The soul of fire and thought: the dream-chasing life of a Russian female mathematician

In the history of mathematics, there is an important Russian mathematician, Sofia Kovalevskaya. She was the first female doctor of mathematics in the modern sense, and later became the first female mathematics professor in the history of Northern Europe. It was the University of Stockholm in Sweden that accepted her and won her the reputation she deserved. In an era when it was difficult for women to study, Kovalevskaya became a model of women's equality. In terms of mathematical research, she was highly appreciated by her mentor, Weierstrass, the "father of modern analytical mathematics". She also wrote novels and plays with the same love for mathematics, leaving her mark in the Swedish and Russian literary circles. Her mathematical work and literary works are still read today. Her talent, spiritual strength and life goals continue to resonate in today's era.

Written by | Fan Ming

In the courtyard of the Mitta-Leffler Mathematical Institute in the northeastern suburbs of Stockholm, there is a bronze bust of a lady, the most famous Russian female mathematician of the 19th century, Sofya Vasilyevna Kovalevskaya (1850–1891). Berlin was where she started her career, and she spent the last seven years of her life in Stockholm. In Sweden, people prefer to call her by her nickname "Sonja Kovalevsky".

In 1889, Sonia was appointed professor of advanced mathematical analysis at the Stockholm Academy (now Stockholm University), becoming the first female mathematics professor in Northern Europe. In addition to her great achievements in mathematics, she was also a famous writer and advocate of the feminist movement. Sonia's groundbreaking work broke the old idea that women were inferior to men in the scientific field. She was and still is a role model for female mathematicians and women all over the world.

Left: Photo of Sonia when she was 18 (reference [1]), Right: Bust of Sonia (photo taken by the author)

On January 15, 1850, Sonya was born in Moscow into a noble family of Russian, Polish, Hungarian and German descent. She grew up in the family estate of Palibino near the border between Belarus and Lithuania, and received multilingual and mathematical education at home. When Sonya was 15 years old, her sister Anjuta's short story was accepted for publication by the magazine Epocha. With the permission of their parents, the two sisters went to St. Petersburg to visit the editor of the magazine, Dostoyevsky. From then on, the seeds of literature sprouted in Sonya's heart, and her interest in mathematics was awakened at the same time. Sonya described her spiritual and personality genes in this way: her desire for knowledge came from her Hungarian ancestors, her mathematics, musicality and lyrical personality came from her German astronomer great-grandfather, and she inherited the habit of wandering from her grandmother's gypsy descent. The Polish national genes made her love freedom and independence, and the rest came from Russia.

Study tour in Europe

In the era when Sonya grew up, the world situation has undergone tremendous changes, and the women's independence and equal rights movement has been surging. Russian society has experienced political turmoil and transformation brought about by the abolition of serfdom. Many educated young people have accepted the creed of nihilism and yearn for freedom and development. Although Sonya has obvious mathematical talent, she was unable to complete her studies in Russia. In the Tsarist era of the 19th century, women could not enter university, and could only study abroad with the written permission of their father (or husband). For this reason, Sonya signed a Platonic "contract marriage" with Vladimir Kovalevskij (1842-1883) at the age of 18, which was a way for many young Russian women to study abroad at that time. Vladimir later became an outstanding paleontologist and worked with Darwin and Huxley.

In 1869, Sonya went to Vienna with her husband and sister. After a short stay, the sisters entered the University of Heidelberg in Germany, and later Vladimir went to the University of Jena. Julia Lermontova (1846-1919), who arrived in Heidelberg a few days earlier than them, recalled Sonya like this: She looked happy, fresh, rosy, with sparkling eyes and full of energy. The two young girls often roamed along the mountains and rivers of Heidelberg, and traveled to Berlin and Paris together to study, forming a lifelong friendship. Julia later became the first female doctor of chemistry in Russia. In her first year at Heidelberg University, Sonya studied mathematics, physics and chemistry courses. The professors there were very impressed by this young, thin, smart and outstanding Russian girl. At the professor's suggestion, Sonya went to Berlin in the fall of 1870 to study under Karl Weierstrass (1815-1897), the "father of modern analytical mathematics."

