Jen-Luc Piquant and I are heading out to Oregon State University today, as I am a featured speaker at OSU's first Sonia Kovaleskaya Mathematics Day, honoring the prominent Russian female mathematician of the same name. The aim is to inspire "middle school students, with an emphasis on young women, to explore the wonderful world of mathematics through fun activities and exciting talks." I'm hoping to convince the kids not to be like me, but to learn to love and appreciate math while they still have a chance to master it -- you know, before grown-up life gets in the way. So if you're in the area, come say hello and bring a young girl who needs math-y inspiration with you. Of course, this means we must dispense with the usual round of weekend linkage, but that's okay: you can all your fellow party goers about Sonya instead. (Full disclosure: The following is a slight adaptation of a prior blog post about this amazing woman.)
Sonya Kovalevsky was a Russian woman who was a protege of the Swedish mathematician Gosta Mittag-Leffler, founder of the journal Acta Mathematica. (Lengthy side note: The question of how to refer to women scientists is a thorny one -- by first name? last name? married name? Plus, she is sometimes referenced as Sofia Kovaleskaya, because no self-respecting 19th century person of Russian descent would have any fewer than three forms of their name, including nicknames. It's all very confusing. So henceforth, she shall be Sonya.) She was a fascinating, admirable woman, whose story doesn't deserve to be gathering dust in the faded archives of scientific history.
Most online entries dutifully cite her list of accomplishments: first woman member of the Russian Academy of Sciences (although still unable to attend actual meetings because of her gender); first modern European woman to attain a full professorship; established the first significant result in the general theory of partial differential equations; and winner of the prestigious Prix Bordin.
She was also a gifted writer (of both novels and magazine articles), and often quoted thusly: "Many who have never had occasion to learn what mathematics is confuse it with arithmetic, and consider it a dry and arid science. In reality, however, it is the science which demands the utmost imagination.... It seems to me that the poet must see what others do not see, must look deeper than others look. And the mathematician must do the same thing."
I wasn't surprised to learn that Sonya was a product of Russia's privileged class, the daughter of a military officer and landowner; her mother was the granddaughter of a Russian astronomer. Education was such a taboo for women, even in the mid-19th century, that only those women who moved in rarefied aristocratic circles were exposed to intellectual pursuits . "All my life I have been unable to decide for which I had the greater inclination, mathematics or literature," Sonya wrote in her autobiography, recognizing that because of her educational opportunities, she'd had a choice. Not that those opportunities were especially stellar: like most early women in math and science, she was doggedly persistent about vaulting over the many obstacles "Society" sought to erect in her path.
Sonya's interest in math was sparked by an eccentric uncle, who taught her chess and discussed all kinds of abstract concepts with her: "squaring the circle, asymptotes, and other things that were unintelligible to me and yet seemed mysterious and at the same time deeply attractive." When her room was redecorated at age 11, there wasn't enough wallpaper to complete the project, so one wall was temporarily papered with her father's old calculus lecture notes from college.
Initially the symbols were little more than hieroglyphics to her, but after reflecting on them night after night, she began making connections between the symbols and the concepts she discussed with her uncle. Another 19th century mathematician, Mary Somerville, had a similar breakthrough around the same age: she stumbled upon algebraic symbols while perusing a puzzle in a magazine, also igniting a lifelong thirst to know more. And like Somerville, Sonya's father eventually grew dismayed at his daughter's "unfeminine" interests and tried to put a stop to them. ("We shall have young Mary in a straitjacket one of these days," Somerville's father supposedly lamented.)
The family of French mathematician Sophie Germain -- inventor of "Germain primes," i.e., double a Germain prime and add 1 to get another prime number -- used a similar tactic to dissuade their equally precocious daughter from studying geometry, algebra and calculus... to no avail. Sonya also studied under the covers at night, borrowing an algebra textbook from one of her tutors.
