Years of life of Sophia Kovalevsky. Kovalevskaya Sofia Vasilievna Increasing the natural gift...

In the history of mankind before Kovalevskaya there was no woman,
equal to her in strength and originality of mathematical talent.

S.I. Vavilov

Sofia Vasilievna Kovalevskaya (January 15, 1850 - February 10, 1891) - Russian mathematician and mechanic, since 1889 a foreign corresponding member of the St. Petersburg Academy of Sciences. The first in Russia and in Northern Europe a female professor and the world's first female professor of mathematics (Maria Agnesi, who previously received this title, never taught).

Sofya Kovalevskaya (née Korvin-Krukovskaya) was born in Moscow, where her father, artillery general Vasily Korvin-Krukovskiy, served as head of the arsenal. Mother, Elisabeth Schubert, was 20 years younger than her father. Subsequently, Kovalevskaya spoke about herself: “I inherited a passion for science from my ancestor, the Hungarian king Matvei Korvin; love for mathematics, music, poetry - from maternal grandfather, astronomer Schubert; personal freedom - from Poland; from a gypsy great-grandmother - a love of vagrancy and an inability to obey accepted customs; the rest is from Russia.”

When Sonya was six years old, her father retired and settled in his family estate Polibino, in the Vitebsk province. The girl was hired by a teacher for classes. The only subject in which Sonya showed neither special interest nor abilities in the first lessons was arithmetic. However, the situation gradually changed. The study of arithmetic lasted up to ten and a half years. Subsequently, Sofya Vasilievna believed that this period of study just gave her the basis of mathematical knowledge.

The girl knew all arithmetic so well, she solved the most difficult problems so quickly that the teacher allowed her to study Bourdon's two-volume arithmetic course, which was used at that time at the University of Paris, before algebra.

Kovalevskaya's first teacher higher mathematics there was a wall. Do not be surprised, the most ordinary wall of a children's room, pasted over with yellowed sheets of the lithographed course of higher mathematics by M.V. Ostrogradsky, according to which his father himself, now a retired artillery general, once studied. Sofa stood for a long time at this mysterious wall, trying to make out the symbols of higher mathematics, the language of differential and integral calculus, unknown to her. She revealed their content in her own way and memorized them on long years. To understand some of the formulas, she needed trigonometry, which she comprehended on her own from the textbook of physics by N. P. Tyrtov, donated to her father by the author himself.

Professor Tyrtov was a frequent and welcome guest of the retired general. Once he noticed how young Sofa was sitting for a long time at his physics textbook, trying to understand and comprehend something.

Sofochka, - he once said, - this book is not for you. It can be comprehended only by knowing trigonometry, which you and your home teacher did not pass.

And yet I know trigonometry, - unexpectedly for the professor, Sofa said.

Trigonometry, as I understand it, she continued, is the science of solving triangles. Its main quantities are sine cosine, tangent, cotangent, secant and cosecant. The sine, for example, can be considered as half the chord of some arc...

Well done Sophie! And who told you all this? asked the surprised professor.

I came to all this with my own thoughts, reading your physics textbook, where you use ready-made trigonometry formulas at every step.

The astonished professor's admiration knew no bounds. He immediately rushed into the general's office and loudly declared that his daughter was a genius, that she could only be compared with Pascal, that her element was mathematics, that such a talent should be protected and developed in every possible way.

Sophia's father, who himself loved mathematics, warmly accepted the words of his friend, and soon Sophia began to take lessons from the famous teacher A.N. Stranolyubsky.

Strannolyubsky, at the first lesson in differential calculus, was surprised at the speed with which Sonya mastered the concept of the limit and the derivative, "as if she knew everything in advance." And the girl, in fact, during the explanation, suddenly clearly remembered those sheets of Ostrogradsky's lectures, which she examined on the wall of the nursery.

In 1863, at the Mariinsky Women's Gymnasium, pedagogical courses were opened with departments of natural-mathematical and verbal. The Krukovsky sisters were eager to go there to study. They were not embarrassed that for this it was necessary to enter into a fictitious marriage, since the unmarried were not accepted. They were looking for a candidate for husbands among the raznochintsy and impoverished nobles.

Vladimir Onufrievich Kovalevsky was found as a "groom" for Anyuta. And it had to happen that on one of the dates he told Anyuta that, of course, he was ready to marry, but only ... with Sofia Vasilievna. Soon he was introduced into the general's house and, with his consent, became Sophia's fiancé. He was 26 years old, Sophia - 18.

On September 15, 1868, a wedding took place in a village church near Polibino. And soon in St. Petersburg, Sophia began to attend lectures. The girl soon realized that only mathematics should be studied, and if now, in her youth, one does not devote herself exclusively to her beloved science, one can irreparably lose time! And Kovalevskaya, having passed the matriculation exam, again returned to Strannolyubsky in order to study mathematics more thoroughly before going abroad.

On April 3, 1869, the Kovalevskys and Anyuta left for Vienna. But Sophia did not find good mathematicians in Vienna. Kovalevskaya decided to try her luck in Heidelberg, which was portrayed in her dreams as the promised land of students.

After all sorts of delays, the university commission did allow Sophia to listen to lectures on mathematics and physics. During three semesters 1869/1870 school year she listened to a course in the theory of elliptic functions from Koenigsberger, physics and mathematics from Kirchhoff, Dubois-Reymond and Helmholtz, worked in the laboratory of the chemist Bunsen - the most famous scientists in Germany.

Professors admired her ability to grasp and assimilate material on the fly. Working with an intensity that amazed everyone, she quickly mastered the initial elements of higher mathematics, opening the way to independent research. At the lectures, she heard Professor Koenigsberger's enthusiastic praise of his teacher, the greatest mathematician at that time, Karl Weierstrass, who was called "the great analyst from the banks of the Spree."

In the name of her higher appointment, as she understood it, Sofya Vasilievna overcame her shyness and on October 3, 1870 went to Weierstrass in Berlin. Wishing to get rid of the annoying visitor, Professor Weierstrass offered her several tasks on hyperbolic functions to test her knowledge from the category of those, even somewhat more difficult, that he gave to the most successful students of the Faculty of Mathematics, and asked her to come next week.

In truth, Weierstrass managed to forget about the visit of the Russian, when exactly a week later she again appeared in his office and announced that the tasks had been solved!

Weierstrass was struck by the speed and originality of mathematical thinking, and the professor began to petition the academic council of the university to let her attend lectures. But the advice was relentless. Then Weierstrass decided to study with a talented woman himself, to pass on to her the content of the lectures he gave to university students.

In less than 4 years from the autumn of 1870 to the spring of 1870, Kovalevskaya learned a university course in mathematics, acquired such mathematical training that Weierstrass could compare few of his students with her in mathematical education. Usually Weierstrass overwhelmed his listeners with his mental superiority, but the lively inquisitive mind of the young Kovalevskaya demanded increased activity from the old professor. Weierstrass often had to take on the solution of various problems himself in order to adequately answer the difficult questions pupils.

“We should be grateful to Sofya Kovalevskaya,” contemporaries said, “for bringing Weierstrass out of a state of isolation.”

She studied the latest mathematical works of world scientists, did not even bypass the dissertations of her teacher's young students.

Kovalevskaya wrote her first independent work - "On the reduction of a certain class of Abelian integrals of the third rank to elliptic integrals." The famous French mathematician, physicist and astronomer Laplace, in his work “Celestial Mechanics”, considering the ring of Saturn as a collection of several thin liquid rings that do not affect one another, determined that its cross section has the shape of an ellipse. But this was only the first, very simplified solution. Kovalevskaya set out to investigate the question of the equilibrium of the ring with greater accuracy. She found that the cross section of Saturn's ring should be oval in shape.

