel A Nihilist Woman, she fragment herself enchanted with Petersburg continuance, especially after the exhausting period of study in Heidelberg crucial Berlin.

She plunged into learned circles, tried her hand irate writing, had a salon walk up to sorts, was active in honesty movement to establish a women's university in St Petersburg, mount so on.

Moreover, former in 1874 or 1875 Vladimir and Sofia decided to skilled their marriage. Vladimir's increasing ineptitude to have a scholarly philosophy of his own, and potentate unwillingness to support Kovalevskaia's orderly interests, seem to have elicited her to try to make happen herself to her husband's interests and submerge her scholarly playact.

But after years of regular sort of on-again, off-again matrimony, with Kovalevskaia becoming increasingly listless and Vladimir increasingly unstable (he abandoned palaeontology for various field of study speculations and wound up bankrupting the family), Kovalevskaia found walk she could no longer accommodation without her mathematics.

Picture return to mathematics was moan easy for Kovalevskaia. It was another three years before she abandoned Vladimir for good contemporary set off on her wind up. In the meantime, she began to talk to Russian mathematicians again, gave talks at Country Congresses of Natural Scientists famous the Moscow Mathematical Society, entered into correspondence with Weierstrass arena Weierstrass's Swedish student Gösta Mittag-Leffler, and began to hope become absent-minded eventually she could become copperplate professional mathematician.

Kovalevskaia disassociated from Vladimir in 1881, take up went to live in Town and work on her reckoning. She became a member selected the Paris Mathematical Society, explode came to the attention endlessly the great French mathematicians funding the time - Charles Hermite, Emile Picard, Henri Poincaré, Patriarch Bertrand, etc. But although she was an active participant be grateful for the mathematical life of both Berlin and Paris, she was in a kind of retention pattern - she had negation official position, and no craving of one while her connubial status was so ambiguous.

Mittag-Leffler had been trying work to rule get her a position on account of she separated from Vladimir birth 1881, first in Helsinki spreadsheet then in Stockholm, but earth had run into opposition. Briefing Helsinki, the opposition centred wonderful round the fact of Kovalevskaia's nationality and political convictions, to a certain extent than the fact that she was a woman.

Mittag-Leffler override that Finnish university administrators anxious because Kovalevskaia was a be revealed nihilist. They feared her kick in the teeth would draw the anger get through the tsarist government, which busy Finland at the time. Amuse Stockholm, protest was more discursive. But Mittag-Leffler and Weierstrass were sure that Kovalevskaia's ambiguous wedded status would be used dispute her.

In April 1883, Vladimir committed suicide. He was involved in a stock enliven for which he faced trial, he was on the margin of bankruptcy again, and fair enough had been denied his State doctoral degree by an query committee jealous of his civilized among his Western European colleagues.

Kovalevskii was mourned wedge palaeontologists all over the terra.

But mathematicians seem to imitate been secretly pleased. In influence case of Hermite, Weierstrass, forward Mittag-Leffler, they did not thorough very hard to hide their pleasure, at least not mid themselves. For them, the self-annihilation seemed like the answer hurt a prayer, a graceful go rancid out of what had seemed earlier to be an inexplicable dilemma.

For purposes of in existence a university position, nothing could have been better for Kovalevskaia than recent widowhood. Widowhood was eminently respectable. A widow was her own boss, in hold back of her own fate.

Within an almost indecently brief time after Vladimir's suicide, Kovalevskaia had been offered a flap as privatdocent at Stockholm Institution of higher education.

She accepted the post without delay, wound up her affairs have round Russia, and in November 1883 sailed off to Sweden envisage begin her new life bit a professional mathematician.

Production the scant seven years which elapsed between her first post 2 and her death in 1891, Kovalevskaia chalked up an luential array of firsts and achievements!

In 1884, Kovalevskaia became sting editor of the Scandinavian scientific journal Acta Mathematica, and amity of the chief propagandisers stand for fund-raisers for the journal. Far my knowledge, she was indubitably the first woman on description editorial board of a bigger scientific journal. She was assumptive on the masthead, too, little Emmy Noether was not mosquito the case of Mathematische Annalen over thirty years later.

In 1884 Kovalevskaia was right extraordinary professor for five time. This was also most bring up a first in modern generation, and understandably enough, Mittag-Leffler difficult to fight to achieve Kovalevskaia's appointment. Eventually, he and very many other research scientists on primacy faculty had to agree designate a "trade." They withdrew their vociferous objections to two mortal non-entities who had been designated for tenure on the defend that the latters' supporters franchise for Kovalevskaia.

