Sofya Kovalevskaya

Gabrielle Birchak/ January 18, 2022/ Late Modern History

PODCAST TRANSCRIPTS

Gen­der dis­par­i­ty is evi­dent in all areas of employ­ment and in acad­e­mia. It is bla­tant­ly evi­dent in sci­ence, tech­nol­o­gy, engi­neer­ing, and math­e­mat­ics. The ratio of men to women, specif­i­cal­ly in physics, engi­neer­ing, and com­put­er sci­ence, remains at four men for every woman. And we are now in the twen­ty-first cen­tu­ry, where we have made “progress.” Even though the eigh­teenth through the twen­ti­eth cen­turies show progress, the improve­ment made was excep­tion­al­ly slow. Thus, when Sofya Kovalevskaya obtained the posi­tion of full pro­fes­sor at Stock­holm Uni­ver­si­ty, it was an excep­tion­al accom­plish­ment on behalf of women. She was the first woman in Europe to hold this posi­tion since the Enlightenment. 

This same year, Sofya also became a cor­re­spond­ing mem­ber of the Russ­ian Acad­e­my of Sci­ences. And right­ly so because she was born and raised in Rus­sia. Yet, Russia’s acad­e­mia nev­er offered her a full pro­fes­sor­ship despite all her accomplishments.

Sofya Kovalevskaya was an extra­or­di­nary woman with mul­ti­ple tal­ents. She not only enjoyed math­e­mat­ics, but she also enjoyed writ­ing and lit­er­a­ture. Sofya was born in Moscow on Jan­u­ary 15, 1850. She had an old­er sis­ter and a younger broth­er. Her father, Lieu­tenant Gen­er­al Vasi­ly Vasi­lye­vich Korvin-Krukovsky, was an artillery gen­er­al for the Impe­r­i­al Russ­ian army. He was also the descen­dant of a Hun­gar­i­an roy­al fam­i­ly. Her moth­er was the daugh­ter of Gen­er­al Theodor Friedrich von Schu­bert, an hon­orary mem­ber of the Russ­ian Acad­e­my of the Sci­ences and direc­tor of the Kun­stkam­era Muse­um. Addi­tion­al­ly, Sofya’s great-grand­fa­ther was the promi­nent astronomer Frei­drich Theodor Schubert.

When she was eight years old, her father retired and moved the fam­i­ly to an estate in Pal­i­b­i­no. In her mem­oir titled Her Rec­ol­lec­tions of Child­hood, Sofya writes that they ren­o­vat­ed the rooms when they moved into the cas­tle. How­ev­er, there was not enough wall­pa­per for all the rooms. As a result, Sofya’s room was only par­tial­ly cov­ered with wall­pa­per. The oth­er walls were cov­ered with lith­o­graphed lec­ture notes that her father wrote while attend­ing a cal­cu­lus class giv­en by the promi­nent Russ­ian math­e­mati­cian, Mikhail Vasi­lye­vich Ostro­grad­sky. In her mem­oir, Sofya writes, “these sheets, spot­ted over with strange, incom­pre­hen­si­ble for­mu­las, soon attract­ed my atten­tion. I passed whole hours before that mys­te­ri­ous wall, try­ing to deci­pher even a sin­gle phrase, and to dis­cov­er the order in which the sheets ought to fol­low each oth­er.”[1] 

So ear­ly on, Sofya found her­self fas­ci­nat­ed and inter­est­ed in cal­cu­lus. This became evi­dent when she was 15 years old. She took her first Dif­fer­en­tial Cal­cu­lus class and impressed her teach­ers with her knowl­edge of these chal­leng­ing topics. 

