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essay Writing of Sonya Kovalevskaya shortly before her untimely death in 1891, Russian mathematician P.A. Nekrasov was especially appreciative of his colleague's unique knack for elegant simplicity in an arcanely complex field, noting that "her clever timing is reflected in the adroitly devised gradual transition from the simple to the more complex, in her masterly ability to bring the very difficult [closer] to the less difficult" (Koblitz, 243). Professional elegance and the exceptionally innate ability to distill the dauntingly complex into the readily apparent were lifetime hallmarks of the extraordinary Russian mathematician, writer and poet, Sonya Kovalevskaya. What is nearly as extraordinary is the haphazard and wayward journey which led me to discover her. Trolling about in hopes of dredging up someone around whom to drape both a mathematics requirement, some connection to Anton Chekhov, and, if at all possible, a link to Hermann von Helmholtz, I discovered Sonya in a search for mid-to-late 19th Century Russian mathematicians. Unfortunately, it took no more than a cursory examination of Kovalevskaya's mathematical career to realize that even her earliest, most rudimentary work was far beyond my grasp as far as expounding upon or even replicating in any coherent sense. Although she produced much significant work during her brief lifetime, Kovalevskaya is best remembered in the scientific world for her definitive analyses in the areas of partial differential equations, and the revolution of a solid body around a fixed point. Partial differential equations describe situations which occur in the physical world, and function amongst one or more variables. A simple -- perhaps simplistic -- example might be atmospheric temperature, a function defined by four variables: latitude, longitude, altitude, and time. An example of a solid body revolving around a fixed point might be, as an obvious example, the earth about the sun. Suffice it to say that the actual calculations and reasoning that form the theorems to define these examples are infinitely more complex, and infinitely beyond my grasp. The fortunate aspect in choosing Ms. Kovalevskaya was that I found not only a connection to Anton Chekhov and Hermann von Helmholtz, but a scientist who was an artist as well. Often, it seems, artists and scientists are divided into two camps devoid of any common ground. The significance of Kovalevskaya's life and work to both this essay and this study is that she crossed the line, she bridged the gap, she forged the common ground of art in science and vice versa, providing the spark for what follows here and, I hope, a true and organic connection to the whole of this study. I will center my attempt to draw similarities between the worlds of art and science on Ann Hibner Koblitz' workmanlike biography of Kovalevskaya, A Convergence of Lives. Supplementary material was drawn from Roger Cooke's challenging and at times downright impenetrable (due to its presupposition of a working knowledge of calculus and trigonometry) The Mathematics of Sonya Kovalevskaya. As this portion of the study expanded and began to take shape, I looked to Scott Buchanan's Poetry and Mathematics and The Visual Mind: Art and Mathematics, Michele Emmer, editor. Along the way, I hope to provide a semblance of the colorful and dramatic life Kovalevskaya led. Kovalevskaya's childhood and coming of age in mid-19th Century Imperial Russia offers an interesting counterpoint to Anton Chekhov's working-class roots, in addition to the challenges she faced being female in a society that largely considered women as but another male appendage. Born in 1850 to a high-ranking military officer and his socialite wife, Sonya's childhood could be equated to an upper-middleclass upbringing in a comparable Western class-tiered society. Twenty years younger than her husband, Kovalevskaya's mother was an apparently highly intelligent and talented woman (an accomplished pianist and amateur actress) whose life slowly dissolved into a bitter "remoteness and general unimportance to the family" (Cooke, 6). Young Sonya's and her older sister Aniuta's upbringing was left largely in the vise-like grip of an English governess, Margaret Smith, whose steely attempts to shield two strong-willed girls from "too much" education was met with increasing resistance when the sisters reached adolescence. Years of acrimony between governess and charges eventually wore Ms. Smith down, and she resigned her position when Sonya was 14 (Cooke, 9). Later that year, sister Aniuta left the household, and the remainder of the Kovalevskaya family, including Sonya and her younger brother, moved to a new house in the town of Palibino in Russia. A shortage of new wallpaper in Sonya's room prompted her father to fill the gap with some of his old lecture notes from college. Consequently, a portion of Sonya's room was papered with notes on differential and integral calculus, a subject she became fascinated with by reading her walls, and determined to understand. Sonya's entrée into the world of advanced mathematics is particularly interesting for two reasons. "Normally," writes Koblitz, "a young girl would not have been exposed to as much mathematics" as was Sonya, but because the subject was dear to her father's heart and young Sonya displayed such extraordinary creativity in the field, her father "was proud of his daughter's inventiveness rather than angry at her