Due to the strict restrictions on female students at the University of Berlin, Weierstrass could only give private lessons to Sonia twice a week for four years. Sonia's mathematical talent and savvy impressed Weierstrass deeply, and she soon became his favorite student. Between 1871 and 1890, there were more than 160 letters between the teacher and the student, and their father-daughter relationship lasted a lifetime. In a letter to Sonia, Weierstrass wrote: "I am stimulated and refreshed by your passionate dreams and ramblings about so many mysteries to be solved, about finite and infinite space, about the stability of the world system, and all other great tasks in future mathematics and physics." Sonia later recalled in her autobiography: "These studies have had the most profound impact on my entire mathematical career and determined the irreversible direction in my later scientific work. All my work was done in accordance with the spirit of Weierstrass."

Sonia's page on the Mathematician Genealogy website MGP

In October 1872, Weierstrass suggested several possible doctoral thesis topics for Sonya and supervised her through three original papers: on the theory of partial differential equations, the dynamics of Saturn's rings, and the reduction of a class of third-order Abelian integrals to elliptic integrals. Sonya had never taken university examinations before, but Weierstrass arranged and recommended that the University of Göttingen award her a doctorate in absentia and without examination in 1874, making Sonya the first woman (in the modern sense) to receive a doctorate in mathematics. Her first paper was on a fundamental theorem of partial differential equations, now usually called the Cauchy-Kovalevskaya theorem, which states the existence, uniqueness, and analyticity of local solutions of such equations under appropriate initial/boundary conditions. She greatly simplified the proof and gave the final form of the theorem. The paper was published in Crelle, the most serious mathematical journal in Germany, a great honor for a novice mathematician.

After both Sonia and Vladimir received their doctoral degrees, they officially married and returned to St. Petersburg. Unable to find a university teaching position, Vladimir switched to real estate business, while Sonia worked in various jobs and soon became the focus of attention in the intellectual and social circles of St. Petersburg. In her own words, "Life in St. Petersburg completely changed my abstinence years of studying in Germany. I was like being poisoned, and I devoted myself to all new things. I met all kinds of people... I absorbed everything with a fanatical curiosity." During these years, Sonia's literary interests also developed. She tried to write novels and reviews for newspapers and magazines, and had many contacts with great writers such as Tolstoy, Dostoyevsky and Turgenev. For six years, Sonia almost gave up mathematical research and even broke off contact with Weierstrass. All these changes could not be explained to her mentor who had high hopes for her.

In October 1878, Sonya and Vladimir's only daughter, Sonya (nicknamed Fufa), was born. Later, Vladimir got a teaching position at Moscow University, and Sonya returned to the world of mathematics with new enthusiasm. In 1880, arranged by the Russian mathematician Pafnuty Chebyshev (1821-1894), she gave a speech on Abel integrals at an academic conference in St. Petersburg. In 1881, Sonya came to Berlin again. At the suggestion of Weierstrass, she focused on the movement of light in crystal media, and Weierstrass also began to help her find job opportunities. Despite this, for women, there was still no possibility of obtaining a university teaching position at that time. In the spring of 1883, Vladimir worked as a scientific consultant for an oil company. He was falsely accused of fraud and was tried, so he committed suicide. Sonya, who was in Paris, was hit hard. She immediately rushed back to Moscow to handle the funeral and cleared her husband of the charges.

Mathematical Home

In the autumn of 1883, Sonia came to Stockholm at the invitation of Swedish mathematician Gösta Mittag-Leffler (1846–1927), and this year marks the 140th anniversary of her arrival. Mittag-Leffler first met Sonia in February 1876 when he visited St. Petersburg, and he described the meeting as the most unforgettable moment of his life in letters to his mother and friends. In Mittag-Leffler's eyes, Sonia was elegant, charming, and intellectual. She was simple and natural in her dealings with people, without any affectation, and expressed mathematics with rare clarity and precision. He immediately understood why Weierstrass was so fond of Sonia. In 1881, as the only mathematics professor at the newly appointed Stockholm Academy, Mittag-Leffler began to plan to invite Sonia to the position. Since the academy was newly established, the plan to hire female teachers became possible and was realized more than two years later. In Berlin at that time, it was unthinkable for women to even go to university.