And even though her par­ents were very smart, Sofya was raised and edu­cat­ed by the ser­vants. Unfor­tu­nate­ly for Sofya, her gov­erness was psy­cho­log­i­cal­ly abu­sive. If she mis­be­haved, the gov­erness would write out the details of her behav­ior and then pin it to her back, which she had to wear to din­ner in front of oth­er fam­i­ly mem­bers. This gov­erness also sep­a­rat­ed her from her sis­ter, Anne, whom Sofya absolute­ly adored. So, grow­ing up was emo­tion­al­ly chal­leng­ing for Sofya.[2] Regard­less, her par­ents ensured that she received an edu­ca­tion from some of the best tutors and teach­ers. Thus, she was trained in math­e­mat­ics by Iosif Male­vich, Alek­san­dr N. Stran­no­li­ub­skii, and physi­cist Niko­lai Tyr­tov, who called her the “new Pas­cal.”

By the time Sofya was ready to attend the uni­ver­si­ty, she was lim­it­ed in obtain­ing a high­er edu­ca­tion because women were not per­mit­ted to obtain col­lege degrees in Rus­sia. Regard­less, Sofya and her sis­ter were deter­mined to receive high­er edu­ca­tion. And so, like many of their friends, they found a workaround. They could obtain a col­lege degree if they were to study in anoth­er coun­try. How­ev­er, unmar­ried women were not allowed to trav­el by them­selves. And so, Sofya and her sis­ter Anne made plans to find a spouse. 

Also, dur­ing this time, Anne was intro­duced to a new pro­gres­sive move­ment called the Russ­ian Nihilist move­ment. This was the 1860s, and the term nihilist was a ref­er­ence to the hero fig­ure in the book Fathers and Chil­dren by Ivan Tur­genev. This hero fig­ure, and the Russ­ian nihilists, believed that sci­ence was a valid tool for help­ing peo­ple live a health­i­er and more vital life. Much like the sev­en­teenth and eigh­teenth century’s enlight­en­ment era, they knew that sci­ence inval­i­dat­ed reli­gion and super­sti­tion and that sci­ence and its dis­cov­er­ies meant progress for society. 

In 1868 Sofya entered into a con­tract with Vladimir Kovalevskij that stat­ed that they were mar­ried. Vladimir was an intel­li­gent, young pale­on­tol­ogy stu­dent, a book pub­lish­er, and one of the first to trans­late and pub­lish in Rus­sia the works of Charles Dar­win. After their mar­riage, they trav­eled from Rus­sia to Vien­na. While in Vien­na, she stud­ied physics and attend­ed lec­tures at the uni­ver­si­ty. How­ev­er, their stay was short, and they moved to Ger­many. In Ger­many, as a woman, she was not allowed to attend class­es at the uni­ver­si­ty. How­ev­er, she found a workaround and obtained per­mis­sion to audit the class­es at the Uni­ver­si­ty of Hei­del­berg. She stud­ied physics and math­e­mat­ics while her hus­band earned his Doc­tor­ate in Paleontology.

They trav­eled to Lon­don for a brief stay. They engaged in intel­lec­tu­al and social cir­cles, where she would meet oth­er bril­liant indi­vid­u­als and writ­ers, includ­ing Thomas Hux­ley, Charles Dar­win, Her­bert Spencer, and George Eliot. In 1870 they moved to Berlin. Sofya was hop­ing to attend the lec­tures of Karl Weier­strass at Friedrich Wil­helm Uni­ver­si­ty in Berlin. Unfor­tu­nate­ly, the uni­ver­si­ty would not allow her to attend or even audit the classes.

And so, Sofya approached Weier­strass with glow­ing rec­om­men­da­tions from her pre­vi­ous pro­fes­sors. Unfor­tu­nate­ly, he had to fol­low the university’s order and told her that she could not attend his lec­tures. And so, he sent her away with a set of math­e­mat­i­cal prob­lems. He was “con­vinced she would not suc­ceed, and gave the mat­ter no fur­ther thought.” But she returned a week lat­er with all the solu­tions that, accord­ing to Weier­strass, were “emi­nent­ly clear and orig­i­nal.”[3] Weier­strass was so impressed that he decid­ed to pro­vide her with pri­vate lessons, using the same lec­tures notes he used at the university.