temerity" (Koblitz, 47). Secondly, the manner in which Sonya received her tutoring is very indicative of the social clime of the times and an early example of the increased challenges Kovalevskaya would face throughout her professional career. Sonya had a "backward" cousin named Mishel, who was struggling through his gymnasium entrance exams and had been supplied a tutor by his desperate father to little avail. Sonya was allowed to participate in the tutoring sessions as a kind of goad to Mishel, to inspire him to work harder lest he be bested by a mere girl. Mishel's tutor was so impressed with Sonya's ability that he strongly encouraged her father to allow her individual tutoring in trigonometry and calculus. Thus, in her fourteenth year, Sonya began a journey that would lead her eventually to a full professorship in Stockholm nineteen years later. As she began to mature mathematically, Sonya's political consciousness was also beginning to take shape. At 15, a young neighbor whom she had a crush on left Palibino to join the Polish uprising in Warsaw, and Sonya followed newspaper accounts fervently, developing a political awareness that was as unusual for bourgeois girls as it was actively discouraged. It was also a source of lifelong guilt for her. "Kovalevskaya never tried to repudiate her connections with conspiratorial circles," Koblitz observes. "...[And] although she did far more than the vast majority of her contemporaries, she was always uncomfortably conscious of having contributed less than she could have" (Koblitz, 258). This lingering sense of bourgeois guilt would be the prime motivation of Kovalevskaya's poetry and playwriting later in life. Among the many social handicaps facing young Russian women in the mid-19th Century was their exclusion from admittance to higher education in their native country, and their inability to travel abroad unless accompanied of their fathers or husbands. All women at this time, regardless of age, were amendments to their "administering" male's passport, and thus were unable to leave Russia "unescorted" to travel to the more progressive European or Scandinavian educational environments. Thus was born the cottage industry of the "fictitious marriage." The basic construct of the arrangement was thus: "a young woman desirous of leaving home to work or study would come to an agreement with a man who would go through the marriage ceremony and then, theoretically at least, leave the woman to pursue her own life. Her father had no further authority over her, and her 'husband' was honor-bound to keep their relationship platonic" (Koblitz, 55-56). The challenge for the 17-year-old Sonya was not finding amenable young men, but rather convincing her dubious father to cnsent to the arrangement. Sonya's first candidate, "an upright, progressive young man whose only drawbacks were extreme ugliness and a slight overfondness for beer" (Koblitz, 69) was rejected outright by Sonya's father. Determined to find a "husband" willing to facilitate her emigration to Europe, Sonya effectively blackmailed her father into agreement. A 25-year-old veteran of the Polish uprising and aspiring publisher named Vladimir Kovalevsky had heard of her plight through "local revolutionary circles" and offered his assistance. Fearful that her father would reject him as well, Sonya paid a visit to Kovalevsky at his apartment and subsequently sent a message to her father that she was not leaving until he agreed to the marriage. Sonya's father, now a high-ranking general in the Imperial Army, and intensely aware of his and his family's reputation, reluctantly agreed (Cooke, 12). Sonya's new "husband," besides having a "truly brotherly way of relating to women," was also "unbalanced," "unstable" and saddled with a "high-strung personality" (Koblitz, 71). Such a combination of traits would both delay Sonya's professional career and provide her a very ironic and key breakthrough later in life. Married in September, 1868, the newlyweds settled first into platonic cohabitation in St. Petersburg. Soon, however, Sonya became anxious to move to Europe to pursue her higher education. "I cannot image a happier existence than a quiet, modest life in some forgotten corner of Germany or Switzerland, among books and studies," she wrote to a friend early the next year. In May, 1869, the Kovelevskys relocated to Heidelberg, Germany to attend classes at the nearby University. Although the official policy of the school denied Sonya admission on basis of her gender, her reputation was already strong enough, at 19, to prompt University professors to welcome her presence as an auditor. Among her professors at Heidelberg was Hermann von Helmholtz. Von Helmholtz was so impressed with the young Sonya's work that he, along with colleagues Leo Königsberger, Emil DuBois-Reymond and Karl Weierstrass, lobbied the faculty senate to have her officially admitted into the University. When the petition was denied, Weierstrass began tutoring Sonya privately, beginning a professional relationship that would continue up to her death. Writing to a friend near the end of her life, Sonya remarked that these sessions "had an extremely important influence on my whole mathematical career. They finally and irrevocably defined the direction which I followed in my future scientific work" (Koblitz, 113). The close relationship also fueled the inevitable rumors and gossip of a romantic pairing between the two, despite the fact that Weierstrass was thirty-five years Sonya's