St. Kovalevskaya. Sofya Kovalevskaya: biography and achievements in science

Sofya Kovalevskaya (1850–1891) Sofya Vasilievna Krukovskaya was born in Moscow on January 3, 1850 in the family of artillery colonel (later lieutenant general) Vasily Vasilyevich Krukovsky and his wife Elizaveta Fedorovna, nee Schubert. In 1858, Sophia's father was able

Kovalevskaya Sofya Vasilyevna (born in 1850 - died in 1891) An outstanding Russian mathematician and writer, the first woman corresponding member of the St. Petersburg Academy of Sciences (1889), professor at Stockholm University (1884), author of works on mathematical analysis, mechanics and

Mathematics

Place of Birth: Moscow

Family status: married to Vladimir Onufrievich Kovalevsky (1868-1883), maiden name: Sofya Vasilievna Korvin-Krukovskaya

Activities and interests: mathematics, mechanics; literary creativity, fiction

Russian universities were closed to women, and to get to Europe, you needed a foreign passport, which was issued with the permission of your father or husband. Sophia's father did not want his daughter to continue her studies, and in 1868 she married fictitiously, to paleontologist-evolutionist Vladimir Kovalevsky, with whom she left for Germany. More facts

Education, degrees and titles

1869, University of Heidelberg (Germany)

1870-1874, University of Berlin

Job

1884-1891, Stockholm University: Professor of Mathematics

Discoveries

In 1888 she received the prestigious Borden Prize for the discovery of the third classical case of solvability of the problem of the rotation of a rigid body around a fixed point. In view of the seriousness of the discovery, the premium was increased from 3 to 5 thousand francs. And today four algebraic integrals exist only in three classical cases: Leonard Euler, Lagrange and Kovalevskaya.

Proved the existence analytical solution Cauchy problems for systems of partial differential equations.

She studied Laplace's problem of the equilibrium of Saturn's ring and obtained a second approximation.

Biography

Russian mathematician and mechanic, the first female professor in Russia and the first female professor of mathematics in the world. She studied abroad, since in Russia at that time women were not accepted into higher education institutions. She was engaged in research in the field of the theory of rotation of a rigid body. Author of many scientific works, Doctor of Philosophy (University of Gottingen, 1874). Since 1881 - member of the Moscow Mathematical Society. For the discovery of the third classical case of solvability of the problem of the rotation of a rigid body around a fixed point, she received prizes from the Paris (1888) and Swedish (1889) Academies of Sciences. In 1889, she was elected a corresponding member of the physics and mathematics department of the Russian Academy of Sciences. She sympathized with revolutionary ideas and, in the besieged Paris of 1871, looked after the wounded communards. She helped rescue Paris Commune activist Victor Jacqulard from prison. The author of several literary works and fiction - she wrote in Russian and Swedish. Many works are autobiographical in nature, and the main character has recognizable features of Kovalevskaya herself. She also wrote poetry and translated from Swedish.

Kovalevskaya Sofya Vasilievna (nee Korvin-Krukovskaya) (1850-1891), mathematician.

Born on January 15, 1850 in Moscow in the family of an artillery general. When Sophia was six years old, her father retired and settled on the family estate of Palibino, Vitebsk province.

A teacher was hired for the girl's classes. The only subject in which the future scientist showed neither special interest nor ability in the first classes was arithmetic. However, gradually she developed serious abilities for mathematics.

In 1868, Sofya Vasilievna married V. O. Kovalevsky, and the newlyweds went abroad. For two years she attended lectures in mathematics at the University of Heidelberg (Germany).

In 1874, the University of Göttingen, after defending her dissertation, awarded her a doctorate.

In 1881, Kovalevskaya was elected a member of the Moscow Mathematical Society. After the death of her husband, she moved with her daughter to Stockholm (1884) and received the chair of mathematics at Stockholm University, with the obligation to lecture in German for the first year, and in Swedish from the second.

Kovalevskaya quickly mastered the Swedish language and published her mathematical works in it.

In 1888, the Paris Academy of Sciences awarded her a prize for her research into the rotation of a rigid body around a fixed point.

In 1889, for two essays in connection with previous work, Kovalevskaya received the Stockholm Academy Prize and became a corresponding member of the St. Petersburg Academy of Sciences.

In April 1890, Sofya Vasilievna returned to Russia in the hope that she would be elected as a member of the academy in place of the mathematician V. Ya. Bunyakovsky, who died in 1889, and that she would gain financial independence, which would allow her to engage in science in her homeland. But when Kovalevskaya wished, as a corresponding member, to attend the scientific meetings, she was told that the participation of women in them was “not in the customs of the Academy.”

In September she went to Stockholm again.

Mathematician.

She lived in Moscow until she was five years old, then in Kaluga. Then - in the village of Palibino, Vitebsk province, on the estate of the father of artillery lieutenant general V.V. Korvin-Krukovsky, who fought in the Balkans and was then appointed head of the Moscow arsenal. The Korvin-Krukovsky estate was huge. There was a park right next to the manor house, which gradually turned into a deep forest, and in the house itself there were many halls and rooms.

“At the age of twelve,” Kovalevskaya wrote in her memoirs, “I was deeply convinced that I would be a poetess. Out of fear of the governess, I did not dare to write my poems, but I composed them in my mind, like the old bards, and trusted them to my ball. Chasing him in front of me, I would rush around the hall and loudly recite two of my poetic works, which I am especially proud of: “The address of a Bedouin to his horse” and “The sensations of a swimmer diving for pearls.” I have a long poem in mind, “The Trickle,” something between “Ondine” and “Mtsyri,” but only the first ten stanzas of it are ready so far...”

Kovalevskaya’s early manifested mathematical abilities were noticed and supported by her uncle P.V. Korvin-Krukovsky and physics professor Tyrtov, who often visited the estate.

And some accidents happily intervened in fate.

“When we moved to live in the village,” Kovalevskaya said in her memoirs, “the whole house had to be redecorated and all the rooms covered with new wallpaper. But there wasn’t enough wallpaper for one of our children’s rooms. This abused room remained for many years with one wall covered with plain paper. But, by a lucky coincidence, this preliminary pasting was used precisely from sheets of lithographed lectures by Ostrogradsky on differential and integral calculus, acquired by my father in his youth.