Sophia soon decided to do another study in the field of differential equations. It concerned the most difficult field of pure mathematical analysis, which at the same time is of great importance for mechanics and physics.

Kovalevskaya devoted the winter of 1873 and the spring of 1874 to the study "On the Theory of Partial Differential Equations". She wanted to present it as a doctoral dissertation. The work of Kovalevskaya aroused the admiration of scientists. True, later, it was established that a similar work, but of a more private nature, had been written by the famous French scientist Augustin Cauchy even earlier than Kovalevskaya.

In her dissertation, she gave the theorem a perfect form in terms of accuracy, rigor, and simplicity. The problem began to be called "the Cauchy-Kovalevskaya theorem", and it was included in all the main courses of analysis. Of great interest was the analysis given in it of the simplest equation (the equation of heat conduction), in which Sofya Vasilievna discovered the existence of special cases, thereby making a discovery significant for her time. Her short years of apprenticeship were over.

The Council of the University of Göttingen awarded Kovalevskaya a PhD in mathematics and a Master of Fine Arts "with the highest praise".

In 1874, Kovalevskaya returned to Russia, but here the conditions for doing science were much worse than in Europe. By this time, Sophia's fictitious marriage "became real." At first in Germany, she and her husband even lived in different cities and studied at different universities, exchanging only letters. But then other relationships began.

In the autumn of 1878, a daughter was born to the Kovalevskys. Kovalevskaya spent almost six months in bed. The doctors lost hope of saving her. True, the young organism won, but Sophia's heart was struck by a serious illness.

There is a husband, there is a child, there is a favorite pastime - science. It seems to be a complete set for happiness, but Sophia was a maximalist in everything and demanded too much from life and from those around her. She wanted her husband to constantly swear his love to her, show signs of attention, but Vladimir Kovalevsky did not do this. He was just another person, passionate about science no less than his wife.

Jealousy was one of the strongest shortcomings of Kovalevskaya's impulsive nature. The complete collapse of their relationship came when the spouses did not do their job - commerce, in order to ensure their material well-being.

“My duty is to serve science,” Kovalevskaya told herself. There was no reason to expect that Russia would allow her to do so. After the assassination of Alexander II, the time for liberal flirting ended, and unbridled reaction began, executions, arrests and exile. The Kovalevskys hastily left Moscow. Sofya Vasilievna and her daughter went to Berlin, and Vladimir Onufrievich went to his brother in Odessa. Nothing connected them anymore.

In the room where Kovalevskaya worked, now there was also little Sonya - Fufa, as she called her. It was necessary to show great courage in order to take on the task, to the solution of which the greatest scientists devoted themselves: to determine the movement of various points of a rotating solid body- gyroscope.

Vladimir Onufrievich finally got confused in his financial affairs and committed suicide on the night of April 15-16, 1883. Kovalevskaya was in Paris (she was elected a member of the Paris Mathematical Society) when she learned about her husband's suicide.

In early July, Sofya Vasilievna returned to Berlin. She was still weak after the shock, but inwardly quite collected. Weierstrass met her very cordially, asked her to live with him "as a third sister."

Upon learning of the death of Kovalevsky, who objected to his wife's plans to make mathematics a matter of life, Weierstrass wrote to his colleague, the prominent Swedish mathematician Mittag-Leffler, that "now, after the death of her husband, there are no more serious obstacles to the fulfillment of his student's plan - to take a professorship in Stockholm,” and was able to please Sophia with a favorable response from Sweden.

Sweden was waiting for Kovalevskaya. Newspapers wrote: “Our city was honored by the visit of the princess of science - Mrs. Kovalevskaya. She will be the first female Privatdozent in all of Sweden.”

On January 30, 1884, Kovalevskaya gave her first lecture at Stockholm University, after which the professors rushed to her, noisily thanking her and congratulating her on a brilliant start.

The course read by Kovalevskaya in German was private nature but he made her an excellent reputation. Late in the evening of June 24, 1884, Kovalevskaya learned that she had "been appointed professor for a term of five years."

As a professor at Stockholm University, Kovalevskaya taught students more than 10 different mathematical courses. Its popularity grew rapidly. She fascinated everyone with her simplicity of handling, grace, wit, brought a revival to Swedish society. Sofia Vasilievna loved sports, took part in horseback riding and skating. But her main business, for which she came to Sweden, was the teaching of higher mathematics.

Kovalevskaya went deeper and deeper into the study of one of the most difficult problems of the rotation of a rigid body. “A new mathematical work,” wrote Kovalevskaya, “is of keen interest to me now, and I would not want to die without discovering what I am looking for. If I succeed in solving the problem with which I am concerned, then my name will be listed among the names of the most eminent mathematicians. According to my calculation, I need another five years in order to achieve good results.

In the spring of 1886, Kovalevskaya received news of the serious illness of her sister Anyuta. She went to Russia and with a heavy feeling returned to Stockholm. Nothing could return to the previous work. Kovalevskaya found a way to talk about herself, her feelings and thoughts, and used it with passion. Together with the writer Anna-Charlotte Edgren-Leffler, she begins to write. Captured by literary work, Kovalevskaya was no longer able to deal with the problem of the rotation of a rigid body around a fixed point.

Kovalevskaya had many friends, mostly in literary circles, but in her personal life she remained lonely. Ideal relationship Sophia imagined this way: joint exciting work plus love. However, such harmony was difficult to achieve. Kovalevskaya was endlessly tormented by the realization that her work was a wall between her and the person to whom her heart should belong. Ambition prevented her from being just a loving woman.

In 1888, the "Princess of Science", as Kovalevskaya was called in Stockholm, nevertheless meets a person with whom she is trying to build a relationship similar to those she dreamed of. This person turns out to be a prominent lawyer and sociologist Maxim Kovalevsky, her namesake. Fate, as if on purpose, arranged such a coincidence.

The friendship of the two scientists soon turned into something resembling love. They were going to get married, but due to Sophia's increased demands, their relationship became so confused that the feeling, without having time to gain height, suffered a complete collapse.

Finally, Kovalevskaya returns to the problem of the rotation of a heavy rigid body around a fixed point, which is reduced to integrating a certain system of equations that always has three definite algebraic integrals. In those cases when it is possible to find the fourth integral, the problem is solved completely. Before the discovery of Sofya Kovalevskaya, the fourth integral was found twice - by the famous researchers Euler and Lagrange.

Kovalevskaya found a new one - the third case, and to it - the fourth algebraic integral. The complete solution was very complex. Only perfect knowledge of hyperelliptic functions allowed her to cope with the task so successfully. And until now, four algebraic integrals exist only in three classical cases: Euler, Lagrange and Kovalevskaya.

On December 6, 1888, the Paris Academy informed Kovalevskaya that she had been awarded the Borden Prize. In the fifty years that have passed since the establishment of the Borden Prize "for improvement in some important point in the theory of the motion of a rigid body," it has been awarded only ten times, and even then not completely, for particular solutions. And before the opening of Sophia Kovalevskaya, this prize was not awarded to anyone at all for three years in a row.

On December 12, she arrived in Paris. The president of the academy, astronomer and physicist Jansen, congratulated Kovalevskaya and said that due to the seriousness of the research, the prize at this competition had been increased from three to five thousand francs.

Scientists did not stint on applause. Sofya Vasilievna, somewhat stunned by her success, with difficulty mastered herself and uttered words of gratitude befitting the occasion.