senior, and a "confirmed bachelor" who lived with his two unmarried sisters. As Koblitz suggests, "[Sonya] succeeded as a professional in a field which, until her advent, had been entirely male. It is not surprising that she excited rancor among men jealous of their prerogatives as the intellectually superior sex" (117). Sonya's living conditions and her arrangements with husband Vladimir were also raising European eyebrows at this time. Sonya had taken to opening their small apartment to fellow Russian female émigrés and expatriates, sometimes supporting them all on the small allowance she received from her father. When the number of houseguests reached seven, Vladimir, still trying to make his fledgling publishing business solvent, fled for solo lodgings elsewhere in the city. Nevertheless, Sonya's studies continued. Under Weierstrass' tutelage and influence, she was able to gain official admittance to the University at Göttingen, where she received her Doctor of Philosophy in August, 1874, becoming, Koblitz claims, "the first woman in the world outside of Renaissance Italy" to receive a doctorate in this field (123). Homesick for her homeland and optimistic about finding a university teaching position with her new degree, Sonya and Vladimir returned to St. Petersburg in the fall of 1874. Instead of a prestigious teaching position, however, "the next nine years were to be a time of increasing disillusionment, frustration and eventual tragedy" for the couple (Koblitz, 123). Repeatedly denied a teaching position by a sexist and xenophobic Russian university political hierarchy, Sonya and Vladimir's connubial life took an odd turn back to her bourgeois roots. Disavowing her mathematical training and goals, Sonya began to emulate her mother as the good society wife, while Vladimir launched the St. Petersburg New Times in 1876 with publisher Alexei Suvorin, later the to be the then 16-year-old Anton Chekhov's friend and longtime publisher. Sonya and Vladimir also consummated their platonic marriage, producing a daughter, Fufa (née Sonya) on October 17, 1878. Impatient with the marginal profitability of the newspaper business and increasingly obsessed with making a lot of money in a short amount of time, Vladimir borrowed heavily from family and friends with an ill-conceived real estate development scheme. Meanwhile, Sonya was becoming restless for reasons of her own. Having "sampled the frivolity of the Petersburg social world," she had become "impatient with its superficiality" (Koblitz, 139), and feared she was sinking irretrievably into the "soft slime of bourgeois existence" (Ibid., 141). Vladimir's real estate endeavor was not going well, and the resultant strain effectively broke their marriage apart in March of 1881. Eager now to resuscitate her mathematical career, Sonya left Petersburg with daughter Fufa in tow and moved to Paris, where she made the acquaintance of prominent Swedish mathematician Gösta Mittag-Leffler. Well aware of her reputation as a theoretical mathematician despite her prolonged absence in the field, Mittag-Leffler introduced her to his circle of prominent French mathematicians. Mittag-Leffler's colleagues, all married, were cordial, but Sonya's status as an unescorted married woman precluded their professional and social association with her, lest gossip be fueled, and she was unable to secure a teaching position. Overall, it was a situation that caused her "ironic amusement and some bitterness" (Koblitz, 163). In an even more ironic turn that was not that amusing, husband Vladimir provided the break Sonya needed to become an esteemed and respected member of proper Parisian society. His real estate house of cards collapsed all about him, and in complete financial ruin, Vladimir killed himself by drinking a bottle of chloroform on the night of April 27, 1883. He left behind the plaintive note, "Write to Sofa [Sonya] that my constant thoughts were of her and of how much I am at fault before her, and how I spoiled her life, which without me would have been bright and happy" (Koblitz, 171). When word reached Paris of Vladimir's demise, doors previously closed to Sonya began immediately to open. "In Europe in the nineteenth century," Koblitz points out, "widowhood was eminently respectable, and at the same time allowed for much greater independence in a woman's life than the single or married state" (174). The following September, with Mittag-Leffler's help, Sonya was offered a faculty position at Stockholm University. She readily accepted. The move to Stockholm opened doors to other creative aspects of Sonya's life as well. She met Mittag-Leffler sister, the playwright Anna Carlotta, and was soon collaborating on a play, and poetry. Sonya's dual career as mathematician and playwright/poet serves to highlight the similarities rather than the disparities of the writer (artist) and the mathematician (scientist). Although less than effusive in her praise of Sonya's dramatic writing talent ("[her] style is uneven, her characterizations are inconsistent, and her narrative point of view too naďve and sentimental to appeal to modern tastes") (Koblitz, 257) and although her strong personality and stridently political themes eventually drove the more subtle Anna Carlotta for cover, Sonya's drive in this direction serves to illuminate an interesting connection between the disciplines of art and science. Poetry and Mathematics offers some thoughtful and intriguing parallels between these two endeavors for the reader patient enough to withstand author Buchanan's antiquated style (the 1962 edition is a reissue of the original 1929 publication) and the author's predisposition to analyze poetry in mathematical terms. Through it all, however, Buchanan has the ability to distill similarities into tasty, bite-sized morsels of observation. Working from the premise that "mathematics and poetry run parallel patterns...sometimes...they can be understood together when they are unintelligible apart," Buchanan posits that "words stand for qualities; ratios stand for relations. Qualities in relation can be built by ratio-cination into the structures of poetry and mathematics, to the words that tragedies and comedies comprehend" (18). Working from this basis of shared mechanics, Buchanan expands his argument into the world of ideas.