These sheets, covered with strange, incomprehensible formulas, soon attracted my attention. I remember how, as a child, I spent whole hours in front of this mysterious wall, trying to make out at least individual phrases and find the order in which the sheets were supposed to follow each other. From long daily contemplation appearance Many of the formulas were engraved in my memory, and the text itself left a deep imprint on my brain, although at the very moment of reading it remained incomprehensible to me.

When, many years later, as a fifteen-year-old girl, I took my first lesson in differential calculus from a famous teacher in St. Petersburg, Alexander Nikolaevich Strannolyubsky, he was surprised at how quickly I grasped and internalized the concept of limit and derivative, “as if I knew them in advance.” And the thing, really, was that at that moment when he was explaining these concepts to me, I suddenly clearly remembered that all this was on the sheets of Ostrogradsky that I remembered, and the very concept of the limit seemed familiar to me for a long time ... "

The decisive influence on the development of Kovalevskaya’s views was exerted by her elder sister Anna. She became interested in literature early. Anna's story "The Dream" was published by F. M. Dostoevsky in his magazine "Epoch". The story was about a girl who wasted her youth. The Korvin-Krukovsky sisters themselves did not want to lose their youth just like that. They dreamed of getting a higher education, and therefore they seriously studied science and literature. Is it true, strict father did not approve of their interests, especially their activities youngest daughter mathematics. Sophia hid Bourdon's A Course in Algebra under her pillow and read the book at night.

To escape from the tutelage of the father, in Russia there was only one way, although it had already been tried by many - a fictitious marriage.

A candidate has been found.

This candidate turned out to be a neighbor, a small nobleman who lived not far from Palibino - a talented young man Vladimir Onufrievich Kovalevsky. About Sophia, who captured his imagination, he wrote to his older brother: “...Despite her 18 years, the little sparrow is excellently educated, knows all languages ​​as if she were her own, and is still mainly studying mathematics. She works like an ant from morning to night, and for all that she is alive, sweet and very pretty.”

Oddly enough, General Korvin-Krukovsky liked Kovalevsky.

Immediately after the wedding, the “newlyweds” left for St. Petersburg, where Kovalevskaya tried to get permission to listen to lectures at the Medical-Surgical Academy. But she was not allowed to attend the lectures, and in the spring of 1869, still full of hope, the Kovalevskys (and Anna with them) left for Germany, to Heidelberg. Here, finally, Kovalevskaya began to diligently attend lectures by G. Kirchhoff, E. Dubois-Reymond and G. Helmholtz.

In 1870, Kovalevskaya moved to Berlin, where she worked for four years with the famous German mathematician Karl Weierstrass, who agreed to give her private lessons, since women were also not allowed at the University of Berlin at that time. At first, Weierstraße was also skeptical, but in the end he recognized Kovalevskaya’s talent. Moreover, he recognized her talent forever. “As for Kovalevskaya’s mathematical education, I can assure you,” wrote Weierstrasse, “that I had very few students who could compare with her in diligence, ability, diligence and passion for science.”

Later, it was Weierstraße who initiated a petition to the University of Göttingen to award Kovalevskaya the degree of Doctor of Philosophy without a mandatory examination. In a presentation dated 1874, Weierstrasse gave very high praise to three mathematical works of Kovalevskaya - “On the theory of partial differential equations”, “Additions and comments to Laplace’s study on the shape of the ring of Saturn” and “On the reduction of a class of Abelian integrals of the third rank to integrals elliptical."

As a result of the initiative taken by Weierstrass, the University of Göttingen awarded Kovalevskaya a doctorate.

In the summer of 1874, the Kovalevskys returned to Russia.

They wanted to work here and Kovalevskaya hoped that the fame she had earned abroad would help her in Russia.

However, Russian mathematicians met Kovalevskaya unfriendly. This was largely due to antipathy towards the German direction in mathematics. Only Chebyshev, who immediately understood the extent of her talent, truly greeted her. But such prominent mathematicians as A. M. Lyapunov and N. E. Zhukovsky did not immediately accept it. However, Kovalevskaya was happy to return to Russia. In her memoirs she wrote:

“...Everything now interested me and made me happy. I was amused by theatres, and charity evenings, and literary circles with their endless, pointless debates about all sorts of abstract topics. For ordinary visitors to these circles, these disputes had already become boring, but for me they still had all the charm of novelty. I devoted myself to them with all the enthusiasm of which a naturally talkative Russian person is capable, who has lived for five years in a non-Metchina, in the exclusive company of two or three specialists, each busy with his narrow, absorbing business and not understanding how one can waste precious time on idle scratching. language..."

By this time, the fictitious marriage of the Kovalevskys became actual, and in 1878 their daughter Sophia was born. Life required considerable funds, and it was difficult to obtain them. The Swedish mathematician Mittag-Leffler, who became friends with Kovalevskaya while studying with Weierstrass, and Chebyshev tried to distract Kovalevskaya from her empty pastime and persuade her to change her new way of life, but Kovalevskaya liked going out. In addition, not a single attempt to get a teaching job was successful. When the Bestuzhev Higher Women's Courses opened in St. Petersburg on the basis of the Alarchin preparatory courses, Kovalevskaya was not even invited there to give free lectures. One of the many officials who refused Kovalevskaya a job remarked smugly: “In our country, teaching has always been done by men. They cope with their responsibilities, thank God, well, so we don’t need any innovations!” Kovalevskaya responded to these words: “When Pythagoras discovered his famous theorem, he sacrificed a hundred bulls to the gods. Apparently, since then the cattle have become afraid of new things!”

Trying to create normal living conditions for his family, Vladimir Kovalevsky collaborated a lot in the newspaper “Novoye Vremya”, translated and published scientific works, – there was still not enough money. Unsuccessful business speculations led the Kovalevskys to ruin; in the spring of 1880 they had to leave for Moscow. There, as director of the Society of Russian Mineral Oil Factories of Ragozin and Company, Kovalevsky became a victim of a new scam. Unable to withstand the pressure of circumstances, in April 1883 he committed suicide.