Sonia spent her first few weeks in Stockholm with Mita-Leffler, his wife Signe, and his sister. Within a month, she had learned enough Swedish to start appearing in Mita-Leffler's so-called "World of Science" in Stockholm. Whether the conversation was in French or German, everyone was impressed by her insights. On February 11, 1884, Sonia gave her first lecture, and the classroom was packed with listeners, many of whom came to see the "Queen of Science" portrayed in the newspapers. She was a little nervous and stuttered at first, but gradually recovered and was applauded at the end of the lecture. Sonia taught "Dirichet's Theorem and Partial Differential Equations" to 16 students twice a week. Her lecture notes are now in the library of the Department of Mathematics at Stockholm University. Sonia and her students attended the seminar held in Mita-Leffler's house every Monday evening. She seemed to have found her new home.

Throughout the spring semester of 1884, Sonia worked as an unpaid lecturer. Before the end of the semester, Mitta-Leffler wrote a long letter to the board of directors of the college, successfully persuading the board to sign a five-year contract with Sonia as an associate professor. From 1885, she also served as a professor of mechanics. In Stockholm, Sonia taught more than ten courses in the fields of partial differential equations, algebraic function theory, Abelian function theory, elliptic function theory, etc., which were widely praised. At that time, mathematical research in Sweden was still in its infancy and did not usher in great development until around 1900. Among the students taught by Sonia, several later became famous mathematicians in the "Stockholm School", including Edvard Phragmén, who later succeeded Sonia's professorship, Ivar Bendixson, Gustaf Kobb, Ivar Fredholm and others. In 1885, Emil Stenberg, who was jointly supervised by Mitta-Leffler and Sonia, received a doctorate from the University of Helsinki.

From right: German mathematician Carl Runge, Sonia, Mitta-Leffler and his sister (1884, reference [5])

Mitta-Leffler created a good academic atmosphere in Stockholm, where Sonya thrived and gave full play to her intelligence. She continued her interests in Berlin and St. Petersburg and further studied them. Sonya published ten mathematical papers in her life. In addition to her early papers on the theory of partial differential equations, her papers included the refraction of light in crystalline media, Abel integrals, the structure of Saturn's rings, and the rotational motion of rigid bodies. The last paper in 1891 was on the theory of potential energy. Mitta-Leffler founded Acta Mathematica in 1882, which is still a world-class journal. Sonya also became an editorial board member of the journal and began to contact mathematicians from all over the world. She used her language advantage to introduce the work of Russian mathematicians to the European mathematical community. For example, she translated two Russian papers by Chebyshev into French and published them in Acta Mathematica.

Between 1826 and 1827, the Norwegian genius mathematician Niels Henrik Abel proposed Abel integrals that were more extensive than elliptic integrals in two papers, proved their addition theorem, and reduced the theory of elliptic integrals to the theory of elliptic functions with the help of inverse functions. Abel's work was one of the highest achievements of mathematics in the 19th century and had a significant impact on the development of modern mathematics. Starting in 1854, the self-taught Weierstrass developed a special type of Abel integral, the inversion theory of hyperelliptic integrals, and reduced it to the theory of Abel functions, which became one of his main topics for research and guidance to Sonia in the future. However, this theory that transcended the times was not accepted by the European mathematical community at the time, and Sonia's related speech in St. Petersburg in 1880 was also ignored. It was not until she came to Sweden that she reorganized and published the second article in her doctoral thesis and taught a course on Abel functions for five consecutive semesters.

In the spring and summer of 1888, Sonya made important work in the study of rigid body rotational motion using the abstract Abel function and the theory of elliptic integrals. A rigid body (such as a gyroscope) rotating around a fixed point under the influence of gravity satisfies a system of ordinary differential equations, which are usually non-integrable and have no exact analytical solution. Euler and Lagrange studied two classical cases: the Euler gyroscope (1765) is a free gyroscope without any specific symmetry and external torque, rotating around the center of gravity; the Lagrange gyroscope (1768) is a symmetrical gyroscope with two equal moments of inertia and the center of gravity on the axis of symmetry. Sonya discovered the "Kovalevskaya gyroscope" named after her - a symmetrical gyroscope with two equal principal moments of inertia at the fixed point and twice the third principal moment of inertia, and with the center of gravity in the plane of equal moments of inertia. This is the only fully integrable analytical solution to the three rigid body rotational motion states about the equilibrium point to date.