Kovalevskaya settled near Paris, in Sevres, and instructed Mittag-Leffler to bring her daughter to her. Here she decided to continue additional research on the rotation of rigid bodies for the competition for the Swedish Academy of Sciences. By the beginning of the autumn semester at the university, Sofya Vasilievna returned to Stockholm. She worked with a kind of desperate determination, finishing her research. She had to have time to submit it to the competition. For this work, Kovalevskaya was awarded the Swedish Academy of Sciences the King Oscar II Prize of one thousand five hundred crowns.

Success did not please her. Not having time to truly rest, to receive treatment, she again tore her health. In this state, Sofya Vasilievna could not do mathematics and again turned to literature. Literary stories about Russian people, about Russia, Kovalevskaya tried to drown out her homesickness. After the scientific triumph that she had achieved, it became even more unbearable to wander in a foreign land. But there were no chances for a place in Russian universities.

A ray of hope flashed after November 7, 1889, Kovalevskaya was elected a corresponding member at the Physics and Mathematics Department of the Russian Academy of Sciences. P. L. Chebyshev informed Kovalevskaya about this by a special telegram.

In April 1890, Kovalevskaya left for Russia in the hope that she would be elected a member of the academy in place of the deceased mathematician Bunyakovsky and she would acquire that material independence that would allow her to engage in science in her country.

In St. Petersburg, Sofya Vasilievna twice visited the President of the Academy, Grand Duke Konstantin Konstantinovich, once had breakfast with him and his wife. He was very kind to the illustrious scientist and kept saying how good it would be if Kovalevskaya returned to her homeland. But when she wished, as a corresponding member, to attend a meeting of the academy, she was told that the presence of women at such meetings "is not in the customs of the academy."

A greater insult, a greater insult could not have been inflicted on her in Russia. Nothing has changed in the homeland after Kovalevskaya was awarded an academic title. She met her fortieth birthday as a very nervous and sick person: all the negative experiences and systematic overwork had an effect. She knew she was suffering from heart disease.

In 1891, on her way from Berlin to Stockholm, Sophia learned that a smallpox epidemic had begun in Denmark. Frightened, she decided to change the route. But apart from an open carriage, there was nothing to continue the journey, and she had to transfer to it. On the way Sophia caught a cold. The cold turned into pneumonia.

On February 10, 1891, without regaining consciousness, Sofya Kovalevskaya died of heart failure, at the age of forty-one, in her prime. creative life. Her cryptic last words: "Too much happiness." Kovalevskaya was buried in Stockholm, at the Northern Cemetery.

In 1896, with funds raised by Russian women and public organizations, a monument was erected on the grave of Sophia Kovalevskaya.

Fritz Leffler, who knew Sofya Kovalevskaya closely, wrote the following heartfelt lines on her death:

Goodbye! We sacredly honor you

Leaving your ashes in the grave.

Let the Swedish land over him

Lies lightly without overwhelming...

Goodbye! With your glory

You, forever parting with us,

You will live in the memory of people

With other glorious minds

As long as the wonderful starlight

From heaven to earth will pour

And in the host of shining planets

The ring of Saturn will not be eclipsed...

The name of Kovalevskaya is:

• gymnasium in Velikiye Luki (Russia)
• school in Stockholm (Sweden)
• many streets in the cities of the former USSR

In 2000, the Bank of Russia issued a 2-ruble silver commemorative coin dedicated to the 150th anniversary of the birth of S.V. Kovalevskaya.

The following mathematical objects bear the name of Kovalevskaya:

• Cauchy-Kovalevskaya theorem

Based on the materials of the book by D. Samin "100 great scientists", sites

Kovalevskaya Sofia Vasilievna was born on January 3, 1850 in Moscow. Her mother was Elisabeth Schubert. Father, General of Artillery Korvin-Krukovsky, at the time of the birth of his daughter, served as head of the arsenal. When the girl was six, he retired, settling in the family estate. Let us consider further, thanks to which Sofia Kovalevskaya is known.

Biography: childhood

After the whole family (parents and two daughters) settled in the father's family estate, the girl was hired by a teacher. The only subject in which the future professor of mathematics showed neither special interest nor any abilities was arithmetic. However, over time, the situation has changed dramatically. The study of arithmetic lasted up to 10 and a half years. Subsequently, Sofia Kovalevskaya believed that it was this period that gave her the basis of all knowledge. The girl studied the subject very well and quickly solved all the problems. Before starting algebra, her teacher Malevich allowed her to study Bourdon's arithmetic (a two-volume course that was taught at that time in one of the neighbors, noting the girl's successes, recommended her father to hire a lieutenant of the fleet Strannolyubsky to continue her education. The new teacher at the first lesson was surprised at the speed with which Sonya learned the limit.

Fictitious marriage

In 1863, pedagogical courses were opened at the Mariinsky Gymnasium, which included the verbal and natural-mathematical departments. Sisters Anna and Sophia dreamed of getting there. But the problem was that unmarried girls were not enrolled in the gymnasium. Therefore, they were forced to conclude a fictitious marriage. Vladimir Kovalevsky was chosen as Anna's fiancé. However, the wedding between them never took place. On one of the dates, he told Anna that he was ready to marry, but with her sister, Sonya. After some time, he was introduced into the house and became, with the consent of his father, the bridegroom of the second sister. At that time he was 26, and Sophia was 18 years old.

New life stage

No one then imagined what tasks Sofya Kovalevskaya would cope with after her wedding. The biography of her husband amazed with its fascination anyone who met him. He began to earn money at the age of 16, making translations of foreign novels for the merchants of Gostiny Dvor. Kovalevsky had an amazing memory, extraordinary activity and humanitarian abilities. He categorically refused official service, choosing publishing in St. Petersburg instead. It was he who printed and translated literature, which was extremely in demand by the progressive people of the country. Having moved with her husband and sister to St. Petersburg, Sofya Kovalevskaya secretly began to attend lectures. She decided to give all her strength only to science. The only thing that Sofia Kovalevskaya wanted to do was mathematics. Having passed the exam and received a matriculation certificate, she again returned to Strannolyubsky. With him, she began to study science in depth, planning to subsequently continue her activities abroad.

Education

In early April 1869, Sophia Kovalevskaya with her sister and husband left for Vienna. There were geologists needed then by Vladimir Onufrievich. However, there were no strong scientists in Vienna. Therefore, Kovalevskaya decides to go to Heidelberg. In her mind, it was the promised land for students. After overcoming a number of difficulties, the commission nevertheless allowed Sophia to listen to lectures on physics and mathematics. For three semesters, she attended the course of Koenigsberger, who taught the theory of elliptic functions. In addition, she listened to lectures on physics and mathematics by Kirchhoff, Helmholtz, Dubois Reymond, worked in the laboratory under the guidance of the chemist Bunsen. All these people were then in Germany. The teachers were amazed at the abilities that Kovalevskaya possessed. Sofia Vasilievna worked very hard. She quickly enough mastered all the initial elements that allowed her to start independent research. She received rave reviews about herself from Koenigsberger to his teacher, the greatest scientist of that time, Karl Weierstrass. The latter was called by contemporaries "the great analyst".

Working with Weierstrass

Sofya Kovalevskaya, in the name of her chosen higher destiny, overcame fear and shyness, and at the beginning of October 1870 went to Berlin. Professor Weierstrass was not in the mood for a conversation and, in order to get rid of the visitor, gave her several problems from the field of hyperbolic functions, inviting her in a week. Having managed to forget about the visit, the scientist did not expect to see Kovalevskaya at the appointed time. She appeared on the threshold and announced that all tasks had been solved. After a while, Weierstrass petitioned for Kovalevskaya to be allowed to listen to mathematical lectures. However, the consent of the high council could not be achieved. At the University of Berlin, not only did they not enroll women as students. They were not even allowed to attend lectures as free listeners. Therefore, Kovalevskaya had to confine herself to private studies with Weierstrass. As contemporaries noted, an outstanding scientist usually overwhelmed his listeners with mental superiority. But the inquisitiveness and craving for knowledge of Kovalevskaya demanded from Weierstrass increased activity. He himself often had to solve various problems in order to adequately answer the rather difficult questions of his student. Contemporaries noted that one should be grateful to Kovalevskaya for the fact that she was able to bring Weierstrass out of isolation.