In November of the tragic year 1883, Kovalevskaya accepted Mittag-Leffler’s invitation to take the position of privatdozent at Stockholm University. In Sweden, Kovalevskaya’s mathematical abilities finally received real recognition, and therefore the opportunity for development. She quickly mastered the Swedish language and already in the summer of 1884 received a position as a professor at Stockholm University, where over the course of eight years she taught twelve full courses, including a course in mechanics.

In 1888, Kovalevskaya published “The problem of the rotation of a rigid body around a fixed point.” After the classical works of L. Euler and J. Lagrange, Kovalevskaya for the first time advanced the solution to the problem of the rotation of a rigid body around a fixed point, finding a new case of rotation of a not completely symmetrical gyroscope.

It should be noted that this work was not simply math game, associated with calculations of the movement of a launched top, although such a top itself has long tormented scientists with its mysteries. It was not clear, for example, why the axis of a rapidly rotating top rotates so slowly; it also seemed surprising why the top always strives to maintain its direction when external forces act on it. An explanation of these properties was awaited by a variety of specialists, for example, astronomers, for whom the planets and suns are, in essence, the same tops, as well as gunsmiths, who have long noticed that bullets and shells hit the target much more accurately if they are given a rotational movement.

In 1888, for her work “The problem of the rotation of a rigid body around a fixed point,” Kovalevskaya was awarded the Borden Prize, issued by the Paris Academy of Sciences.

IN next year For her work, also devoted to the rotation of a rigid body, Kovalevskaya received a prize from the Swedish Academy of Sciences.

Kovalevskaya received universal recognition abroad, but she always wanted to work in Russia. Trying to help Kovalevskaya, she cousin General A.I. Kosich addressed a letter to the President of the Academy of Sciences, Grand Duke Konstantin. In the letter, he reminded the Grand Duke of Napoleon’s famous words that every state should value the return outstanding people more than by conquering a rich city. Unfortunately, the general said almost nothing about Kovalevskaya’s outstanding scientific achievements, and therefore his letter had no real effect.

In October 1889, Chebyshev wrote to Kovalevskaya with grief:

“Dear Sofya Vasilievna!

No one doubts that you are devoted to your fatherland with all your heart and that you would happily move from the Swedish University to the Russian University. There can be no doubt about this; one can only doubt that you will agree to exchange a university chair in Sweden for a position as a teacher of mathematics at the Higher Women's Courses here. I believe that such a change would be a great sacrifice on your part and a sacrifice to the detriment of the development of higher mathematics.

Under our current regulations for men's educational institutions, who certainly do not allow women into any departments, we can only rejoice and be proud that our compatriot so successfully occupies a department at a foreign university, where the national feeling is far from in her favor. I heard that a response has already been sent to Mr. Kosich’s letter, which raised the question of providing you with a place in Russia instead of the one you have in Stockholm. I had the opportunity to read this letter and, I confess, I was extremely surprised at how little your relative is familiar with what is generally known about your academic career ... "

The efforts of friends to return Kovalevskaya to Russia were unsuccessful.

All her life, Kovalevskaya wanted to do exactly what she did best.

In Russia she was not allowed to do this.

True, on the proposal of academicians P. L. Chebyshev, V. G. Imshenetsky and V. Ya. Bunyakovsky, in December 1889 she was elected a corresponding member of the St. Petersburg Academy of Sciences. To achieve this, the fundamental issue of allowing women to be elected as corresponding members had to be resolved at the government level. “Our Academy of Sciences has just elected you as a corresponding member,” Chebyshev telegraphed to Kovalevskoy, “thus allowing for an innovation for which there has been no precedent until now. I am very happy to see one of my most ardent and just desires fulfilled.”

Unfortunately, Kovalevskaya did not celebrate the long-awaited victory for long.

On January 29, 1891, she died of pneumonia while returning from Paris to Stockholm. She was forty-one years old, she was in the prime of her mental strength and talent. Fritz Leffler, a friend of Kovalevskaya, wrote poetry on her death.

Soul of flame and doom!
Has your airship arrived?
to the country where your mind soared,
obedient to the call of truth?

In those areas there are numbers, a number of functions,
following a different order,
maybe you'll be allowed
immortality is an eternal mystery.

Soul of flame and doom!
In hours of hope and enlightenment
your mind considered one love
a reliable anchor of salvation.

Goodbye! With your glory
you, having parted with us forever,
you will live in people's memory
with other glorious minds,

as long as the wonderful starlight
it will pour from heaven to earth
and in a host of shining planets
Saturn's ring will not be eclipsed.

The memory of Kovalevskaya remains not only in science.

Her novel “The Nihilist” (1891) was very popular among her contemporaries, and the drama “The Struggle for Happiness” (1887), written in collaboration with the Swedish writer A. S. Leffler-Edgren (sister of the mathematician Mittag-Leffler), was staged.

“I understand,” Kovalevskaya wrote in her memoirs published in 1890, “that you are so surprised that I can study both literature and mathematics at the same time. Many who have never had the opportunity to learn more about mathematics confuse it with arithmetic and consider it a dry and sterile science. In essence, this is a science that requires the most imagination, and one of the first mathematicians of our century says absolutely correctly that you cannot be a mathematician without at the same time being a poet at heart...

It seems to me that a poet should only see what others do not see, to see more deeply than others. And so should a mathematician.

As for me, all my life I could not decide: what am I more inclined towards - mathematics or literature? As soon as your head gets tired of purely abstract speculation, it immediately begins to gravitate towards observations of life, to stories, and vice versa, at other times everything in life begins to seem insignificant and uninteresting; and only eternal, immutable scientific laws attract oneself..."

Like every Russian person, Kovalevskaya was close to the ideas of sympathy, so well expressed by N. G. Chernyshevsky in “The First Dream of Vera Pavlovna,” probably the most piercing of all four dreams.

