Joan Spicci writes about the life of the mathematician Sofya Kovalevskaya in her book ‘Beyond the Limit’, which is unique in being a biography written in the form of a novel.
Sofya Kovalevskaya, (3 January 1850 – 10 February 1891) was a Russian mathematician who was the first woman in the modern academic setting to get a doctorate and become a tenured professor in mathematics. She got married to leave Russia and pursue research in Europe. She made important contributions to mathematics, wrote plays, a novel and a memoir, and rubbed shoulders with the likes of Fyodor Dostoevsky, George Eliot, and Charles Darwin. In a restrictive, male-dominated society how was her journey possible?
Recently, I went to two Kendriya Vidyalaya schools in Tamilnadu, as part of the Vigyan Pratibha program that promotes science and math talent among government school students. When asked about their favourite scientist, the students hesitated before one of them mentioned Einstein. Maybe the media, popular culture and conversations with family and friends have instilled in their minds that Einstein is the scientist. I feel that there is a need to talk about many more scientists in an appealing way so that students know about the diverse people who engage in science.
One such story that captivated me was Beyond the Limit: The Dream of Sofya Kovalevskaya by Joan Spicci, which I read many years ago. Her story has stayed in my memory, thanks to the format Spicci has chosen, a biography in the form of a novel. As Spicci mentions in her book, “...most all named characters, and all major characters, in the novel are based on historical persons…purely created characters and scenes are used for narrative continuity.” The book draws from two autobiographical works by Sofya, A Russian Childhood and A Nihilist Girl, among other sources.
It is set in the historical context of 19th century Europe and Russia where new ideas were questioning existing systems. Charles Darwin’s book The Origin of Species and Karl Marx’s Communist Manifesto had recently been published.
‘Nihilist Girl’ authored by Sofya Kovalevskaya was published in 1892. It is a coming-of-age story of a young girl and a social commentary on Russia.
Sofya’s father, Vasily Vasilyevich Korvin-Krukovsky, was a lieutenant general and a member of the Russian nobility, and her maternal great-grandfather, Theodore Von Schubert, was an astronomer. She was curious about mathematics from a very young age and was privately tutored in mathematics along with other subjects and languages.
Sofya was given all the opportunities to nurture her talent in mathematics. However, Russian women could only work or live outside their family homes with permission from their fathers or husbands during this period. So Sofya and her sister, Anyuta, began to see marriage as a solution for achieving their goals. They, especially Anyuta, also became deeply involved in the Russian nihilist movement, which believed in equality, freedom in marriage, and education for all.
Sofya got into a marriage of convenience with Vladimir Onufrievich Kovalevsky to pursue her interest in mathematics. Vladimir was a paleontologist, who was the first to translate Darwin’s The Origin of Species into Russian. Along with Vladimir and her sister Anyuta, Sofya left St Petersburg for Europe and attended lectures in maths and science while there. Here, she learned from and worked with some of the well-known mathematicians and physicists of the time like Karl Weierstrass, Hermann von Helmholtz, Gustav Kirchhoff and Robert Bunsen.
Sofya joined as a faculty in Stockholm University as an unpaid faculty without an official affiliation for a few years before being appointed as a full professor. She worked in the fields of partial differential equations, mechanics and mathematical physics, analysis and complex function theory, and dynamical systems and integrability. She made research contributions such as the Kovalevskaya top, where she discovered a new integrable case of motion of a rigid body around a fixed point beyond Euler and Lagrange’s classical solutions. She also came up with the Cauchy–Kovalevskaya theorem, among her most famous results, which provides conditions under which a unique solution exists to a partial differential equation with analytical initial data.
SVM Satyanarayana was a rare mentor who helped students strengthen their basics in physics and clear entrance exams through his Sunday classes.
Looking back at the book and having interacted with many teachers and students through IMSc’s outreach programs, I see some parallels to the situation today. Despite the many positive changes over the last century, the challenges faced by Sofya continue to exist. Women are still forced to make career decisions with permission from their families and are sometimes asked to sacrifice their careers.
In the Indian context, The Life of Science has profiled several Indian women scientists and co-founders of the platform, Aashima Dogra and Nandita Jayaraj, have written a book about it. There is also Lilavati’s daughters, a collection of biographies of Indian women scientists edited by Rohini Godbole and published by the Indian Academy of Sciences. Additionally, an in-depth biography of Janaki Ammal by Savithri Preetha Nair published a few years ago.
In Sofya’s case, she was privileged to have access to private tutors and opportunities to interact with scientists willing to nurture and support her early interest in mathematics. Many with a similar passion for science and mathematics do not have access to such opportunities. SVM Satyanarayana, a Professor of Physics at Pondicherry University, was a rare mentor who organised Sunday classes for students in Chennai for over two decades. The classes were open to everyone and covered the fundamentals of physics, which helped many postgraduate students pass entrance exams. In my time at IMSc, I have seen faculty, PhD students and researchers immersing themselves in outreach programs, interacting with students, teachers and the general public, which is invaluable.
Sofya’s talent and passion for mathematics were recognised early on and nurtured by some of the leading mathematicians and scientists of her time. She also had discussions with some of the brightest minds about politics, literature and her many interests outside of science. That is how her journey was realised. And maybe in the future, more spaces of learning and open discussions will be created, nurtured and sustained, so that journeys like Sofya’s are possible for many more women.
Excerpts from the book:
Sofya laughed shyly. “I saw the notation of calculus years ago.”
“Really? Where?”
“On the wall in my nursery.”
Strannoliubsky blinked at her, as if he suspected a joke. But already he had come to know his student too well to disbelieve on first impulse. “Really?” he repeated at last, with a tentative smile. He sat back in his chair, folded his arms and said, “There must be a story behind that comment.”
She nodded her head. “When we first moved to Palibino, I was about eight years old. Mother hadn’t ordered quite enough new wallpaper for all the rooms. So when it came to the playroom, there was a definite shortage. To get one more room’s worth from Petersburg, five hundred versts away, would have taken forever and was simply not worth the trouble. So Mother had the walls covered with papers from Father’s old chest in the attic. The papers were comprised mainly of the lectures of Ostrogradsky on differential and integral calculus, delivered during my father’s student days…”
Do you seriously mean that you taught yourself mathematics from this wallpaper?” He leaned forward, one elbow on the table.
“A little, anyway. I was just mesmerized by the strange symbols. I’d stare at them for hours, trying to figure out which page came first, which next, and so on. Naturally it was quite beyond me, but still I loved to try to penetrate the secret code.”
--
Eyes gleaming, the lecturer continued, “Ten years ago, the Prussian Academy of Sciences offered a substantial prize to the mathematician who could provide a general solution to the problem of determining the position of the spinning object at any time, or who could contribute substantially to the solving of these, or similar equations. No mathematician was able to claim the prize. But many great minds have been intrigued by the problem and have uncovered, from time to time, bits and pieces of the puzzle. The elusive solution has so intrigued the mathematical community that it has come to be known as the Mathematical Mermaid…”
“As I mentioned, the mathematical description of the rotation of a rigid body occupied the mind of one of the greatest mathematicians who ever lived, Leonard Euler. Who, as we all probably know, made his home here in Petersburg. Tonight I will touch on some of the works of this great man, this man who adopted our city as his home.”
As the lecture continued, easing down into less rarefied levels of thought, Sofya ceased to follow. The problem on the easel behind the speaker still held her attention…”
Further reading:
Sofia Kovalevskaya, Leigh Ellison. MacTutor (web resource) - maintained by Edmund Robertson and John O'Connor, School of Mathematics and Statistics, University of St Andrews.