Then a neighbor, who taught science, gave the family a copy of a basic physics book he'd written. Sonya turned to the section on optics, and discovered trigonometry. Even though she'd never encountered it before, she managed to make sense of the derivations for small angles by substituting "a chord for the mysterious sine." In short, she independently rediscovered the same method by which the whole concept of a sine had been developed historically. Impressed, the neighbor convinced Sonya's father to let her study analytic geometry and calculus privately in St. Petersburg. She mastered both subjects in a single winter. Her astonished tutor noted that it was almost as if she'd known the concepts in advance.
Someone with such a formidable innate aptitude couldn't be satisfied for long with simple calculus, but Sonya's opportunities for further study were severely limited because of her gender. She entered into a marriage of convenience with a young paleontologist named Vladimir Kovalevsky, and the couple moved to Heidelberg, Germany. She still couldn't formally enroll in a university, but she managed to get permission to "unofficially" attend lectures by some of the foremost scientists in Europe. In that respect, she fared a bit better initially than Germain, who was forced at one point to impersonate a male student who had passed away in order to study with Joseph LaGrange (via correspondence) at L'Ecole Polytechnique in Paris. But in both cases, the women performed so spectacularly that they won the admiration and mentorship of prominent men: LaGrange and later Carl Friedrich Gauss, in German's case, and Karl Weierstrass (and, later, Mittag-Leffler) in Sonya's case.
At the time he was the most renowned German mathematician, a professor at the University of Berlin. Sonya came to him bearing glowing recommendations from her Heidelberg professors, yet even then, he was skeptical, and far from enthusiastic about taking her on. To discourage the young woman, he gave her a set of problems he'd prepared for his most advanced students, assuming she'd never make sense of them. Instead, she solved them in record time; not only that, her solutions were clear and original, demonstrating a grasp of the material lacking in most of his male students (Mittag-Leffler being one notable exception). So he agreed to teach her privately, and came to consider her among the most brilliant and promising of all his students.
Sonya didn't disappoint her mentor. By the age of 25, she had produced three original papers, each of which was deemed worthy of a PhD degree: one on the shape of Saturn's rings, another on elliptical integrals, and a third on partial differential equations. Not that Berlin would ever award a woman a PhD, especially one that had never been officially matriculated. Anywhere. (And how could she possibly matriculate when they wouldn't allow it? Yes. Exactly.) To his credit, Weierstrass fought for her, eventually convincing the University of Gottingen to award her a PhD in mathematics, summa cum laude.
I would like to tell you this story has a happy ending, or at least that Sonya's intellectual struggles ended with her PhD. Alas, such is not quite the case. She and Vladimir returned to Russia, where she found she could only get a job teaching basic arithmetic at a girl's elementary school. The irony wasn't lost on her: "I was, unfortunately, weak in the multiplication tables," she acidly observed in her memoirs.
Instead, she began reviewing theater performances and writing articles about science and technology for a local newspaper, as well as starting a novel. And her platonic marriage mysteriously turned non-platonic: she gave birth to a daughter during this period, too. That didn't make the marriage a happy one. Eventually she left Vladimir and moved first to France, and then Stockholm, when the university there offered her a probationary position, thanks to the urging of Mittag-Leffler. By then, she was a widow: Vladimir had committed suicide, distraught and depressed over his many failed business ventures, among other things.
Sonya, in contrast, proved so popular with her students that she was given a five-year professorship at Stockholm, and also became an editor of Acta Mathematica. In 1888, she reached the pinnacle of her career when she won the French Academy of Sciences' prestigious Prix Bordin for her treatise, On the Problem of the Rotation of a Solid Body About a Fixed Point. They might have excluded her from the competition on the basis of gender -- the French Academy was far from welcoming, as Sophie Germain could attest -- but the papers were all submitted anonymously and the judges weren't aware they'd selected a woman until it was, as it were, "too late." Still, so impressed were they by her work that they actually doubled the prize. It seems too cruel a twist of fate that, only three years later, she succumbed to pneumonia following an influenza epidemic.
By now we hope you're convinced that Sonya deserves wider repute. I'm delighted to be celebrating her accomplishments, and those of all the other women before and after who defied conventional stereotypes and social pressures to pursue the subjects they loved.