“She dreams that she is locked in a damp, dark basement. And suddenly the door opened, and Verochka found herself in a field, running, frolicking and thinking: “How could I not die in the basement?” - “That’s because I didn’t see the field; If I had seen him, I would have died in the basement,” and again he runs and frolics. She dreams that she is paralyzed, and she thinks: “How is it that I am paralyzed?” Old men and women are broken, but young girls are not.” “They happen, they often happen,” says an unfamiliar voice, “and now you’ll be healthy, as soon as I touch your hand, you see, you’re already healthy.” Get up... I want my sisters and grooms to choose only each other. Were you locked in the basement? Was she paralyzed?” – “I was” – “Now I’m free?” – “Yes.” - “It was I who released you, I cured you. Remember that there are still many who have not been released, many who have not been cured. Release, heal. Will you?” – “I will.”

Maybe this is the key to the Russian soul.

Maybe Sofia Kovalevskaya repeated Verochka’s dream to herself more than once, both on happy and tragic days.

1. Biography

Sofya Vasilievna Kovalevskaya is the greatest female mathematician, university professor. Although her work took place in areas of science that are very far from not only the school mathematics course, but also from the courses of higher educational institutions, the life and Personality of S.V. Kovalevskaya’s works are very interesting and instructive, and her name represents the pride of Russian science.

Sofya Vasilievna Kovalevskaya was born on January 3 (15), 1850 in Moscow, in the family of General V.V. Korvin-Krukovsky, who soon retired and settled on his estate in. Vitebsk province. In the metric book of the Moscow Ecclesiastical Consistory of the Nikitsky Forty, Znamenskaya Church outside the Petrovsky Gate, for 1850 there is an entry:

Born on January 3, Sofia was baptized on January 17; her parents are Artillery Colonel Vasily Vasilyevich, son of Krukovskaya, and his legal wife Elizaveta Fedorovna; the husband is of the Orthodox confession, and the wife is of the Lutheran confession. Receiver: retired Artillery second lieutenant Semyon Vasilyevich, son of Krukovskaya, and provision master Vasily Semyonovich, son of Krukovsky, daughter, maiden Anna Vasilyevna. The sacrament of baptism was performed by local priest Pavel Krylov with deacon Pavel Popov and sexton Alexander Speransky ]

The general's daughters, the younger Sophia and the eldest Anna, were brought up under the supervision of governesses, studied foreign languages and music to become well-mannered noble ladies. Sophia's first years were spent under the exceptional influence and care of a nanny, who replaced both her mother and father. To the father who lost a large sum money, there was no time for children, and the mother, upset by the birth of a daughter and not a son, did not even want to look at her. When Sophia grew up, the upbringing and education of the “savage” passed into the hands of Malevich’s home teacher and the strict English governess Mrs. Smith. Since childhood, Sophia was distinguished by a rich imagination and fantasies, as well as increased nervous excitability, she even had nervous attacks, and in mature age she suffered from nervous diseases.

Sophia also had such a sign of great nervousness as an aversion to deformities reaching the point of horror, for example, stories about pets being born with five legs or three eyes, as well as fear of all kinds of cruelty. Even the sight of a broken doll filled her with panic. One day, it was just such a doll, with a knocked-out black eye dangling from its head, that brought her to convulsions. As is known, due to her “female gender,” she could neither receive a full-fledged higher education in her time, nor have the opportunity to freely realize herself as a mathematician. And only her colossal hard work, will and talent, combined with the help and support of friends, helped her overcome all life's obstacles and obstacles.

Hardening began in childhood. Considering herself “unloved” and striving to somehow earn her parents’ love, Sonya studied diligently. And she soon became the pride of the family, realizing that everyone considered her very knowledgeable for her age. She showed signs of perseverance, discipline and strong will, so characteristic of Capricorns.

Her teacher Joseph Malevich describes the beginning of his studies with Sophia as follows: “At the first meeting with my gifted student, I saw in her an eight-year-old girl, quite strong built, sweet and attractive appearance, in whose eyes a receptive mind and spiritual kindness shone. In the very first training sessions, she discovered rare attention, quick assimilation of what was taught, perfect complaisance, precise execution of what was required and a constantly good knowledge of the lessons.”

In turn, the strict governess created almost Spartan conditions for the girl: early rise, dousing cold water, tea, music lessons, homework, at noon - breakfast and a short walk, then more homework and completing assignments for tomorrow. A strict daily routine for Capricorn is not a difficult matter - it is the education of the individual and the development of a value system in harsh conditions.

Interest in mathematics did not appear immediately; the stimulus was the most ordinary conversation between the girl and her father, who one day at dinner asked his daughter: “Well, Sofa, have you fallen in love with arithmetic?” “No, daddy,” was her answer. To which the teacher reacted with some excitement: “So love it, and love it more than other scientific subjects!” Less than four months had passed when Sofa said to her father: “Yes, daddy, I like to do arithmetic: it gives me pleasure.”

Kovalevskaya is the first woman mathematician to become a professor. In her scientific research, Kovalevskaya went through all possible solutions to the problem, simultaneously analyzing and improving the already existing solutions of other mathematicians, and made a tangible contribution to the development of mathematics in the 19th century.

As soon as Kovalevskaya was carried away into the world of mathematics, she was completely forgotten; from that moment on, all troubles, difficulties and everyday problems faded into the background and had no meaning.

“I just have to touch mathematics,” she said, “and I’ll forget about everything in the world again.”

How great is the power of the inspiration that embraces you! - a feeling that cannot be described verbally...

Mathematics is, first of all, logic. And also a strict structure and system. The main scientific works of S.V. Kovalevskaya are devoted to mathematical analysis, mechanics and astronomy. In July 1874, on the basis of three works by Kovalevskaya presented by Weierstrass - “On the theory of partial differential equations” (ed. 1874), “Additions and comments to Dallas’s study on the shape of the ring of Saturn” (ed. 1885), “On the reduction of one class of Abelian integrals of the third rank to elliptic integrals" (ed. 1884) - the University of Göttingen awarded in absentia to S.V. Kovalevskaya degree of Doctor of Philosophy. In the analytical theory of partial differential equations (the majorization method), one of the theorems is called the Cauchy-Kowalevskaya theorem. In 1888, Kovalevskaya wrote the work “The Problem of the Rotation of a Rigid Body Around a Fixed Point.” After the classical works of L. Euler and J. Lagrange, only the work of Kovalevskaya advanced the solution of this problem: Kovalevskaya found a new case of rotation of a not completely symmetrical gyroscope, when the solution is completed.