First independent work

It explored the question of the balance of the ring of Saturn. Prior to Kovalevskaya, Laplace (a French astronomer, physicist and mathematician) dealt with this problem. In his work, he considered the ring of Saturn as a complex of several subtle elements that do not affect each other. During his research, he found that cross section it is presented in the form of an ellipse. However, this solution was only the first and very simplified. Kovalevskaya set about research to more accurately establish the balance of the ring. She determined that in cross section one should be presented in the form of an oval.

Thesis

From the beginning of the winter of 1873 to the spring of 1874, Kovalevskaya was engaged in the study of partial derivatives. She intended to present the work in the form of a doctoral dissertation. Her work was admired in scientific circles. A little later, however, it was found that Augustin Cauchy, an outstanding French scientist, had already carried out a similar study. But in her work, Kovalevskaya gave the theorem a form that is perfect in its simplicity, rigor, and accuracy. Therefore, the problem began to be called the "Koshi-Kovalevskaya theorem". It is included in all basic analysis courses. Of particular interest was the analysis of the heat equation. In the study, Kovalevskaya revealed the existence of special cases. It was a significant discovery for that time. This marked the end of her apprenticeship. The Council of the University of Göttingen awarded her the degree of Doctor of Mathematical Philosophy and Master of Fine Arts "with the highest praise".

Relationship with husband

In 1874 Sophia Kovalevskaya came back to Russia. However, at that time there were terrible conditions in her homeland, which could not in any way allow her to do science the way she wanted. By that time, a fictitious marriage with her husband had become real. The first time they were in Germany, they lived in different cities, received education in different institutions. Communication with her husband was carried out through letters. However, the relationship subsequently took a different form. In 1878, the Kovalevskys had a daughter. After her birth, Sophia spent about six months in bed. Doctors no longer hoped for a recovery. The body still won, but the heart was struck by a serious illness.

The collapse of the family

Kovalevskaya had a husband, a child, a favorite pastime. It would seem that this should have been enough for complete happiness. But Kovalevskaya was characterized by maximalism in everything. She constantly made high demands on life and on everyone around her. She wanted to constantly hear vows of love from her husband, she wanted him to show her signs of attention all the time. But Kovalevsky did not. He was a different person, just as passionate about science as his wife. A complete collapse in the relationship came when they decided to do business. However, despite this, Kovalevskaya remained faithful to science. But in Russia, she could not continue to work. After the assassination of the king, the situation in the country deteriorated sharply. Sophia and her daughter went to Berlin, and her husband went to Odessa, to her brother. However, Vladimir Onufrievich became very confused in his commercial affairs and on the night of April 15-16, 1883 he shot himself. Kovalevskaya was in Paris when she received the news. After the funeral, returning to Berlin, she went to Weierstrass.

Stockholm University

Weierstrass, having learned about the death of her husband Kovalevskaya, who had always interfered with Sophia's plans to make science the goal of her whole life, wrote to Mitgag-Leffler, his colleague. In the letter, he said that now nothing prevents the student from being able to continue her activities. Soon Weierstrass was able to please Kovalevskaya with a positive response from Sweden. On January 30, 1884, she gave her first lecture. The course that Kovalevskaya taught in German was of a private nature. Nevertheless, he made her an excellent recommendation. At the end of June 1884, she received the news that she had been appointed to the position of professor for 5 years.

New labor

More and more, the female professor went deeper into research work. Now she was studying one of the most difficult problems regarding the rotation of a rigid body. She believed that if she could solve it, then her name would be listed among the most prominent world scientists. According to her calculations, it took another 5 years to complete the task.

Writing activity

In the spring of 1886, Sofya Vasilievna received news of her sister's grave condition. She went home. Kovalevskaya returned to Stockholm with heavy feelings. In this state, she could not continue her research. However, she found a way to talk about her feelings, about herself, her thoughts. Literary work became the second important matter, which was handled by Sofia Kovalevskaya. The book she was writing at the time with Anna-Charlotte Edgren-Lefler so captivated her that she did not return to research during all this time.

Historic discovery

Having recovered from the shocks, Kovalevskaya again returns to scientific activity. She is trying to solve the problem of the rotation of a rigid heavy body around a static point. The problem is reduced to integrating a system of equations that always has three definite integrals. The problem is completely solved when the fourth one can be found. Before the discovery of Kovalevskaya, it was found twice. The scientists who investigated the problem were Lagrange and Euler. Kovalevskaya discovered the third case and the fourth integral to it. The solution in its entirety was rather complicated. Perfect knowledge of hyperelliptic functions helped to successfully cope with the task. And currently 4 algebraic integrals exist only in three cases: Lagrange, Euler and Kovalevskaya.

Borden Award

In 1888, on December 6, the Paris Academy sent a letter to Kovalevskaya. It said that she had been awarded the Borden Prize. It should be said that in the half century since its inception, only 10 people have become its owners. Moreover, all these ten times it was not awarded in full, but for separate, private decisions. Prior to the opening of Kovalevskaya, no one had been awarded this prize for three years in a row. A week after receiving the news, she arrived in Paris. The President of the Academy Jansen, an astronomer and physicist, warmly welcomed Sofya Vasilievna. He said that in view of the seriousness of her research, the prize had been increased from 3,000 to 5,000 francs.

Swedish Academy Award

After receiving the Borden Prize, Kovalevskaya settled near Paris. Here she continued her research on the rotation of bodies for the competition for the King Oscar II award from the Swedish Academy. In the autumn, at the beginning of the semester at the university, she returned to Stockholm. The work went very quickly. Kovalevskaya wanted to have time to complete her research in order to submit her work to the competition. For her work, she received a prize of one and a half thousand crowns.

Attempt to return to Russia

Despite the successes, Kovalevskaya was not pleased with anything. She went to treatment, but did not finish it. After a short period of time, her health deteriorated again. In this state, Kovalevskaya could not continue her research and again turned to the literature. She tried to drown out her longing for Russia with stories about people and her homeland. It was extremely unbearable for her to be in a foreign land. But, despite the overwhelming success, she did not have a chance to take a place in domestic universities. Hope appeared when, on November 7, 1888, she was elected a corresponding member of the Physics and Mathematics Department of the Russian Academy. In April 1890 she went home. Kovalevskaya hoped that she would be elected a member of the academy instead of the deceased Bunyakovsky. Thus, she could acquire material independence, which would contribute to the continuation of research in her country.

last years of life

In St. Petersburg, Kovalevskaya visited the president of the Russian Academy several times. Konstantinovich was always courteous and kind to her, saying that it would be great if she returned to her homeland. But when Kovalevskaya wanted to be present as a corresponding member at a meeting of the Academy, she was refused, because it was "not customary." She could not have been more insulted in Russia. In September, Kovalevskaya came back to Stockholm. On January 29, 1891, she died at the age of 41 from heart failure.

Conclusion

Kovalevskaya was outstanding person. She was extremely demanding of everything that surrounded her. This is not an ordinary Russian mathematician and mechanic, this is a great scientist who devoted all his strength to science. It is sad to realize that in Russia at that time she was not given due attention, her merits were not recognized, despite her high popularity in scientific circles abroad. Not far from Velikiye Luki is the Museum of Sofia Kovalevskaya. Polibino was hers small homeland, the place where her craving for science manifested itself.

