“People have already concerned themselves too much with a woman who, in the last analysis, was a nihilist.” - Russian Minister of the Interior Ivan Durnovo, on the mathematician Sofya Kovalevskaya (1893)
Anyone who has ever doubted that a slight variation in the inputs of dynamic systems can lead to wildly divergent outcomes need only witness the sudden meltdown of a small child in their care, and believe.
Should we have left the park/zoo/splash pad/children’s museum five minutes earlier? Three minutes later? Was that extra cupcake the difference between a merely disappointing third-birthday party and said birthday party climaxing with my child inconsolable, beating the ground, an epically long string of snot dangling from his nose?
Tearful selfie, circa 2016.
There are likely plenty of caregivers out there who are unfazed by tantrums. I am not one of them. Despite arming myself with matter-of-fact parenting advice and even attending a very informative workshop on the subject, whenever a tantrum strikes, I am drawn into its capricious and unstable orbit.
Public breakdowns are better (in my opinion). One can look around and see the classic laws of physics ‘out there,’ on the blurry periphery of the storm. The sympathy and even disapproval in the eyes of other adults are reassuringly familiar, something concrete to grab onto as the surreal-ness of the situation takes hold.
But in the privacy of the home, time slows, then stops. Daily life is held hostage; routines are rendered absurd in the face of such absolute, unfettered emotion.
We end up crouched on the floor together. My son tries to simultaneously hit me and hug me closer. The conflicting signals (“She is my mortal enemy!” “She is the source of all comfort!”) generate only interference, noise.
We both surrender to the chaos of a prefrontal cortex on the fritz.
This post began with an exercise in free association.
Contemplating the chaos that children can bring into one’s life, I wondered: had any female mathematicians or physicists contributed to chaos theory?
This question led me, in turn, to one of the most fascinating celebrities of modern science, a female scientist nearly as famous in the late-nineteenth century as Marie Curie would become in the early twentieth.
The Russian mathematician Sofya Kovalevskaya was the first woman to earn a Ph.D. in math, and the first woman in modern times to teach at a European university. Her doctoral research on partial differential equations was a precursor to modern chaos theory. As historian Frank Wang explains:
Before the discoveries of Poincaré and Kovalevskaya, it was thought that a nonlinear system would always have a solution; we just needed to be clever enough to find it. But such a view is wrong. Kovalevskaya and Poincaré showed that no matter how clever we are, we will not be able to solve most of the differential equations. The belief in determinism, that the present state of the world determines the future precisely, was shattered.
Photograph of Kovalevskaya, 1880.
The intrigue around Kovalevskaya, however, extends far beyond her pioneering work in math. Although born to minor nobility, she joined a liberal youth movement known as nihilism. As a Russian émigré in Germany, France, and Sweden, her ‘radical’ sympathies, almost as much as her sex, repeatedly got her in trouble with the academic establishment. Her sister Anyuta, a socialist, participated in the Paris Commune of 1871. Her husband committed suicide after making wild financial speculations. And Sofya’s death, at age 41, was tragically premature.
Kovalevskaya’s life, it turns out, would read like a Russian novel. Pardon the cliché – which is made even more tempting because the Russian novelist Fyodor Dostoevsky once courted her older sister!* And by the fact that Kovalevskaya herself turned, toward the end of her life, to literary pursuits. She penned, among other works, a semi-autobiographical novella titled Nihilist Girl.
Chaos. Anarchy. Disorder. These were my initial associations as I began investigating Kovalevskaya's relationship with nihilism. And in popular usage, nihilism conveys this sense of rejecting all existing institutions and systems of belief.
It turns out, though that the nihilism of Kovalevskaya’s youth refers to something quite tamer (by modern standards). It reads a lot more like today’s liberal, progressive ideology.** Nihilism did reject what was seen as religious superstition, along with tsarist repression, but the movement also affirmed faith in self-actualization, education, and above all, in science as the path to a more egalitarian society.
Another of the core beliefs among these “children of the sixties” (the 1860s, that is) was in women’s inherent equality to men. What’s intriguing from a 2018 perspective is that 150 years ago, the nihilists had already formulated the concept of male allies – of men using their privilege to advance women’s education and self-realization.***
One way that young male nihilists supported their female counterparts was through fictitious marriages. In order to travel outside of Russia without their parents’ permission, young women would marry willing compatriots. Once outside of the country, they could pursue an education and live independently from their nominal spouses.
Our protagonist, Sofya, actively sought such an arrangement – not only to free herself but also to enable her sister and cousin to become educated as well. Sofya finally found a taker in Vladimir Kovalevsky, an aspiring paleontologist. Together, but separate, they settled in Germany, where both would obtain advanced degrees.
Kovalevskaya’s daughter, also named Sofya, was the product of this initially platonic relationship with Vladimir. By the mid-1870s, it had drifted into a more traditional marriage (though the two would drift apart again).