The student turned out to be understanding and diligent. In the fifth year of study, a 13-year-old student, when finding the ratio of the circumference to the diameter (number ) showed her mathematical abilities: she gave her independent conclusion of the required ratio. When Malevich pointed out the somewhat roundabout way of deduction used by Sophia, she began to cry. As is known, in scientific research Kovalevskaya was accompanied by her teacher, a German mathematician and professor at the University of Berlin, Karl Weierstrass, without consulting with whom, she was afraid to bring her mathematical research to court.

Even herself, having become great and famous, she considered herself only a student of the Weierstrass school, for which her colleagues constantly reproached her for not being independent and even doubted whether these were her works. Which is completely wrong! The great Weierstrass, having raised and educated Kovalevskaya the mathematician, subsequently only reviewed the student’s works, but did not participate in any way in their development. If Kovalevskaya had not had her own mathematical talent and innate natural diligence, she would never have become what she became!

The question about love for mathematics was asked so often by Kovalevskaya that she herself gave a very definite answer: “I owe the initial systematic teaching of mathematics to I.I. Malevich. Malevich taught arithmetic in particular well and in a unique way. However, I must confess that at first, when I began to study, arithmetic did not particularly interest me. Only after becoming somewhat familiar with algebra did I feel such a strong attraction to mathematics that I began to neglect other subjects. My love for mathematics manifested itself under the influence of my uncle Pyotr Vasilyevich Korvin-Krukovsky... from him I first heard about some mathematical concepts that made a particularly strong impression on me. My uncle talked about the squaring of the circle, about asymptotes - straight lines to which the curve gradually approaches without ever reaching them, and about many other things completely incomprehensible to me, which, nevertheless, seemed to me something mysterious and at the same time especially attractive."

Sofya Vasilievna herself says in her memoirs that her uncle had a great influence on awakening her interest in mathematics with his stories about the squaring of a circle (an unsolvable problem of constructing a square with a compass and a ruler, having an area equal to the area of ​​a given circle) and other fascinating mathematical questions. These stories influenced the girl’s imagination and created in her an idea of ​​mathematics as a science in which there are many interesting riddles. Sofya Vasilievna talks about another incident that strengthened her interest in mathematics. By luck, even the walls of the children's room were covered with notes on differential and integral calculus. It turns out that when the Korvin-Krukovskys moved from St. Petersburg to their Palibino estate, they re-furnished and wallpapered the rooms of the house. There wasn’t enough wallpaper for one of the children’s wallpapers, it was difficult to order them from St. Petersburg, so we decided to cover the wall with plain paper until the opportunity was right. In the attic they found sheets of lithographed lectures by Ostrogradsky on differential and integral calculus. Sonya became interested in the strange signs that dotted the sheets, and stood in front of them for a long time, trying to make out individual phrases. From daily examination, the appearance of many formulas, although they were incomprehensible, was imprinted in my memory. When, at the age of fifteen, she began to take lessons in higher mathematics with the solution of differential equations, from the very famous teacher A.N. Strannolyubsky and listened to the presentation of the same questions that she had read about on the “wallpaper” without understanding the meaning, then the new concepts communicated to her by the teacher seemed old, familiar, and she learned them, to the surprise of the teacher, very easily, amazing the teachers - “as if she knew about this before."

Despite the prohibitions on higher “female” education, she obtained permission to listen to I.M.’s lectures. Sechenov and study anatomy with V.L. Gruber at the Military Medical Academy. Kovalevskaya's path in mathematics was thorny like no other, for the simple reason that she was... a woman. But even before that, fourteen-year-old Sophia surprised her father’s friend, physics professor N.P. Tyrtova, with his abilities. The professor brought Sophia his physics textbook. It soon turned out that Sophia, who had not yet taken a course in school mathematics, independently understood the meaning of the mathematical (trigonometric) formulas used in the textbook. After this, the general, proud of his daughter’s successes, allowed her to take mathematics and physics lessons during her winter stays in St. Petersburg, which fifteen-year-old Sofa was quick to take advantage of.

However, this was not enough for her. Sofya Vasilievna strived to obtain higher education in full. The doors of higher educational institutions in Russia were closed to women at that time. The only option left, which many girls of that time resorted to, was to seek opportunities for higher education abroad. To travel abroad, permission was needed from the father, who did not want to hear about such a trip for his daughter. Then Sofya Vasilievna, who was already eighteen years old, fictitiously married Vladimir Onufrievich Kovalevsky, a later famous natural scientist, and as his “wife” she left with her sister for Germany, where she managed, not without difficulties, to enter the University of Heidelberg, where studied mathematics and attended lectures by German scientists Kirchhoff, Helmholtz and Dubois-Reymond. The university professors, among whom were famous scientists, were delighted with the abilities of their student. It became a landmark of the small town. Meeting her on the streets, mothers pointed her out to their children as an amazing Russian girl who was studying mathematics at the university.

In 1870 she moved to Berlin, where she worked for four years with the great mathematician Weierstrass, who agreed to give her private lessons (women were also not allowed at the University of Berlin). For three years, Sofya Vasilyevna, with very intensive studies, completed a university course in mathematics, physics, chemistry and physiology. She wanted to improve in the field of mathematics with the largest mathematician in Europe at that time, Karl Weierstrass in Berlin. In July 1874, the University of Geltingen in absentia, without formal protection, on the basis of three mathematical works Kovalevskaya, represented by Weierstrass, awarded her the degree of Doctor of Philosophy in Mathematics and Master of Fine Arts “with the highest praise” for defending the dissertation “Zur Theorie der partiellen Differentialgleichungen” (Russian: . "Towards the theory of differential equations"). Three excellent works were enough for the University of Geltingen to forgive, in the words of Weierstrass, “Sonia’s belonging to the weaker sex.”