Scientific activity

Literary activity

Printed publications

(nee Korvin-Krukovskaya) (January 3 (15), 1850, Moscow - January 29 (February 10), 1891, Stockholm) - Russian mathematician and mechanic, since 1889 a foreign corresponding member of the St. Petersburg Academy of Sciences. The first female professor in Russia and Northern Europe and the first female professor of mathematics in the world (Maria Agnesi, who previously received this title, never taught).

Biography

Daughter of Lieutenant General of Artillery V. V. Korvin-Krukovsky and Elizaveta Fedorovna (maiden name - Schubert). Grandfather Kovalevskaya, Infantry General F.F. Schubert, was an outstanding mathematician, and great-grandfather F.I. Schubert was an even more famous astronomer. Born in Moscow in January 1850. Kovalevskaya spent her childhood years on the estate of Polibino's father, Nevelsky district, Vitebsk province (now the village of Polibino, Velikoluksky district, Pskov region). The first lessons, in addition to governesses, were given to Kovalevskaya from the age of eight by a home tutor, the son of a small-scale gentry Iosif Ignatievich Malevich, who placed memories of his student in Russian Antiquity (December 1890). In 1866, Kovalevskaya traveled abroad for the first time, and then lived in St. Petersburg, where she took lessons in mathematical analysis from A. N. Strannolyubsky.

The admission of women to higher educational institutions in Russia was prohibited. Therefore, Kovalevskaya could continue her studies only abroad, but it was possible to issue a foreign passport only with the permission of her parents or husband. The father was not going to give permission, because he did not want to further educate his daughter. Therefore, Sophia organized a fictitious marriage with a young scientist V.O. Kovalevsky. True, Kovalevsky did not suspect that he would eventually fall in love with his fictitious wife.

In 1868, Kovalevskaya married Vladimir Onufrievich Kovalevsky, and the newlyweds went abroad.

In 1869 she studied at the University of Heidelberg with Koenigsberger, and from 1870 to 1874 at the University of Berlin with K. T. W. Weierstrass. Although, according to the rules of the university, she could not listen to lectures as a woman, Weierstrass, interested in her mathematical talents, led her classes.

She sympathized with the revolutionary struggle and the ideas of utopian socialism, so in April 1871, together with her husband V. O. Kovalevsky, she arrived in besieged Paris, cared for the wounded Communards. Later, she took part in the rescue from prison of the leader of the Paris Commune V. Jaclar, the husband of her revolutionary sister Anna.

Sophia's emancipated friends demanded that the fictitious marriage not develop into a real one, and therefore her husband had to move to another apartment, and then to another city altogether. This situation weighed heavily on both, and in the end, in 1874, a fictitious marriage became an actual one.

In 1874, the University of Göttingen awarded Kovalevskaya a Ph.D.

In 1878, a daughter was born to the Kovalevskys.

In 1879 she made a presentation at the VI Congress of Naturalists in St. Petersburg. In 1881 Kovalevskaya was elected a member of the Moscow Mathematical Society (Private Associate Professor).

After her husband's suicide (1883) (tangled in his commercial affairs), Kovalevskaya, left without funds with her five-year-old daughter, arrives in Berlin and stops at Weierstrass. At the cost of enormous efforts, using all his authority and connections, Weierstrass manages to secure a place for her at Stockholm University (1884). Having changed her name to Sonya Kovalevsky, she becomes a professor of mathematics at the University of Stockholm (Högskola), with the obligation to lecture the first year in German, and the second year in Swedish. Soon Kovalevskaya masters the Swedish language and publishes her mathematical works and fiction in this language.

In 1888 - winner of the Paris Academy of Sciences for the discovery of the third classical case of the solvability of the problem of the rotation of a rigid body around a fixed point. The second work on the same topic in 1889 was awarded the prize of the Swedish Academy of Sciences, and Kovalevskaya was elected a corresponding member of the Physics and Mathematics Department of the Russian Academy of Sciences.

In 1891, on her way from Berlin to Stockholm, Sophia learned that a smallpox epidemic had begun in Denmark. Frightened, she decided to change the route. But apart from an open carriage, there was nothing to continue the journey, and she had to transfer to it. On the way Sophia caught a cold. The cold turned into pneumonia.

On January 29, 1891, Kovalevskaya died at the age of 41 in Stockholm from pneumonia. She died in the Swedish capital all alone, without a single close person nearby. She was buried in Stockholm, at the Northern Cemetery.

Scientific activity

The most important research concerns the theory of rigid body rotation. Kovalevskaya discovered the third classical case of the 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 of the Cauchy problem for systems of differential equations with partial derivatives, investigated the Laplace problem on the equilibrium of the Saturn ring, obtained the 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 theory, mathematical physics, celestial mechanics.

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

Of the mathematical works of Kovalevskaya, the most famous are: "Zur Theorie der partiellen Differentialgleichungen" (1874, "Journal für 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); "Zusätze 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 problème de la rotation d'un corps solide autour d'un point fixe" (1889, Acta Mathematica, 12.2); "Sur une propriété du système d'equations differentielles 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 the Mathematical Collection, vol. XVI, published and separately (Moscow, 1891).

Literary activity

Thanks to her outstanding mathematical talents, Kovalevskaya reached the heights of the scientific field. But the nature is lively and passionate, she did not find satisfaction in abstract mathematical research and manifestations of official glory alone. First of all, a woman, she always craved intimate affection. In this regard, however, fate was not very favorable to her, and it was precisely the years of her greatest glory, when the award of the Paris Prize to a woman drew the attention of the whole world to her, that were for her years of deep spiritual anguish and broken hopes for happiness. Kovalevskaya passionately treated everything that surrounded her, and with subtle observation and thoughtfulness, she had a great ability to artistically reproduce what she saw and felt. Literary talent awakened in her late, and premature death did not allow her to sufficiently determine this new side wonderful, profoundly and versatilely educated woman. In Russian, from the literary works of K. appeared: “Memories of George Elliot” (“Russian Thought”, 1886, No. 6); family chronicle "Childhood Memories" ("Bulletin of Europe", 1890, No. 7 and 8); “Three days at a peasant university in Sweden” (“Northern Herald”, 1890, No. 12); posthumous poem ("Bulletin of Europe", 1892, No. 2); together with others (translated from the Swedish story “Vae victis”, an excerpt from the novel in the Riviera), these works were published as a separate collection under the title: “Literary Works of S. V. K.” (St. Petersburg, 1893).

Memoirs about the Polish uprising and the novel The Vorontsov Family were written in Swedish, the plot of which refers to the era of unrest among Russian youth in the late 60s of the 19th century. But of particular interest in characterizing Kovalevskaya's personality is "Kampen för Lyckan, tvänne paralleldramer of K. L." (Stockholm, 1887), translated into Russian by M. Luchitskaya, under the title: “The Struggle for Happiness. Two parallel dramas. The work of S. K. and A. K. Leffler ”(Kyiv, 1892). In this double drama, written by Kovalevskaya in collaboration with the Swedish writer Leffler-Edgren, but entirely according to Kovalevskaya's thought, she wanted to depict the fate and development of the same people from two opposite points of view, "how it was" and "how it could be ". Kovalevskaya put a scientific idea at the basis of this work. She was convinced that all the actions and actions of people are predetermined in advance, but at the same time she recognized that there may be such moments in life when various opportunities for certain actions are presented, and then life develops in different ways, in accordance with the which path will be chosen.