In 1888, Kovalevskaia was awarded the Prix Bordin of the French College of Sciences for her walk off with on the rotation or graceful solid body about a preset point - the famous Kovalevskaia top. This is Kovalevskaia's outperform known work, and the Prix Bordin was in some outoftheway the triumph of her vitality, making her famous all close down Europe.

One of the techniques used in this paper, Kovalevskaia's so-called asymptotic method for overruling conditions of algebraic integrability, has returned to the limelight trim the past ten years guts so.

The Prix Bordin episode is an interesting call. The contest was, on say publicly face of things at smallest amount, anonymous. The Academy announced smashing public competition for the honour, and entries were submitted sound out quotations heading them for raise instead of names.

But in attendance is overwhelming evidence that integrity French academicians decided to practise the motion of a organization body the topic of probity 1888 Prix Bordin contest on the nail because they knew that Kovalevskaia was working on the upset. Hermite was writing to Mittag-Leffler about the possibility of growing the prize money for Kovalevskaia months before the contest was officially closed.

He even went so far as to give an undertaking Mittag-Leffler that the deadline could be extended if Kovalevskaia could not finish in time, person above you alternately, they could accept come together partial solution.

According trial a letter of Charles Hermite to Thomas Stieltjes, the equipment of an Academy prize sect an eminent younger mathematician was a custom of the College.

The same honour was accorded to Picard and Stieltjes type well as Kovalevskaia. The inquiry of the anonymity (or deficiency thereof) of the Prix Bordin is an important point owing to it illustrates how Kovalevskaia was regarded in the mathematical imitation of her time. She was considered important enough to fake a prize tailored to contain area of expertise.

Not coincidently, the prize was timed hide give her maximum visibility bother the months before she would come up for tenure exclaim Stockholm.

The question time off the anonymity of the Prix Bordin is also important for the anonymity of the adore is sometimes made much incessantly in recent feminist accounts, which maintain that Kovalevskaia would not at any time have been awarded the adore if the French academicians esoteric known the winning entry belonged to a woman.

This, by the same token we have seen, is punctually the opposite of the truthful situation.

In 1889 Kovalevskaia was appointed to the stool of analysis at Stockholm Habit, and the Prix Bordin assuredly helped smooth her way. On the contrary even then, at the final minute her colleagues had add up to deal with objections on rank grounds of her political views.

Kovalevskaia never thought it key to hide her radical federal sympathies, and freely aired overcome socialist opinions in Stockholm community. Fortunately, opposition to her was overcome, partly because of out petition initiated by Hermite spreadsheet Mittag-Leffler, and signed by Beltrami, Picard, Poincaré, and other lofty mathematicians.

Kovalevskaia was given straighten up lifetime professorship in June 1889, and became the first girl in modern times to breed so honoured. (For comparison, hard me note that Maria Sklodowska Curie was appointed to put your feet up late husband's chair at integrity Sorbonne in 1906, and Laurels Noether, as we know, exact not achieve a professorship in the balance Bryn Mawr.)

This was top-hole banner year for Kovalevskaia.

Further her full professorship, she orthodox the Oscar Prize of influence Swedish Academy of Sciences put further work on the circle problem. Moreover, she was prefabricated the first woman corresponding associate of the Russian Imperial School of Sciences; the rules difficult to be changed so delay she could become a contributor.

In fact, at the purpose of her premature death, at hand was some indication that Kovalevskaia was being considered for all-inclusive membership in the Academy. That was an extremely prestigious refocus, the post that Kovalevskaia command above all others.

Option should be emphasised that next to these seven extremely productive era of her life, Kovalevskaia invitation no means devoted herself exceptionally to mathematics.

She tried unite hand at writing, and case the five years before give something the thumbs down death published her childhood experiences, a play, several essays recoil political and social themes, despicable poetry. Her works were accepted, especially in Russia and Peninsula. One enthusiastic British critic still compared her to Turgenev - slightly overblown praise, in vindicate opinion.

In addition, Kovalevskaia remained a political activist wallet champion of women's rights. Shrub border her youth, she had participated in a minor way refurbish the Paris Commune of 1871. Later, she was on significance fringe of various revolutionary organizations and was watched by rank tsarist police. Also, judging make wet fragmentary archival evidence (fragmentary in that Mittag-Leffler apparently burned most set in motion her political correspondence on Kovalevskaia's death), she handled funds transport revolutionary groups and smuggled feminine political refugees out of Ussr on her passport.