Since women were not admitted to the University of Berlin, Weierstrass, admiring Sofia Vasilievna’s exceptional abilities, studied with her for four years, repeating to her the lectures he gave at the university. In his submission, Weierstrass indicated that among his many students who came to him from all countries, he did not know anyone whom he “could place above Mrs. Kovalevskaya.” With a diploma of “Doctor of Philosophy with the highest praise,” twenty-four-year-old Sofya Vasilievna and her husband returned to Russia. Inspired by success, the “certified” Kovalevskaya rushed to her homeland to teach mathematics at St. Petersburg University. However, not only could she not get a place at the university, but she was not even involved in teaching at the Higher Women’s Courses that had opened by that time, after which she withdrew from scientific work for almost 6 years, taking an active part in the political and cultural life of her homeland. In 1879, at the suggestion of the mathematician P.L. Chebyshev, at the VI Congress of Russian Naturalists and Doctors, Kovalevskaya read a report on Abelian integrals. In the spring of 1880, she moved to Moscow in search of work, but Moscow University also did not allow her to take the master's exams. The attempt of Professor Mittag-Leffler of the University of Helsingfors to arrange Sofya Vasilievna as a teacher at this university was also unsuccessful.

Kovalevskaya’s attempts to get a professor’s position at the Higher Women’s Courses in France were also unsuccessful. In 1881 a new university was opened in Stockholm, the chair of mathematics of which was given to Professor Mittag-Leffler. After very difficult efforts, he managed to persuade the liberal circles of Stockholm to the decision to invite Sofya Vasilievna to the position of assistant professor at the new university. In 1883 she returned to Russia again. At the VII Congress of Russian naturalists and doctors in 1883, Kovalevskaya reported her work “On the refraction of light in crystals,” which was met with a bang, but again there were no job offers... Sofya Kovalevskaya received an invitation to take the position of privatdozent at the Stockholm University and in November 1883 she left for Sweden. A little later, in the summer of 1884, she was appointed professor at Stockholm University and over the course of eight years she gave twelve courses of lectures, including a course in mechanics.

Huge help Sofya Kovalevskaya was assisted in this matter by her longtime friend, also a student of Karl Weierstrass, the Swedish mathematician Mittag-Leffler. The Democratic newspaper greeted her arrival with the words: “Today we are announcing the arrival of not some vulgar prince... The Princess of Science, Mrs. Kovalevskaya, honored our city with her visit and will be the first female associate professor in all of Sweden.”

Conservative layers of scientists and the population greeted Sofya Vasilyevna with hostility, and the writer Strindberg argued that a female professor of mathematics is a monstrous, harmful and inconvenient phenomenon. However, the talent of a scientist and the talent of a teacher that Sofya Vasilievna possessed silenced all opponents. Sophia met the Helsingfors professor back in 1876. And from the first minute of their acquaintance, he, a great supporter of women's education, passionately wanted to open up the opportunity for her to teach at the university. He immediately tried to obtain an assistant professorship for her at the University of Helsingfors, but without success. A year later, she was elected a full-time professor, and she was assigned, in addition to mathematics, temporary lectures on mechanics.

In 1888, the Paris Academy of Sciences announced the theme for one of its biggest prizes: “The problem of the rotation of a rigid body around a fixed point.” This problem was solved to the end only in two special cases. These solutions belonged to the greatest mathematicians of their time: the St. Petersburg academician L. Euler (1707-1783) and the French mathematician J. Lagrange (1736-1813). It was necessary to “improve the problem in some significant point.” Among the 15 works submitted to the competition, a work was submitted with the motto: “Say what you know, do what you must, let what be done.” This work was so superior to all others that the academic commission, consisting of the greatest mathematicians in France, awarded the author a prize increased from 3,000 to 5,000 francs. Its author turned out to be Sofya Vasilievna Kovalevskaya. She, as a French magazine of that time notes, who came to receive the prize, was the first woman to cross the threshold of the Academy.

The joy of Sofia Vasilyevna is understandable, as she wrote on this occasion: “The problem that had eluded the greatest mathematicians, the problem that was called the mathematical mermaid, turned out to be captured... by whom? Sonya Kovalevskaya!

The attempt made by Sofia Vasilievna’s friends to “return S.V. Kovalevskaya to Russia and Russian science” ended with a hypocritical reply from the Tsar’s Academy of Sciences that “in Russia, Mrs. Kovalevskaya cannot obtain a position as honorable and well-paid as the one she occupies in Stockholm.” " Only at the end of 1889 did academic mathematicians manage to achieve the election of Sofia Vasilievna as a corresponding member of the St. Petersburg Academy, and first the Academy had to resolve the fundamental issue of “admitting female persons to election as corresponding members.” Since this honorary title did not provide any financial means, Kovalevskaya’s return to her homeland remained impossible as before.”

At the beginning of 1891, Sofya Vasilievna, returning from the winter holidays, which she spent in Italy, caught a cold; On February 10, she died in Stockholm and was buried there.

S.V. Kovalevskaya, during her life, published nine scientific works, receiving another award from the Swedish Academy of Sciences for one of them. Her works relate to the field of pure mathematics, mechanics, physics and astronomy (about the ring of Saturn). In work on mechanics, she completed what the famous Euler and Lagrange began, in mathematics she completed Cauchy’s ideas, and in the question of the ring of Saturn she supplemented and corrected Laplace’s theory. Euler, Lagrange, Laplace, Cauchy - these are the greatest mathematicians late XVIII And early XIX century. To supplement or correct the work of such luminaries of science, you need to be a very great scientist. Such a scientist was S.V. Kovalevskaya. New scientific results obtained by her are presented in large university courses.

Sofya Vasilievna at the same time was a wonderful fiction writer. Her autobiographical "Childhood Memories", the novel "Nihilist" and excerpts from unfinished or lost stories provide an interesting picture of social and political life Russia of the second half of the 19th century. Critics noted that from the pages of her stories “there is a whiff of Turgenev.” She also wrote, together with the Swedish writer Mittag-Leffler, an interesting drama “The Struggle for Happiness,” the only work in world literature written according to a mathematical plan.