Kovalevskaya based her hypothesis on the work of A. Poincare on differential equations: the integrals of the differential equations considered by Poincare are, from a geometric point of view, continuous curved lines that branch only at some isolated points. The theory shows that the phenomenon flows along a curve to the place of bifurcation (bifurcation), but here everything becomes uncertain and it is impossible to foresee in advance which of the branches the phenomenon will continue to flow (see also Catastrophe theory (mathematics)). According to Leffler (her memoirs of Kovalevskaya in the Kiev Collection to Help Those Affected by Harvest Failure, Kyiv, 1892), in the main female figure of this double drama, Alice, Kovalevskaya depicted herself, and many of the phrases uttered by Alice, many of her expressions were taken entirely from the own lips of Kovalevskaya herself. Drama proves the omnipotent power of love, which requires that lovers give themselves completely to each other, but it is everything in life that only gives it brilliance and energy.

Printed publications

• Kovalevskaya S.V. "Scientific works" - M .: Publishing house of the USSR Academy of Sciences, 1948.
• Kovalevskaya S. V. "Memoirs and letters" - M .: Publishing house of the USSR Academy of Sciences, 1951.
• Kovalevskaya S. V. “Memories. Tales "- M .: Nauka, 1974. - ("Literary monuments")
• Kovalevskaya S. V. “Memories. Tales" - M.: Pravda Publishing House, 1986.

Family (notable representatives)

• Great-grandfather - F. I. Schubert, astronomer
• Grandfather - F. F. Schubert, surveyor, mathematician
• Father - V. V. Korvin-Krukovsky, General
• Husband - V. O. Kovalevsky, geologist and paleontologist
• Sister - Anna Jacquelar, revolutionary and writer
• Brother - F. V. Korvin-Krukovsky, General

Memory

• Kovalevskaya (crater)
• Sofia Kovalevskaya School
• Kovalevskaya street
• Sofia Kovalevskaya Street (St. Petersburg)

To the cinema

• 1956 - "Sofya Kovalevskaya" (film-play, dir. Iosif Shapiro)
• 1985 - "Sofya Kovalevskaya" (TV film, dir. Ayan Shakhmaliyeva)
• 2011 - "Dostoevsky" (7-episode TV movie) - Elizaveta Arzamasova

She was born on 01/3/15/1850 in the family of a general, at the time of the birth of her second daughter, the military man was already retired. Sophia's maiden name is Korvin-Krukovskaya.

The family was quite wealthy. Sophia Vasilievna had good genes, her maternal ancestors were scientists. Grandfather was a member. A great-grandfather - a famous astronomer and mathematician. So it’s not worth being surprised that Sofya Vasilyevna became a famous scientist.

Until the age of 18, Sophia lived in the Palibino estate. This estate was located near the town of Velikiye Luki. Kovalevskaya received an excellent home education under the strict guidance of talented teachers.

In the 60s of the 19th century, various Western teachings and morals are increasingly penetrating. At this time, it became fashionable to leave home, to be independent.

Sophia, they say, did not have a relationship with her parents. She was the second child in the family, her parents were expecting a boy, and she was born. Therefore, the girl did not receive warmth, affection and wanted to leave home.

It was harder for girls in this regard. To leave her parents' house, she had to get married. So, at the age of 18, she entered into a fictitious marriage with Vladimirov Kovalevsky.

Having married, she begins to attend Sechenov's lectures on natural science. Natural science, in the end, did not attract her, but her husband achieved great success in this area, several well-known works related to this science are listed behind his authorship.

In 1869, Sophia with her husband and sister Anna went to study abroad of the Russian Empire, where they lived for about five years. During this time, the marriage of the Kovalevskys ceased to be formal. The young people were imbued with tender feelings for each other, in many ways they were united by a love of science.

In 1874, Sofya Vasilievna's studies ended. Getty University, where she studied, awarded her a Ph.D. in mathematics. She soon returned to Russia.

In Russia, Kovalevskaya's mathematical knowledge turned out to be unclaimed. Higher mathematics was not taught then, and she could only count on the work of an arithmetic teacher. It was not easy for her, and she began to engage in literary work, even writing novels.

In 1878, she had a daughter, who was named Sophia. Husband Vladimir, mired in debt, and shot himself when his wife was 33 years old. Sofya Vasilievna was called to work in Stockholm to give mathematical lectures.

In Sweden, the arrival of a Russian scientist made a lot of noise, this event was actively written in the press. In Scandinavia, she combined the work of a lecturer with the work of an editor of a mathematical journal. The magazine has found its readership throughout Europe, including Russia.

Sophia Kovalevskaya made a huge contribution to the development of mathematics not only in Russia, but throughout the world. She proved that the Cauchy problem has an analytical solution. She also solved the problem of reducing a certain class of Abelian integrals of the third rank to elliptic integrals. It was a major success.

The main success of Sofya Kovalevskaya in mathematics, scientists call the research carried out with the problem of rotating a rigid body around a fixed point.

Sofya Vasilievna died in February 1891. On the way from Italy to Sweden, she caught a serious cold. The cold developed into pneumonia, which ended in death.

1. Biography

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

Sofia 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 in his estate in. Vitebsk province. In the metric book of the Moscow ecclesiastical consistory of the Nikitsky Magpie, the Znamenskaya Church outside the Petrovsky Gates, for 1850 there is an entry:

January 3rd was born, on the 17th - Sophia was baptized; her parents - Artillery Colonel Vasily Vasilyevich, son of Krukovskaya and his legal wife Elizaveta Fedorovna; husband of the Orthodox confession, and wife of the Lutheran. Receiver: retired Artillery Lieutenant Semyon Vasilyevich, son of Krukovskaya and Proviantmaster Vasily Semyonovich, son of Krukovsky, daughter Anna Vasilievna. The sacrament of baptism was performed by a 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 in order to become well-bred ladies of the nobility. The first years of Sophia passed under the exceptional influence and care of the nanny, who replaced both her mother and father. The father, who lost a large amount of money, was not up to the children, and the mother, upset by the birth of her daughter, and not her 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 the home teacher Malevich and the strict English governess, Mrs. Smith. Sophia from childhood was distinguished by a rich imagination and fantasies, as well as increased nervous excitability, she even had nervous attacks, and in adulthood she suffered from nervous diseases.

Sophia also had such a sign of great nervousness as an aversion to deformities that reached horror, for example, stories about pets born with five paws or three eyes, as well as a fear of all kinds of cruelties. Even the sight of a broken doll filled her with panic fear. Once it was just such a doll, from whose head a gouged black eye dangled, that brought her to convulsions. As is known, due to the "female gender" she could neither receive a full-fledged higher education at one time, nor be able to freely realize herself as a mathematician. And only her colossal diligence, will and talent, combined with the help and support of her friends, helped her overcome all life's obstacles and obstacles.

Tempering began from childhood. Considering himself "unloved" and striving to somehow deserve parental love Sonya studied hard. And soon she became the pride of the family, realizing that everyone considers her very knowledgeable for her age. She showed signs of perseverance, discipline and strong will, so inherent in Capricorns.

Her teacher Iosif 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 build, sweet and attractive appearance, in whose eyes shone a receptive mind and spiritual kindness. In the very first training sessions, she showed rare attention, quick assimilation of what was taught, perfect complaisance, exact fulfillment of the required and 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, lessons, at noon - breakfast and a short walk, then more lessons and assignments for tomorrow. A strict daily routine for Capricorn is a simple matter - it is the upbringing of a personality 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 once asked his daughter at dinner: “Well, Sofa, have you fallen in love with arithmetic?” "No, daddy," was her reply. To which the teacher reacted with some excitement: “So love her, and love her more than other scientific subjects!” Less than four months later, Sofa said to her father: "Yes, daddy, I love doing arithmetic: it gives me pleasure."