A year into her stud­ies with Weier­strass, she and Vladimir went to Paris to find her sis­ter, whom she believed was miss­ing. When they arrived, she dis­cov­ered that her sis­ter and her broth­er-in-law Vic­tor Jaclard had been arrest­ed because of their extreme social­ist views and efforts to imple­ment rights for the work­ers. Her sis­ter escaped to Lon­don, but her broth­er-in-law had been sen­tenced to exe­cu­tion. Sofya and her sis­ter reached out to their father, who had polit­i­cal sway in Paris as Russia’s Lieu­tenant Gen­er­al. With his help, they were able to save Jaclard.

Sofya went back to Berlin and con­tin­ued to study from Weier­strass for three more years. For her doc­tor­al dis­ser­ta­tion, she pre­sent­ed three papers to the Uni­ver­si­ty of Göt­tin­gen. These papers cov­ered top­ics on par­tial dif­fer­en­tial equa­tions, ellip­tic inte­grals, and the dynam­ics of the rings of Sat­urn. In 1874, she earned her doc­tor­ate in absen­tia, sum­ma cum laude. This was an excep­tion­al accom­plish­ment because she was the first woman to earn a doc­tor­ate in math­e­mat­ics in mod­ern Europe.

Her work with par­tial dif­fer­en­tial equa­tions was foun­da­tion­al to her Cauchy Ini­tial Val­ue prob­lem analy­sis. In 1842, Augustin Cauchy pre­sent­ed a spe­cial case of the Ini­tial Val­ue prob­lem. How­ev­er, it wasn’t com­plete­ly solved until 1875, when Sofya pro­vid­ed the com­plete solu­tion and for­mu­lat­ed the most gen­er­al proof. 

In 1874, Sofya and her hus­band moved back to Rus­sia. How­ev­er, because Vladimir was active­ly involved in an unfa­vor­able polit­i­cal move­ment, he could not secure a job. Addi­tion­al­ly, Sofya could not secure a job because she was a woman. As a result, they strug­gled finan­cial­ly. Around this time, her father died, which pos­si­bly drew them clos­er togeth­er. As a result, she became preg­nant. Sofya had a daugh­ter that she named Sofya, that she nick­named “Fufa.”  Unfor­tu­nate­ly, Vladimir was tem­pera­men­tal and strug­gled with anger. This was prob­a­bly height­ened because the gov­ern­ment was pros­e­cut­ing him for fraud­u­lent activ­i­ties with a stock exchange. Sofya decid­ed to leave Vladimir, put her daugh­ter under the care of friends and fam­i­ly, and go back to work as a math­e­mati­cian and professor.

This endeav­or led her back to Swe­den, where she obtained a posi­tion at Stock­holm University. 

That same year, in 1883, Vladimir fell into a deep depres­sion and com­mit­ted sui­cide. His sui­cide left Sofya filled with grief, dev­as­ta­tion, and heart­break. She was incon­solable. To regain her com­po­sure, she deeply immersed her­self in math­e­mat­ics.[4]

In 1884 Sofya obtained the posi­tion of assis­tant pro­fes­sor at Stock­holm Uni­ver­si­ty as well as edi­tor of the jour­nal ACTA Math­e­mat­i­ca. By 1888, the French Acad­e­my of Sci­ence award­ed her the Prix Bor­din prize for her the­sis titled, Faces on a Par­tic­u­lar Case of the Prob­lem of the Rota­tion of a Heavy Body around a Fixed Point, where the Inte­gra­tion is Car­ried Out Using the Ultra Ellip­ti­cal Func­tions of Time. Despite the excep­tion­al­ly long title for a the­sis, it was foun­da­tion­al in show­ing how rigid body motion is com­plete­ly inte­grable on rota­tion­al bod­ies and ellip­ti­cal func­tions. This award was well deserved because this was the dis­cov­ery of what is now called the Kovalevskaya Top. 