S.V. Kovalevskaya, in addition to her scientific and literary merits, has an exceptional place in the history of the struggle for women's equality. She repeatedly says in her letters that her success or failure is not only her personal matter, but is related to the interests of all women. Therefore, she was extremely demanding of herself. In one of her poems she writes:

“A lot will be demanded from that person, to whom many talents were given!”

Sofya Vasilyevna realized that she had been given many talents, that she had invested them in the cause of all women, and that a lot would be asked of her. When Sofya Vasilievna in the eighties sought recognition of her academic rights in Russia, the Tsar’s minister replied that Mrs. Kovalevskaya and her daughter would not live to see the time when a woman in Russia would gain access to a professorial chair.

The royal ministers were not only bad politicians, but also bad prophets. Sofia Vasilievna’s daughter, doctor Sofya Vladimirovna Kovalevskaya, who died in 1952 in Moscow, lived for 35 years under Soviet rule, when all fields of activity were open to women.

Before Sofia Vasilievna Kovalevskaya, the history of mathematical sciences knows only a few women mathematicians. These are: the Greek Hypatia in Alexandria, torn to pieces in the year 415 by a crowd of Christians, excited by the agitation of monks who feared the influence of the beautiful and learned pagan Hypatia on the head of the city; Marquise du Chatelet (1706-1749), translator of Newton's works into French"; she studied historical sciences from Voltaire and taught Voltaire mathematical ones; her biography notes that for both of them this teaching turned out to be ineffective; professor of mathematics at the University of Bologna, Italian Maria Agnesi (1718 -1831). The name of which is borne in higher mathematics by the curved line of Agnesi's curl"; the Frenchwoman Sophia Germain (1776-1831), whose name is found in number theory and higher analysis, the Frenchwoman Hortense Lenot (1723-1788), a famous calculator, whose name is the name of the hydrangea flower, brought from on India.

There are many women professors of mathematics in the Soviet Union, among whom we can mention such outstanding professors as Vera Iosifovna Schiff (died in 1918), Nadezhda Nikolaevna Gernet (1876-1943), Ekaterina Alekseevna Naryshkina (1895-1940), a friend of S. V. Kovalevskaya Elizaveta Fedorovna Litvinova (1845-1918), and many living ones. At the same time, one cannot but agree with Corresponding Member of the USSR Academy of Sciences, Doctor of Physical and Mathematical Sciences Pelageya Yakovlevna Polubarinova-Kochina that “Kovalevskaya surpassed her predecessors in talent and the significance of the results obtained. At the same time, she determined the general level of women who strived for science in her time." S. V. Kovalevskaya remains for all times the pride of Russian science.

Scientific activity

The most important studies relate to the theory of rotation of a rigid body. Kovalevskaya discovered the third classical case of solvability of the problem of the rotation of a rigid body around a fixed point. This advanced the solution of the problem begun by Leonhard Euler and J.L. Lagrange.

She proved the existence of an analytical (holomorphic) solution to the Cauchy problem for systems of partial differential equations, studied the Laplace problem on the equilibrium of the ring of Saturn, and obtained a second approximation.

Solved the problem of reducing a certain class of Abelian integrals of the third rank to elliptic integrals. She also worked in the field of potential, mathematical, and celestial mechanics.

In 1889 she received a major prize from the Paris Academy for her research on the rotation of a heavy asymmetrical top.

The most famous of Kovalevskaya’s mathematical works are: “Zur Theorie der partiellen Differentialgleichungen” (1874, “Journal f ü r die reine und angewandte Mathematik", volume 80); "Ueber die Reduction einer bestimmten Klasse Abel scher Integrale 3-ten Ranges auf elliptische Integrale” (“Acta Mathematica”, 4); "Zus ä tze und Bemerkungen zu Laplace s Untersuchung ü ber die Gestalt der Saturnsringe" (1885, "Astronomische Nachrichten", vol. CXI); “Ueber die Brechung des Lichtes in cristallinischen Medien” (“Acta mathematica” 6.3); "Sur le probl è me de la rotation d un corps solide autour d un point fixe" (1889, "Acta mathematics", 12.2); "Sur une propri é t é du syst è me d equations differentelles qui definit la rotation d un corps solide autour d un point fix e" (1890, "Acta mathematica", 14.1). Abstracts about mathematical works were written by A. G. Stoletov, N. E. Zhukovsky and P. A. Nekrasov in “ Mathematical Collection", volume XVI published separately (M., 1891).

A system of partial differential equations with unknown functions u1,u2,...,uN of the form

Niui(x,t)?tni=Fi(t,x,ui,...,uN,...,?auj?ta0?xa11...?xann,...),

where x=(x1,...,xn) , a=a0+a1+...+an , a?nj , a0?nj?1 , i,j=1,...,N , that is, the number of equations equal to the number of unknowns, is called the Kovalevskaya system. The independent variable t is distinguished by the fact that among the derivatives of the highest order ni of each function of the system there is a derivative with respect to t of order ni and the system is resolved with respect to these derivatives.

The following notation is used:

Yes? ?ki(x)=?a?? ki(x)?xa11...?xann,

where a?=a0+a1+...+an , ai?0 , i=1,...,N

Formulation:

If all functions ?ki(x) are analytic in a neighborhood of the point x0=(x01,...,x0n), and the functions Fi are defined and analytic in a neighborhood of the point (t0,x01,...,x0n, ?ki(x0),...,Da? ?ki(x0),...), then the Cauchy problem has an analytical solution in a certain neighborhood of the point (t0,x01,...,x0n), which is unique in the class of analytical functions.

Kovalevskaya's theorem on the existence of analytical (that is, representable in the form of power series) solutions of partial differential equations finds numerous applications in all the most important sections of the modern theory of differential equations and related areas of mathematics. Its use is essential in the proofs of many important and difficult theorems.

Formulation of the Cauchy-Kovalevskaya theorem for the simplest ordinary differential equation with the initial condition (0) = 0.

If the function f (x, y) is an analytic function of x and y in a neighborhood of the point (0, 0), then there is a unique analytic solution y(x) of equation (1) in some neighborhood of the point x = 0, satisfying the initial condition (2) .