Kovalevskaya is the first female mathematician to become a professor. In her scientific research, Kovalevskaya went through all the possible solutions to the problem, simultaneously analyzing and improving the already existing solutions of other mathematicians, and made her 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 the troubles, difficulties and everyday problems faded into the background and had no meaning.

“I have only to touch mathematics,” she said, “and again I will forget about everything in the world.”

How great is the power of inspiration! A feeling beyond words...

Mathematics is, first of all, logic. And also - a strict structure and system. The main scientific works of S.V. dedicated to Kovalevskaya mathematical analysis, mechanics and astronomy. In July 1874, on the basis of three papers by Kovalevskaya presented by Weierstrass - "On the Theory of Partial Differential Equations" (ed. 1874), "Additions and Remarks to the Study of Dallas on the Shape of the Ring of Saturn" (ed. 1885), "On the Reduction of One of the class of abelian integrals of the third rank to elliptic integrals” (ed. 1884) - the University of Göttingen appropriated S.V. Kovalevskaya Ph.D. In the analytic theory of partial differential equations (majorization method), one of the theorems is called the Cauchy-Kovalevskaya 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 quite symmetrical gyroscope, when the solution is brought to the end.

The student was understanding and diligent. In the fifth year of study, a 13-year-old student, when finding the ratio of the circumference to the diameter (numbers ) showed her mathematical abilities: she gave her own derivation of the required ratio. When Malevich pointed out Sophia's somewhat roundabout way of deduction, she burst into tears. As you know, in her scientific research, Kovalevskaya was accompanied by her teacher, a German mathematician, 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, later only reviewed the works of the student, but did not participate in their development in any way. If Kovalevskaya had not possessed her own mathematical talent and innate natural industriousness, she would never have become what she has become!

The question of love for mathematics was so often asked by Kovalevskaya that she herself gave a very definite answer to it: “I owe I.I. Malevich. In particular, Malevich taught arithmetic well and in a peculiar way. However, I must confess that at first, when I began to study, arithmetic did not particularly interest me. It was only after I got a little familiar with algebra that I felt 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 Vasil'evich Korvin-Krukovsky... I heard from him for the first time about certain mathematical concepts that made a particularly strong impression on me. My uncle talked about the squaring of a circle, about asymptotes - straight lines, to which the curve gradually approaches, never reaching them, and about many other things that were 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 big influence to awaken her interest in mathematics, her uncle had his stories about the squaring of a circle (an unsolvable problem of constructing a square with an area equal to the area of ​​\u200b\u200ba given circle with a compass and ruler) and other fascinating mathematical questions. These stories acted on the girl's fantasy and created in her the idea of ​​mathematics as a science in which there are many interesting riddles. Sofya Vasilievna tells about another incident that strengthened her interest in mathematics. By a happy coincidence, even the walls of the children's room were pasted over 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 was not enough 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. Sheets of lithographed lectures by Ostrogradsky on differential and integral calculus were found in the attic. Sonya became interested in the strange signs that streaked the sheets, and stood in front of them for a long time, trying to make out individual phrases. From daily looking at, the appearance of many formulas, although they were incomprehensible, was imprinted in the memory. When, at the age of fifteen, she began to take lessons in higher mathematics with the solution of differential equations, the very famous teacher A.N. Strannolyubsky and listened to the presentation of the same questions that she, without understanding the meaning, read on the “wallpaper”, 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, striking the teachers - “as if she knew about this before."

Despite the prohibitions of higher "female" education, she obtained permission to listen to lectures by I.M. Sechenov and study anatomy with V.L. Gruber at the Military Medical Academy. The path of Kovalevskaya 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, professor of physics 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 school mathematics course, independently figured out the meaning of the mathematical (trigonometric) formulas used in the textbook. After that, the general, proud of his daughter's success, allowed her to take lessons in mathematics and physics during her winter stays in St. Petersburg, which fifteen-year-old Sofa was not slow to take advantage of.

However, this was not enough for her. Sofya Vasilievna aspired to receive higher education in full. The doors of higher educational institutions in Russia for women at that time were closed. The only thing left was the path that many girls of that time resorted to, to look for opportunities to receive higher education abroad. A trip abroad required the permission of 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 marries Vladimir Onufrievich Kovalevsky, later a famous naturalist, and as his “wife” leaves with her sister for Germany, where she manages, not without difficulty, to enter Heidelberg University, where studied mathematics and attended lectures by the German scientists Kirchhoff, Helmholtz and Dubois-Reymond. University professors, among whom were famous scientists, were delighted with the abilities of their student. It has become a landmark in the small town. When mothers met her on the streets, they pointed her out to their children as an amazing Russian girl who studies mathematics at the university.

In 1870 she moved to Berlin, where for four years she worked for the great mathematician Weierstrass, who agreed to give her private lessons (women were also not allowed at the University of Berlin). For three years, Sofia Vasilievna, with very intensive studies, took a university course in mathematics, physics, chemistry and physiology. She wanted to improve in the field of mathematics with the then largest mathematician in Europe, Karl Weierstrass, in Berlin. In July 1874, the University of Heltingen, in absentia, without a formal defense, on the basis of three mathematical works of Kovalevskaya presented by Weierstrass, awarded her the degree of PhD in mathematics and Master of Fine Arts "with the highest praise" for defending her dissertation "Zur Theorie der partiellen Differentialgleichungen" ( rus . "On the theory of differential equations"). Three excellent papers were enough for the University of Heltingen to forgive, according to Weierstrass, "Sonia's belonging to the weaker sex."

Since women were not admitted to the University of Berlin, Weierstrass, admiring the exceptional abilities of Sofya Vasilievna, studied with her for four years, repeating her lectures that he read at the university. In his presentation, Weierstrass pointed out that among his numerous students who came to him from all countries, he did not know anyone whom he "could put higher than 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, "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 retired 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, in search of work, she moved to Moscow, but at Moscow University she was also not allowed to take the master's exams. The attempt of Mittag-Leffler, a professor at Helsingfors University, to arrange Sofya Vasilievna as a teacher at this university was also unsuccessful.

Kovalevskaya's attempts to get a professorship 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 post of assistant professor at the new university. In 1883 she returned to Russia again. At the 7th 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 there were no job offers again ... Sofya Kovalevskaya received an invitation to take the position of Privatdozent at the Stockholm university and in November 1883 left for Sweden. A little later, in the summer of 1884, she was appointed professor at Stockholm University and delivered twelve courses of lectures over the course of eight years, including a course in mechanics.

Sofya Kovalevskaya was greatly 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 announce the arrival of not some vulgar prince ... The princess of science, Ms. Kovalevskaya, honored our city with her visit and will be the first female assistant professor in all of Sweden.”

The conservative layers of scientists and the population met Sofya Vasilievna 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, which Sofya Vasilievna possessed, silenced all opponents. Sophia met the Helsingfort professor back in 1876. And from the first minute of their acquaintance, he, a great supporter women's education, passionately desired to open her the opportunity to teach at the university. He immediately tried to secure an associate professorship for her at the University of Helsingfors, but was unsuccessful. A year later, she was elected tenured professor, and in addition to mathematics, she was entrusted with temporary lectures on mechanics.

For 1888, the Paris Academy of Sciences announced for one of its biggest prizes the topic: "The problem of the rotation of a rigid body around a fixed point." This problem was solved to the end only in two particular cases. These solutions belonged to the greatest mathematicians of their time: the St. Petersburg academician L. Euler (1707-1783) and the French mathematician Jean Lagrange (1736-1813). It was necessary to "improve the problem in some essential point." Among the 15 works submitted to the competition was the work under the motto: "Say what you know, do what you must, let it be, what will be." This work was so superior to all others that the academic commission, which consisted of the leading mathematicians of France, awarded the author a prize increased from 3,000 to 5,000 francs. Its author was Sofia Vasilievna Kovalevskaya. She, as noted by the French magazine of that time, who came to receive the award, was the first woman to cross the threshold of the Academy.