Left: Sonya’s Boulding Award certificate (eta.impa.br), Right: Kovalevskaya’s spinning top (researchgate.net)

In 1888-1889, Sonia had the highlight of her career. Her research on "the problem of asymmetric rigid body rotating around a fixed point" won the 1888 Prix Bordin awarded by the French Academy of Sciences in an anonymous selection of 15 papers. A grand award ceremony was held in Paris on Christmas Eve of that year. Before that, only French female mathematician Sophie Germain won a similar award from the French Academy of Sciences in 1816 for her work on elasticity theory. On December 29, 1888, Sonia was elected as a visiting member of the St. Petersburg Academy of Sciences. In her reply to the Academy, she expressed pride and gratitude for the recognition of her motherland. Even so, Sonia still could not get a university teaching position in France or Russia. Finally, at the recommendation of Mittag-Leffler, the Stockholm Academy appointed Sonia as a tenured professor of advanced mathematical analysis on June 6, 1889. This appointment caused a sensation throughout Europe.

Social and cultural circle

Sonya's elegant demeanor and Russian background soon became a fascinating element in the social circle of Stockholm. She joined the elite women's society "Nya Idun" engaged in scientific, literary, artistic, educational and social activities. The writer and feminist Ellen Key (1849-1926) and the socialite Therese Gyldén were the central figures of Nya Idun. Ellen was the principal of the elementary school where Sonya's daughter, Sonya, studied, and the two soon became close friends. Therese was the wife of Hugo Gyldén (1841-1896), the director of the Stockholm Observatory, and a hospitable hostess. Their home at the Observatory became an important gathering place for the scientific and cultural circles in Stockholm. There Sonya also met the writer and poet Viktor Rydberg and the pioneer of the Swedish social democratic movement Hjalmar Branting.

As a woman, Sonia had good access to higher education. Her great mathematical achievements were not only due to her own talent and diligence, but also to the women's rights movement in Europe and the United States in the late 19th century, especially the support and help of Weierstrass, Mitta-Leffler and others. Sonia was deeply involved in the struggle to provide more women with learning and career opportunities, such as joining the first women's association in Sweden and writing for feminist magazines such as Dagny. She often commented on Swedish literature in the Russian journal Severnyj vestnik, for example, in an article she described her impressions of visiting a folk high school. Sonia had a wide range of interests and often went riding, skating, hiking and enjoying nature with her friends. However, she would suddenly interrupt her travels and rush home to do mathematics according to the call of her heart. She was not good at daily chores, such as managing finances, buying clothes, taking care of children, and finding her way, but fortunately she always had friends to help her.

In Stockholm, Sonja realized her literary dream when she was young. Mitta-Leffler's sister, Anne Charlotte Leffler (1849–1852), was one of the most famous Swedish writers in the late 19th century, famous for her feminist works. Her plays were performed on stages all over Sweden every year. Sonja and Anne Charlotte were of similar age and had similar interests. They soon became good friends. For three or four years, the two spent almost every day together, often traveling together, and kept close correspondence when they were not in the same place. Sonja and Anne Charlotte co-wrote a nine-act two-person play, "Kampen för lyckan", with the theme of marriage and work rights. Sonja was responsible for the content of the script and Anne Charlotte was responsible for the lines. The two got great pleasure from their collaboration. In December 1887, the play was published as a book, and two different versions are now in the Royal Library in Stockholm.

Sonja (seated third from left), Sigourney (seated second from left), Anne Charlotte (standing third from left) and Alan, dressed in Icelandic Old Norse costumes, at a folklore event (1885, Wikimedia Commons)

Sonya admired the works of her contemporary, the great Swedish writer August Strindberg. She wrote: "Strindberg is considered the founder of a new literary genre - some of his stories, especially those from folk life, are very successful and suitable for translation into Russian..." Strindberg had strong prejudices against women. Although the two had never met, he had difficulty accepting Sonya's appointment as a professor at the Stockholm Academy, saying that "female professors are useless, harmful and unpleasant." Strindberg also wrote articles to slander Sonya's character and scientific work, although he knew nothing about mathematics. Sonya responded: "It is precisely because of his one-sided and unreasonable attacks that I am fortunate to be able to express my admiration for the genius of Strindberg. We women should try to teach ourselves that men know so little and not let a person's weaknesses or mistakes obscure his true meaning."