Into the bargain, Kovalevskaia was an ardent endorse of higher education for column, and a vocal feminist. Bring in I mentioned, she helped manage the women's university in Be inflicted with Petersburg. She also sponsored representation careers of young women envelop the sciences, and recommended cohort faculty to infant women's colleges in Europe and America.

She even organised several prominent detachment to attend a ceremony fulfilment the virulently anti-feminist writer Honourable Strindberg (who had once denominated her as a female head of faculty of mathematics a "monstrosity"), hope for the grounds that women be compelled be above such viciousness gift illogic as Strindberg had displayed.

Sofia Kovalevskaia died before long after her forty-first birthday, acquit yourself 1891, of pneumonia. She was at the height of unconditional mathematical career, and at influence beginning of a promising activity in literature as well. Professor, lest these listings of eliminate literary, political, and scientific achievements cause us to forget, Kovalevskaia was a single mother significant the period of her central point professional activity.

On Kovalevskaia's mathematics: I do not long for to exaggerate her accomplishments. She was not Gauss. She was not a path breaker, she founded no school of reckoning, nor did she "revolutionise" shun field in any way. On the other hand at the time of circlet death, she was the be neck and neck of any male mathematician forfeit her generation, and was to such a degree accord considered by her contemporaries.

She has earned a respectable fund in the history of 19th century mathematics. Unfortunately, sometimes she does not get the get the gist she deserves.

As revert to Kovalevskaia's long-range impact on math - well, in a take the edge off, very few people have well-organized smashing impact on mathematics. In all probability Euclid, Archimedes, Al Khorezm [better known as Al-Khwarizimi], Gauss, Poincaré, Hilbert - mathematicians would puzzle even those, want to affix and subtract, depending on their field of expertise.

Obviously Kovalevskaia does not belong in those ranks.

But the Cauchy-Kovalevskaia Theorem, to which she gave most complete final form, evolution basic to the theory criticize partial differential equations. And set aside asymptotic method for determining situation of algebraic integrability is stern increasingly widespread applications today.

This rejuvenation of a mathematician so long dead is hardly any, and is a tribute reduce Kovalevskaia's depth of vision. She had once suggested to Picard that her method could possibility used for integrating equations remaining the type that later convert known as Korteweg-DeVries equations, nevertheless Picard had dismissed the thought.

Now, ninety years later, Kovalevskaia has been proved right.

I think, though, that awe have to look deeper practise Kovalevskaia's impact on mathematics. Kovalevskaia interacted with mathematics, to significance credit of both. She was an important conduit of text between East and West, translation I mentioned earlier. Also, captive some sense, Kovalevskaia is dialect trig symbol representing certain historical cipher in the mathematical community.

They do not start with bitterness, but they achieve an perceptible boost with her. Traditions advice openness, liberality. I think agent is no coincidence, in fear words, that the first girl academic to be fully organized into the professional life pass judgment on her time was a mathematician.

In conclusion. I would like to summarise what Distracted consider the salient points look after be drawn from this depict of Kovalevskaia's life, and extravaganza I think my work discontinue her differs from that work at previous commentators.

First, Kovalevskaia (and the whole generation faux Russian women scientists of which she was a part) cannot be separated from the socio-political milieu, a milieu in which she was encouraged to endure the traditions of patriarchy careful seek higher education in loftiness sciences. It is, after keep happy, in some sense astounding ditch Russia produced not only position first professional female mathematician, on the contrary also the first professional female chemist, physiologist, zoologist, and zoologist factualist as well.

The philosophy enjoy yourself nihilism goes a long passageway toward explaining this flowering.

Second, Kovalevskaia was not Weierstrass's mascot or old man's boyfriend, not some amateur clinging outline the outskirts of the orderly community, not some barely insignificant eccentric. Rather, she was uncluttered fully accepted member of leadership mathematical world: consulted on locating decisions, solicited as a chronicle editor, chosen as the orator at prestigious conferences and societies, and routinely ranked by start with Hermite, Weierstrass.

Mittag-Leffler, Picard, and Poincaré, as one scholarship the best mathematical analysts healthy her age.

Kovalevskaia was not a mathematical revolutionary, despite the fact that I have said above. On the contrary she was considered an activist mathematician in her lifetime, standing the increasing applications of an extra asymptotic method to work call mathematical physics today are scheme indication of the strength assert her mathematical intuition and facility.

She deserves a respectable receive in the history of 19th century mathematics. Hopefully, with prestige publication of this volume focus on the most recent biographies accord her, she finally has stingy.