The proof of a similar theorem for a differential equation of any order and for a system of such equations was carried out by O. Cauchy using the majorant method. Using the example of problem (1), (2), the majorant method is as follows. The function f (x, y) in equation (1) is replaced by a majorant, that is, an analytical function F (x, y), the coefficients of the power series expansion of which are non-negative and not less than the absolute values ​​of the corresponding power series expansion coefficients of the function f (x, y) . The majorant is chosen as simple as possible so that equation (1) can be integrated explicitly, that is, from the explicit form of the solution y(x) of the problem, the convergence of the corresponding power series would follow, which is obviously a majorant for solving problem (1), (2 ). Cauchy used majorants of the form, which led to cumbersome calculations. S.V. Kovalevskaya, apparently, did not know these works by Cauchy; there are no references to them in her works (it is interesting to note that Cauchy is the author of 789 published works, not counting several voluminous monographs). At the beginning of her work, she gives formulations of theorems for the existence of analytical solutions of ordinary differential equations and notes that they are taken from the lectures of “the respected teacher Mr. Weierstrass.” S.V. Kovalevskaya in her work proved a theorem about the existence of an analytical solution that satisfies the given initial conditions, first for a quasilinear system of first-order partial differential equations, and then for a general nonlinear system of any order of normal form by reducing it to a quasilinear system. The famous French mathematician A. Poincaré (1854-1912) wrote: “Kovalevskaya significantly simplified the proof and gave the theorem its final form.” To prove S.V. Kovalevskaya applied the majorant method using majorants of the form.

Kovalevskaya's theorem is used where it is necessary to construct asymptotic solutions, that is, solutions that satisfy the equation only with a certain accuracy. Such solutions are used, for example, in establishing the necessary conditions for the correctness of the Cauchy problem for hyperbolic equations with multiple characteristics - this is a question that last years attracted the attention of many researchers. The Cauchy-Kovalevskaya theorem and its modifications play a major role in questions in the theory of hyperfunctions related to solvability linear equations with partial derivatives. Any hyperfunction can be represented as a sum of boundary values ​​of analytical functions. The basic scheme for solving equations in hyperfunctions is as follows: 1) the right-hand sides, initial and boundary functions are represented as sums of boundary values ​​of analytical functions; 2) in analytical functions the solution is found by applying the Cauchy-Kovalevskaya theorem; 3) to obtain a solution in hyperfunctions, the boundary values ​​of the obtained analytical solution are taken. Spend two last stage It doesn't always work out. It is interesting to note that the French mathematicians J.-M. Boni and P. Shapirz proved a theorem on the existence of a solution to the Cauchy problem in the class of hyperfunctions for hyperbolic equations with characteristics of arbitrary multiplicity. This fact does not hold in the class of generalized functions.

Thus, Kovalevskaya’s theorem has a deep and, in a certain sense, complete character. Weierstrass wrote to Dubois-Reymond in 1874 regarding the dissertation of S.V. Kovalevskaya: “In the dissertation in question, I (apart from correcting numerous grammatical errors) did not take any other part than setting the task for the author. And in this regard, I should also note that I, in fact, , did not expect a different result compared to what is known from the theory of ordinary differential equations. I was, in order to remain in the simplest case, of the opinion that a power series in many variables, formally satisfying a partial differential equation, must also always be convergent within a certain region and must, therefore, represent a function that actually satisfies the differential equation. That this is not the case, as you can see from the example of an equation considered in the dissertation, was discovered, to my great amazement, by my student completely independently, and, moreover, first for much more complex differential equations , than given, so that she even doubted the possibility of obtaining a general result; seeming like this simple means which she found to overcome the difficulty thus arising, I highly valued as proof of her correct mathematical instinct." Kovalevskaya's theorem finds important and significant applications in research on the theory of partial differential equations, carried out until recently, and subtle modern research increasingly reveal its deep and complete character.

Memory of S.V. Kovalevskaya

· Kovalevskaya (lat. Kovalevskaya) - lunar crater; The name was approved by the International Astronomical Union in 1970.

· In memory of S. Kovalevskaya, the minor planet (1859) Kovalevskaya, discovered by the astronomer of the Crimean Astrophysical Observatory Lyudmila Zhuravleva on September 4, 1972, was named.

· Gymnasium named after S.V. Kovalevskaya - educational institution in the city of Velikie Luki (Russia), founded in 1958. It has had the honorary name “named after S.V. Kovalevskaya” since 2000.

· Secondary school named after Sofia Kovalevskaya in Vilnius (lit. Vilniaus Sofijos Kovalevskajos vidurin? mokykla ) - 49th secondary school in Vilnius (Lithuania) opened on September 1, 1980. In 1998, the school was named after Sofia Kovalevskaya.

· Sofia Kovalevsky School (Swedish: Sonja Kovalevsky-skolan) is the former name of the Metapontum secondary school (gymnasium) (Swedish: grundskolan Metapontum) in Stockholm (Sweden), founded in 1996

· Kovalevskaya Street and Sofia Kovalevskaya Street are street names in many cities of the former USSR.

Kovalevskaya mathematician scientist professor

Literature

1.Polubarinova-Kochina P.Ya. Sofya Vasilievna Kovalevskaya. 1850-1891: Her life and work. - M.: Gostekhizdat, 1955. - 100 p. - (People of Russian science).

2. “Mathematicians, mechanics” - biographical reference book. M., 1983.

Malinin V.V. Sofia Kovalevskaya is a female mathematician. Her life and scientific activities. - CIT SSGA, 2004.

When writing this article, material from Encyclopedic Dictionary Brockhaus and Efron (1890-1907).

Kochin P.Ya. Sofya Vasilievna Kovalevskaya. - Moscow: Science, 1981. - P. 7.8. - 312 s.

L.A. Vorontsova. Sofya Kovalevskaya: Life of wonderful people. Young Guard, 1959. Pp. 266.

7.Kovalevskaya S.V. “Memoirs and Letters” - M.: Publishing House of the USSR Academy of Sciences, 1951.

Tutoring

Need help studying a topic?

Our specialists will advise or provide tutoring services on topics that interest you.
Submit your application indicating the topic right now to find out about the possibility of obtaining a consultation.