In 1886, her sister Anyuta became seriously ill and died the following year, which was another devastating blow to Sonya. She almost resigned from her teaching position in Stockholm to take care of her sister. Thanks to her good friend Julia and Dostoyevsky's widow Anna Vasilievna, she lent a hand. Unlike Sonya's personality and hobbies, Anyuta, who was six years older than her, was a radical revolutionary with beautiful blonde hair and a slender figure. Anyuta was always the center of the crowd. She was Sonya's idol since childhood and one of the closest and most important people in her life. Anyuta's ideal was to become a writer. Dostoyevsky was her admirer when he was young. Soon after arriving in Heidelberg, Anyuta was tired of the study life there. She moved to Paris and devoted herself to political activities. In 1871, when Sonya went to Paris to visit Anyuta and her boyfriend, she personally experienced the bloody battle of the Paris Commune.

At Anyuta's bedside, Sonya began to conceive two novels. In 1889, her autobiographical novel Ur ryska lifvet: systrarna Rajevski was published. The younger sister Tanja in the book was Sonya herself. The novel was a huge success and was translated into eight languages. Sonya's posthumous work Vera Vorontzoff: berättelser ur ryska lifvet, titled "Nihilist Girl" in English, was finally completed by Anne Charlotte and published in 1892 with a preface by Allen. The protagonist Vera is a young girl who, with the spirit of a martyr, gave up all possibilities of a normal life and married a political prisoner exiled to Siberia. Sonya wrote this book for Anyuta. She often lamented with her Swedish friends such as Anne Charlotte that she was born in such an era of change.

The final journey

In February 1888, Sonya met Maksim Kovalevsky (1851–1916), a distant relative of her late husband. Maksim was a Russian sociologist and revolutionary who was invited to Stockholm as a guest lecturer and was later nominated for the 1912 Nobel Peace Prize. During their stay in Stockholm, Sonya and Maxim became very good friends and developed a romantic relationship, but Sonya was always struggling with whether to marry Maxim. During the Christmas season of 1890, Sonya traveled to the Gold Coast of southern France and vacationed with Maxim in his villa. Sonya had never been accustomed to the cold Nordic winter, so she enjoyed the Mediterranean sun, sea water and flowers very much. On the way back, she stayed briefly in Paris and Berlin to visit relatives and friends. Sonya went through many twists and turns on the way back, and caught a bad cold on the way, and returned to Stockholm in the early morning of February 4, 1891.

The next evening after Sonia returned, Mita-Leffler came to visit her at home. She talked a lot about her travels, news of old friends, and research plans for the new year. Despite her illness, Sonia still stood on the podium on February 6 and insisted on teaching the first class of the spring semester, which was a new topic she started in the previous semester - the application of analysis in number theory. After class, Sonia had lunch with Mita-Leffler and attended a party at her friend Theresa's house that night. She took the wrong tram on her way home and had to walk back to her residence in the cold wind. Soon, her severe cold turned into pneumonia. In the next few days, Mita-Leffler invited the best doctors for Sonia. Theresa and Allen took turns to take care of her at home, but they ultimately failed to save her life. At 4 a.m. on February 10, Sonia passed away quietly at the age of 41 years and 26 days. From the first class to the last class, she went through seven years of dream coming true.

The news of Sonya's death spread throughout Europe, and mathematicians, artists, and intellectuals from various countries sent condolences and flowers. One of the white lilies had a message: "Dedicated to Sonya Weierstrass." The lonely and sad old man burned all the letters of his beloved disciple. Six years later, the 82-year-old Weierstrass also passed away. Sonya's funeral was held six days after her death. She was buried in the Norra Begravningsplatsen Cemetery in Stockholm. The mourners lined up in a long line in the cold wind of February in Northern Europe. Mitta-Levler gave a eulogy at the funeral, and Maxim, who came from afar, thanked her in French. He never married in his life. Mitta-Levler was heartbroken to see Sonya's 12-year-old daughter suddenly grow up overnight. Theresa took care of little Sonya until she finished her studies in Sweden and returned to her family in Russia. She grew up to become a doctor.