Indeed, who else but a true scientist could love poetry for its "utter ineffectualness"? The further Buchanan explores his theory, the more poetry gets pushed aside. His chapter on "Numbers" offers up a valid attempt to transfer the cardinal/ordinal system of number delineation in mathematics to poetry (e.g., where the ordinal "a, b, c..." is a subset of the cardinal system "A" and how that might translate to a poet's application of images through words), but by the time Buchanan reaches "Proportions and Equations" deep into his analysis, poetry has been reduced to the role of redheaded stepchild. Anticipating Arthur C. Clarke, Buchanan also takes his numbers game beyond the temporal into the realm of mystical speculation, beyond "the mysticism of the commonplace where ideas illuminate and create facts...[into] the mysticism of the extraordinary where God, the Infinite, the Real, poses the riddles of desire and disappointment, sin and salvation, effort and failure, question and paradoxical answer" (42). We may forgive author Buchanan the rather florid nature of his enthusiasm as his closing phrase serves to capture both the personal and professional life of Sonya Kovalevskaya rather effectively. Itself riddled with desire and disappointment, effort and failure, Sonya's life was nothing if not paradoxical, and one she seemed often ironically amused by. Following her appointment to the University of Stockholm in the fall of 1883, Sonya commented to a friend, "Look at that! I've been made into a princess! It would have been better if they had given me a salary" (Koblitz, 179). The ironies and paradoxes would continue throughout the remainder of Sonya's professional and personal life. Appointed, finally, to a lifetime teaching position at the University of Stockholm, Sonya was also awarded the prestigious Prix Bordin in December, 1888, for her groundbreaking work on the revolution of a solid body around a fixed point, and immediately sank into a deep depression. "I receive so many letters of congratulation," she wrote to Gösta Mittag-Leffler in January, 1889. "And, by strong irony of fate, I have never felt so miserable in my life" (Koblitz, 211-212). The misery of recognition continued unabated, and Sonya was hospitalized later that month for exhaustion. Heeding her doctors' advice for a change of scene, Sonya took a rare vacation to the South of France in February, 1889, where she made the acquaintance of the 29-year-old acclaimed short story writer and budding playwright Anton Chekhov. A fan of his writing, Sonya kept in touch with Chekhov through their mutual friend, Maksim Kovalevsky, a politically-active law professor at Moscow University and "distant relative" of Sonya's doomed husband, Vladimir (Koblitz, 205). Sonya was particularly interested in Chekhov's 1890 journey to Sakhalin, and expressed interest in reading any fiction that may have come out of the trip (218). Restless amongst the gambling idle of Monte Carlo, Sonya was soon back at work with her research, University lectures, and writing. In addition to her playwriting collaborations with Anna Carlotta, Sonya also wrote a novella, Nihilist Girl, a novel, Vae Victus ("Woe to the Vanquished"), and perhaps her most famous piece, the fictionalized memoir, Memories of Childhood, published in July, 1890 (Koblitz, 220;228). Returning to Stockholm by train from the Christmas holidays in France with Maksim Kovalevsky, whom she was planning to marry, Sonya caught a cold. Ironically, her return trip was extended due to her circumvention of Denmark to avoid a raging smallpox epidemic, and her condition rapidly deteriorated. She died in Stockholm on February 10, 1891, at age 41. Biographer Koblitz is oddly evasive as to the cause of her death, stating only that her cold "worsened", leading one to believe pneumonia as the cause. Donald Rayfield, however, in his exhaustive biography, Anton Chekhov: A Life is more direct, stating that Sonya "perished of TB" (Rayfield, 439). Koblitz, curiously, never mentions the word. As one who moved fluidly between the worlds of art and science, Sonya was well aware of the perceived disparity, even amongst her contemporaries at the time. In a letter to the "belle lettrist" A.S. Shabelskaya in the fall of 1890, Sonya observed:
Works Cited Buchanan, Scott. Poetry and Mathematics. Chicago: University of Chicago Press, 1962. Cooke, Roger. The Mathematics of Sonya Kovalevskaya. New York: Springer-Verlag, Inc., 1984. Emmer, Michele, et al. The Visual: Art and Mathematics. Cambridge: The MIT Press, 1993. Koblitz, Ann Hiber. A Convergence of Lives. Boston: Birkhäuser Boston, Inc., 1983. Copyright © 2001 The Write Word, Inc. All rights reserved. |