Sofya spent the first two years at home with her daughter, nicknamed Fufa:
However, the demands of her work often took Sofya away from her daughter. As her marriage with Vladimir crumbled, Kovalevskaya realized she needed to revive her math career. As a result, she left two-year-old Fufa with her godmother Iulia Lermentova**** for over two months in order to visit Sofya's famous mentor Weierstrass in Berlin.
Initially, Sofya felt “reluctant to give [Fufa] up. She was comforted by her daughter, and felt that the child needed her mother in these early years.” But when three-year-old Fufa fell seriously ill in Paris, Sofya decided to send her to live with friends and family in Russia. The mother and daughter lived apart for the next several years, as Kovalevskaya returned to math and tried to make her way toward a university teaching position. Only after Sofya established herself at Stockholm University did she send for her now 9-year-old daughter.
Kovelevskaya’s accomplishments in both math and literature are impressive. Her work on the revolution of a solid body about a fixed point earned her the prestigious Prix Bordin in 1888. Her research on partial differential equations, known as the Cauchy-Kovalevskaya Theorem, is essential to the field. Her literary output – a memoir titled A Russian Childhood, the novella Nihilist Girl, a play she co-wrote with the Swedish writer Anna Carlotta Leffler – was astoundingly prolific given that she took up writing late in life, and while actively immersed in mathematical teaching and research.
Sofya recognized the connection between these two facets of her creative self. Writing to a friend in 1890, she explained:
You are surprised at my working simultaneously in literature and in mathematics. Many people who have never had occasion to learn what mathematics is confuse it with arithmetic and consider it a dry and arid science. In actual fact, it is the science that demands the most imagination.
In the same letter, she also set out to correct popular misconceptions about poetry. Sofya writes, “It seems to me that the poet must see what others do not see, must see more deeply than other people.”
But what particularly fascinates me about Kovalevsakaya’s story is the interplay of science and social change. Nihilism didn’t necessarily begin as a creepy, eugenics-like vision of scientists engineering the perfect society. Instead, it assumed that the inward pursuit of scientific learning was fully compatible with social and political activism out in the world.
Kovalevskaya’s beliefs pose such a striking contrast to today's scientific culture, where many contemporary scientists seem reluctant to engage with the very real social and environmental issues that threaten our survival. This hesitation to step outside of one’s area of specialization is a part of the academic culture that needs changing in the face of a planet going haywire. Scientists have a more active role to play in staving off the chaos that awaits us.
On an early episode of the Mom Rage podcast, author Edan Lepucki talked about the role of chaos in parenting. On the one hand, the cruelty and randomness of our world seem fully at odds with the innocence of young children. The tension between the two can create a disconnect in parents’ lives.
Lepucki argued, in contrast, that children are themselves chaotic beings. Not only do they make messes, literal and figurative, of our pre-baby environments; they are themselves unregulated creatures, not fully governed or governable by their own brains.
Lepucki subscribes to what I think of as the Ursula Franklin school of parenting. Franklin, too, saw mothers in particular – historically tasked with managing unpredictable schedules and unreasonable toddlers – as inhabiting that space on the edge of disorder, on the verge of disaster.
Kovaleskaya existed there, too. Math for Kovalevskaya was a source of order in a life that was often unsettled and financially precarious. After the early deaths of Vladimir and her sister Anyuta, the nihilist mama Sofya Kovalesvskaya found meaning in the creative work of doing math. Even if the math that she did challenged our ability to find meaning, predictability, in the universe itself.
My doctored photo of Kovalevskaya, to better reflect her punk-rock image.
The more I consider the phrase nihilist mama, the more I like the sound of it. There’s something a little bit punk-rock about its implied rejection of the social order. I’m all in favor of imbuing motherhood, which our culture views as the dowdiest and squarest of roles, with the potential to be badass and subversive and anti-establishment.
And sometimes our roles as mothers and creators require a nihilist sensibility. Sure, caregiving, along with any creative pursuit, provides ample moments of attention and purpose. But both kinds of work can also tax our preconceived notions of order, reason, control.
They can take us close to the void.
NOTES
* Apparently, 15-year-old Kostalevskaya also had a crush on the middle-aged author.
**Nihilism did take a more radical turn in the next generation, and it is this shift in the movement that Kostalevskaya explores in Nihilist Girl.
***Another of Kostalevskaya's male allies would be the Swedish mathematician Gosta Mittag-Leffler, who put his own reputation on the line to secure her a teaching position - and then a full professorship - at Stockholm University.
****Fufa's godmother, btw, was also the first woman to earn a Ph.D. in chemistry! Lermentova decided to abandon a promising career in chemistry, however, to pursue agriculture and cheese-making on her Russian estate. She would adopt Fufa after Sofya's untimely death in 1891.