Left: Sonia and Anne Charlotte (litteraturbanken.se), Right: Sonia and her daughter (reference [6])

In early December 1890, Sonia came to Mitta-Leffler's house to say goodbye before traveling. That was the last time Anne Charlotte saw Sonia. Soon after, she and her husband went to Naples, Italy for vacation, but she didn't expect that this would be the last time. When the news of Sonia's death came, Anne Charlotte felt that she had lost her "soul of soul". She had long planned to write a biography of her friend, which was also the wish of Sonia before her death, who had a premonition that she might die young. Mitta-Leffler sealed all of Sonia's documents and later handed them over to her sister for writing. In 1892, Anne Charlotte's "Sonia Kovalevsky" was completed and published, and later translated into many languages. The writer herself also passed away in the same year. At Sonia's funeral, Mitta-Leffler and Anne Charlotte's brother Frits Leffler recited a poem they wrote for her, "Soul of Fire and Soul of Thought", which is included in this biography.

When Anne Charlotte first met Sonia in the autumn of 1883, she was deeply attracted by the dreamy and intelligent light in her eyes. In early 1888, Anne Charlotte moved to Italy, and the two did not see each other for nearly two years. Before Christmas 1889, Anne Charlotte went to Paris with Sonia for vacation and found that she had changed a lot. The overwork of studying mathematics for many years, the early death of her sister Anyuta, and the emotional entanglement with Maxim almost exhausted Sonia's energy, and her eyes became dim. In the early summer of the following year, Anne Charlotte met Sonia again in Berlin who had just returned from a trip to St. Petersburg. Sonia was warmly welcomed in Helsinki and St. Petersburg, and she kept giving speeches and attending banquets. Few women were surrounded by external success like Sonia, but Anne Charlotte could feel her inner loneliness and loneliness, and her heart gradually closed to her closest friends.

Deep down, Sonya was always afraid of the great unknown. In the summer of her 19th year, when she visited the British writer George Eliot (pseudonym) in London, she said: "The belief in death gave me the courage to live." Sonya often quoted lines from Shakespeare's tragedy Hamlet during her lifetime: "For in death - when we get rid of this rotten skin, in that sleep of death, what dreams we will have, it is worth pondering." Anne Charlotte wrote in her biography: A person's life, whether long or short, does not actually mean much, everything depends on how rich it is for oneself and others. In this sense, Sonya's life is longer than others; she indulges in the springs of happiness and sadness, draws spiritual strength from the well of wisdom; she climbs to all the heights that can be reached by imagination, and shares her rich knowledge, experience, fantasy, and feelings with others...

Immortality

After Sonya's death, Allen wrote in two memorial articles in Dagny magazine: There was no trace of scholarly pride in Sonya, who expanded her horizons by constantly penetrating new spiritual realms. Sonya was made up of extreme opposites, an extraordinary cultural background and a powerful and wild natural force; a fragmented, subtle, and susceptible heart and an energetic, unified, and intense spirit; a modern, analytical, penetrating wisdom and a rich oriental imagination; a precise mathematician and an idealistic dreamer. When you count these opposites, you will find that there are hundreds of characteristics that have not been mentioned. Her extraordinary pleasure may lie mainly in these incompatible opposites, a personality whose wealth is inexhaustible and whose essence cannot be measured, with a triple nature of genius, woman and Slavic people.

Sonia's life was full of adventure, tragedy and a brilliant career. She traveled to many places and constantly pursued new goals. However, no matter how far she went, Sonia always returned to her favorite mathematics and literature. Her greatest ability was to constructively combine emotion and wisdom. Sonia described her experience in a letter to a friend: "Many people who have not studied mathematics confuse this science with arithmetic and think it is boring, but it is a science that requires great imagination." In her eyes, mathematics exists independently of anything in the world, just like the northern lights, it is a gift from nature. Sonia never tried to decide whether she was more inclined to mathematics or literature. She could switch between the two freely. A sentence in Weierstrass's letter became her motto: "A mathematician who is not a poet will always be imperfect."