Though it is called a top, it is not a toy. Instead, it is a ques­tion that asks the math­e­mati­cian to per­fect a the­o­ry that address­es the move­ment of a sol­id body around an immov­able point. One of the best analo­gies I’ve heard is to watch a fig­ure skater spin with their arms out, and then when they pull them in, they spin faster. The work behind the Kovalevskaya Top about 100 years ear­li­er when Leonard Euler and then Joseph Lagrange ana­lyzed the move­ment of a spin­ning top. Euler ana­lyzed tops and referred specif­i­cal­ly to the cen­ter of grav­i­ty as the fixed point. Lagrange also ana­lyzed tops; how­ev­er, his fixed point was where the top touched the ground. But, when Sofya ana­lyzed the top, she found that on a spin­ning top that looks at a sol­id body around an immov­able point, there are three instances of iner­tia. These three instances are ref­er­enced as three coor­di­nate axes that are cen­tered at one point on the top. Two of the three instances are the same val­ue, but the third instance is half of that value.

And so, we are back to where I start­ed this pod­cast. In 1889, Sofya was appoint­ed full pro­fes­sor at Stock­holm Uni­ver­si­ty. How­ev­er, this was not her only exten­sive accom­plish­ment. She also wrote a mem­oir, two plays, and an auto­bi­o­graph­i­cal novel.

Sad­ly, short­ly after she returned from a vaca­tion in Nice, France, she died from an epi­dem­ic flu com­pli­cat­ed by pneu­mo­nia. She was only 41 years old.

Sofya’s life serves as an inspi­ra­tion for many women who pur­sue edu­ca­tion and careers in math­e­mat­ics. She was a bril­liant woman who whole­heart­ed­ly pur­sued the dis­cov­ery of math­e­mat­ics. Her lega­cy includes events host­ed by the Asso­ci­a­tion for Women in Math­e­mat­ics. Addi­tion­al­ly, there are funds and schol­ar­ships in her name and a lunar crater named in her hon­or. Because of Sofya Kovalevskaya, many women world­wide are inspired by her sto­ry and con­tin­ue to walk the path of STEM, which becomes well-tread as more women pur­sue mathematics. 

With this ongo­ing progress of more women enter­ing sci­ence, tech­nol­o­gy, engi­neer­ing, and math, we can only hope to reduce the ratio of men to women in acad­e­mia. And not just women, but also women of col­or, mem­bers of the LGBTQ com­mu­ni­ty, and all those who are mar­gin­al­ized. Bril­liance comes in all shapes, sizes, con­structs, and gen­ders. And the more that the world of STEM embraces our dif­fer­ences, the more dis­cov­er­ies we can obtain. But hope is just a thought. We can do more than hope; we can be part of that inspi­ra­tion. We can encour­age and inspire mar­gin­al­ized indi­vid­u­als to pur­sue these won­der­ful sub­jects. And I just know that if you are a woman, a woman of col­or, les­bian, gay, bisex­u­al, trans­gen­der, queer, or dis­abled and you work in STEM, I know that you are inspir­ing some­one at this very moment. And for all my lis­ten­ers in STEM, includ­ing those who do not fit into the mar­gin­al­ized groups but do all they can to dimin­ish the dis­crim­i­na­tion, thank you for help­ing to reduce the ratio!

 Until next time, carpe diem. 

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[1] Anna Car­lot­ta Lef­fler, Sonya Kovalevsky (Lon­don: T. Fish­er Unwin, 1895), 22–23.

[2] Teri Perl, Math Equals (Men­lo Park, CA: Addi­son-Wes­ley Pub­lish­ing Com­pa­ny, 1978), 129.

[3] Anna Car­lot­ta Lef­fler, Sonya Kovalevsky (Lon­don: T. Fish­er Unwin, 1895), 22–23.

[4] Teri Perl, Math Equals (Men­lo Park, CA: Addi­son-Wes­ley Pub­lish­ing Com­pa­ny, 1978), 134.