The joy of Sofya Vasilyevna is understandable, who wrote on this occasion: “A task that eluded the greatest mathematicians, the problem, which was called the mathematical mermaid, turned out to be seized ... by whom? Sonya Kovalevskaya!

The attempt made by Sofya Vasilyevna’s friends to “return S. V. Kovalevskaya to Russia and Russian science” ended in the hypocritical replies of the tsarist Academy of Sciences that “in Russia, Mrs. Kovalevskaya cannot get a position so honorable and well paid as the one she occupies in Stockholm ". Only at the end of 1889 did the mathematicians succeed in electing Sofya Vasilievna a corresponding member of the St. Petersburg Academy, and the Academy had to decide beforehand fundamental question on "admission of female persons to be elected as correspondent members". Since this honorary title did not provide any material resources, the return of Kovalevskaya to her homeland remained still impossible.

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

S.V. Kovalevskaya, in her life, published nine scientific papers, receiving another prize from the Swedish Academy of Sciences for one of them. Her works belong to the field of pure mathematics, mechanics, physics and astronomy (on the ring of Saturn). In her work on mechanics she completed what the famous Euler and Lagrange had started, 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 are the greatest mathematicians of the late 18th and early 19th centuries. 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. The new scientific results obtained by her are presented in large university courses.

Sofya Vasilievna at the same time was a wonderful writer-fiction writer. Her autobiographical Childhood Memoirs, the novel The Nihilist, and excerpts from unfinished or lost stories provide an interesting picture of the social and political life Russia in the second half of the 19th century. Criticism noted that from the pages of her stories "breathes 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 equal rights for women. She repeatedly says in her letters that her success or failure is not only her own business, but is connected with the interests of all women. Therefore, she was extremely demanding of herself. In one of her poems she writes:

“From that person a lot will be exacted, To whom many talents were given!”

Sofya Vasilievna realized that she had been given many talents, that she had invested them in the cause of all women, and that much would be required of her. When Sofya Vasilievna in the 1980s lobbied for recognition of her academic rights in Russia, the tsarist minister replied that Mrs. Kovalevskaya and her daughter would not live to see a woman in Russia gain access to a professorial chair.

The tsarist ministers were not only bad politicians, but also bad prophets. The daughter of Sofya Vasilievna, the 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 a woman.

Before Sofya 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 of our era by a crowd of Christians, excited by the agitation of the 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 history with Voltaire and taught Voltaire mathematics; her biography notes that for both this teaching turned out to be fruitless; professor of mathematics at the University of Bologna, Italian Maria Agnesi (1718 -1831). Whose name is in higher mathematics the curved line of Agnesi's curl"; Frenchwoman Sophia Germain (1776-1831), whose name is found in number theory and higher analysis, Frenchwoman Hortense Lenot (1723-1788), a famous calculator, whose Shen is named a hydrangea flower, brought from on India.

There are many women professors of mathematics in the Soviet Union, among whom one can mention such outstanding professors as Vera Iosifovna Schiff (d. V. Kovalevskaya Elizaveta Fedorovna Litvinova (1845-1918), and many who are still alive. At the same time, one cannot but agree with Pelageya Yakovlevna Polubarinova-Kochina, Corresponding Member of the USSR Academy of Sciences, Doctor of Physical and Mathematical Sciences, that “Kovalevskaya surpassed her predecessors in talent and the significance of the results obtained. However, she determined general level women who aspired to science in her time. " S. V. Kovalevskaya remains for all time the pride of Russian science.

Scientific activity

The most important research concerns the theory of rigid body rotation. Kovalevskaya discovered the third classical case of the 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 of the Cauchy problem for systems of differential equations with partial derivatives, investigated the Laplace problem on the equilibrium of the Saturn ring, obtained the 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, celestial mechanics.

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

Of the mathematical works of Kovalevskaya, the most famous 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 mathematica", 12.2); "Sur une propri é t é du syst è me d equations differentielles 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 the Mathematical Collection, vol. XVI, published and separately (Moscow, 1891).

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 , i.e. 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 highest order ni of each function of the system contains a derivative with respect to t of order ni, and the system is resolved with respect to these derivatives.

The following notation is used:

Da? ?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), while 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 analytic solution in some neighborhood of the point (t0,x01,...,x0n), which is unique in the class of analytic functions.

Kovalevskaya's theorem on the existence of analytic (i.e., representable as 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.

Statement 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 analytical solution y(x) of Eq. (1) in some neighborhood of the point x = 0 that satisfies 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 by the majorant method. The majorant method on the example of problem (1), (2) is as follows. The function f (x, y) in equation (1) is replaced by a majorant, that is, an analytic function F (x, y), whose expansion coefficients in a power series are non-negative and are not less than the modules of the corresponding coefficients in the expansion in a power series of the function f (x, y) . The majorant is chosen as simple as possible so that equation (1) is 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 the 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 existence theorems for analytic solutions of ordinary differential equations and notes that they are taken from the lectures of "the respected teacher Herr Weierstrass". S.V. Kovalevskaya in her work proved a theorem on the existence of an analytical solution that satisfies given initial conditions, first for a quasilinear system of equations with partial derivatives of the first order, and then for a general nonlinear system of any order of the normal form by reducing it to a quasilinear system. The famous French mathematician A. Poincare (1854-1912) wrote: "Kovalevskaya greatly simplified the proof and gave the theorem its final form." To prove S.V. Kovalevskaya applied the majorant method using the species majorants.

The Kovalevskaya theorem is used where it is required 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 well-posedness of the Cauchy problem for hyperbolic equations with multiple characteristics - this is a question that, in last years attracted the attention of many researchers. The Cauchy-Kovalevskaya theorem and its modifications play a major role in questions of the theory of hyperfunctions related to solvability linear equations with partial derivatives. Any hyperfunction can be represented as a sum of boundary values ​​of analytic functions. The main scheme for solving equations in hyperfunctions is as follows: 1) the right parts, initial and boundary functions are represented as sums of boundary values ​​of analytic functions; 2) in analytic 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. It is not always possible to carry out the last two stages. 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 about S.V. Kovalevskaya: "In the dissertation in question, I (apart from the fact that I corrected numerous grammatical errors) did not take any other part than setting the task for the author. And in this regard, I must also note that I, in fact , did not expect a different result than that 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 that formally satisfies a partial differential equation must also always converge inside a certain region and must therefore then represent a function that actually satisfies the differential equation.That this is not the case, as you see from the example of the equation considered in the dissertation, was discovered, to my great amazement, by my student quite independently, and, moreover, at first for much more complex differential equations than the above, so that she even doubted the possibility of obtaining overall result; seeming so simple means which she found to overcome the difficulty thus arisen, I highly appreciated as proof of her correct mathematical instinct. " more 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, a 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 Velikiye Luki (Russia), founded in 1958. The honorary title "named after S. V. Kovalevskaya" has been worn since 2000.

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

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

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

Kovalevskaya mathematician scientist professor

Literature

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

2. "Mathematics, Mechanics" - a biographical guide. M., 1983.

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

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

Kochina P.Ya. Sofia Vasilievna Kovalevskaya. - Moscow: Nauka, 1981. - S. 7.8. - 312 p.

L.A. Vorontsov. Sofia Kovalevskaya: The 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.

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