Alice Munro, a Canadian female writer and winner of the 2013 Nobel Prize for Literature, describes Sonia's final journey in her short story Too Much Happiness, replaying the moments of her life in a dreamlike and waking form. The novel opens with Sonia and Maxim walking in the old cemetery in Genoa on New Year's Day 1891. Sonia says to Maxim, "One of us will die this year." Who knew that her words would come true. It reminds us of another foreigner who died in Stockholm - René Descartes (1596-1650), the founder of modern Western philosophy. In the autumn of 1649, he was invited to Stockholm to serve as a private tutor to Queen Christina of Sweden. He died on February 11 of the following year in this "land of bears, snow and rocks." Sonia was born 200 years after Descartes' death, and the two died only one day apart.

When Weierstrass and Sonya met, Munro wrote in the novel: "All his life, he had been waiting for such a student to walk into his study. A student who could challenge him comprehensively, a student who could not only keep up with his intellectual achievements but also fly further... In the heart of a first-class mathematician, there must be something like intuition, a flash of lightning that reveals what has always been there. Precision, meticulousness, it must be like this, as is the case with great poets." When she said goodbye to Weierstrass for the last time, Sonya thought: "His name will exist for some time, in textbooks and among mathematicians. If he had been more enthusiastic about building his own reputation, he might have stood at the forefront of the career he chose and worked hard for for a longer time. He cares about his work far more than his reputation, while most of his colleagues care about the two to a certain extent."

Monroe also wrote: "Sweden is the only country in Europe that is willing to hire a female mathematician for its new university. Their cities are too clean and tidy, their habits are too regular, and their parties are too polite. Once they feel that certain procedures are correct, they immediately implement them. The endless, exciting, and even dangerous debates in Petersburg and Paris are simply not here." "How she loved Paris before... It was in this Paris that she was introduced to mathematicians and political thinkers. It was in this Paris that she claimed that there was no boredom, no snobbery, and no deception. Then they gave her the Boulding Award, kissed her hand, let her speak in the most luxurious and bright elegant rooms, and gave her flowers. But when she needed a job, they closed the door. They would not think about it for any longer than they would think about hiring a trained chimpanzee."

Sonya's former residence and tombstone (photographed by the author)

I first learned about this Russian female mathematician when I learned the Cauchy-Kovalevskaya theorem in a partial differential equation class in college. After living in Sweden for many years, the name "Sonia" is constantly heard. Whenever I stand in front of her statue, I always feel like I'm traveling through time. A few days ago, based on the literature, I found Sonia's former residence in Stockholm, Sturegatan 56. This is a downtown street built in the second half of the 19th century. There is no sign in front of the door, and I think the current owner would not know that a great woman once lived here. In 1948, the Russian Women's Organization raised funds to erect an Orthodox cross stone monument in front of Sonia's tomb, and engraved the monument inscription in Russian and Swedish. The birth and death dates in the Russian inscription are the Julian calendar used by the Orthodox Church. Every year, people come here to mourn and offer flowers. Although Sonia has been gone for 132 years, as Weierstrass said: "People are dead, but their thoughts are still there."

References

[1] P. Kurasov: (editor), 27th Nordic congress of mathematicians, celebrating 100th anniversary of Institut Mittag-Leffler, Stockholm 2016.

[2] AC Leffler: Sonja Kovalevsky, Albert Bonniers förlag 1892.

[3] A. Munro: Too Much Happiness, McClelland and Stewart 2009.

[4] G. Mittag-Leffler: Weierstrass et Sonja Kowalewsky, Acta Mathematica, 39 (1923).

[5] A. Stubhaug: Gösta Mittag-Leffier, A man of conviction, Springer Verlag 2010.

[6] GJ Tee: Sofya Vasilyevna Kovalevskaya, Math. Chronicle 5 (1977).

This article is supported by the Science Popularization China Starry Sky Project

Produced by: China Association for Science and Technology Department of Science Popularization

Producer: China Science and Technology Press Co., Ltd., Beijing Zhongke Xinghe Culture Media Co., Ltd.

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