Life and scientific discoveries of Sofia Kovalevskaya - Студенческий научный форум

XII Международная студенческая научная конференция Студенческий научный форум - 2020

Life and scientific discoveries of Sofia Kovalevskaya

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SofyaVasilievnaKovalevskaya (1850-1891)

In the history of science there are few female names that would be known to the whole world, which every educated person knew, at least by hearsay. Among such world-famous names is the name of Sofya Vasilievna Kovalevskaya, a remarkable Russian woman, whose activities “contributed a lot to the glorification of the Russian name”, as Nikolai Yegorovich Zhukovsky, the largest Russian scientist in the field of aviation theory, said about her.

Sofya Vasilievna Kovalevskaya was born on January 15, 1850 in Moscow. Her father, Vasily Vasilievich Korvin-Krukovsky, was a lieutenant general of artillery.

Sofia Vasilievna spent her childhood in the estate of her parents, in the village of Palibino, Vitebsk province. She received an excellent upbringing and education at that time. Purposefulness and perseverance in achieving the goal were a characteristic feature of S.V. Kovalevskaya. In her own expression, "intensity was the very essence of her nature." Teaching in all sciences was conducted in the Korvin-Krukovsky family by a home teacher, Joseph Ignatievich Malevich. This was an educated teacher, with vast experience, who knew how to arouse interest in the subject. Sofya Vasilyevna subsequently said that she owed the solidity of knowledge acquired from Malevich to the ease with which she was given further study of the sciences.

Sophia Vasilievna's parents opposed the too free development of her mind and tried to lead her in the usual routine way, which could not satisfy her ardent and receptive nature. They tried to give her education in accordance with the concepts of the environment in which her family lived, that is, sought to make her a secular well-bred young lady. Sofya Vasilievna had to fight for the freedom of her education.

In the Korvin-Krukovsky family, conversations were sometimes held on mathematical topics. Her uncle P.V. Korvin-Krukovsky, whose mathematical reasoning "acted on the girl’s imagination, inspired her with reverence for mathematics, as a higher and mysterious science, opening up a new wonderful world inaccessible to the initiates, Sofya Vasilievna’s love for mathematics. mere mortals "(from" Childhood Memories "). Mathematical conversations were also supported by the visiting mathematics professor Korvin-Krukovskikh Lavrov and the physics professor Tyrtov. The latter drew attention to the mathematical abilities of a fourteen-year-old girl who tried, without knowing trigonometry, to independently understand the sense of trigonometric formulas that she met in a physics course. From this moment, the father of Sofya Vasilievna changes her views on her education. Proud of his daughter's recognition of outstanding abilities, he allowed her to take higher mathematics lessons from the teacher of the Maritime College A.N. Strannolyubsky. From the age of fifteen, Sofya Vasilievna, during the winter visits of her family to St. Petersburg, systematically studied mathematics.

At that time, women developed a desire for higher education, which they could get only in some foreign universities, since higher schools for women in Russia did not yet exist, and they were not allowed into male ones. In order to free themselves from parental guardianship, which prevented them from entering foreign universities, some girls entered into fictitious marriages with people who sympathized with the women's movement and left their fictitious wives full freedom.

Eighteen years old Sofya Vasilievna fictitiously married Vladimir Onufrievich Kovalevsky, one of the representatives of the advanced intelligentsia, who was engaged in publishing at that time. Subsequently, their marriage became actual. Some details of this marriage are interesting: a fictitious marriage was needed for Anna, the elder sister of Sophia Vasilievna, who had a literary talent. But when V.O. Kovalevsky was introduced to both sisters, he resolutely declared that he would marry only the younger, who completely fascinated him and by marrying whom he could benefit science. He writes to his brother: “Despite his 18 years, the little sparrows (the so-called Sofya Vasilyevna for her youthfulness and small stature. - Auth.) Are well educated, she knows all languages ​​as her own, and still studies mainly mathematics. It works like an ant from morning to night, and with all that it is alive, sweet and very pretty. " Under the influence of his brother, the famous embryologist A.O. Kovalevsky, Vladimir Onufrievich began to study the natural sciences. With his classic works, made a few years after meeting with Sofia Vasilievna, V.O. Kovalevsky laid the foundation for evolutionary paleontology.

After the wedding, in the fall of 1868, the Kovalevsky couple went to St. Petersburg, where each of them worked diligently in his own science, and Sofya Vasilyevna, in addition, obtained permission to listen to lectures at the Medical and Surgical Academy. Then the Kovalevskys went abroad. In the spring of 1869, S.V. Kovalevskaya settled in Heidelberg with her friend Yu.V. Lermontova, who was engaged in chemistry. At first, the sister of Sophia Vasilievna Anna lived with them, who soon left for Paris, where she became close to revolutionary circles.

There she married V. Jacquard, with whom she took an active part in the struggle of the Paris Commune in 1871.

In Heidelberg S.V. Kovalevskaya studied mathematics, attended lectures by prominent scientists: Kirchhoff, Du Bois-Reymond and Helmholtz. In 1870, S.V. Kovalevskaya moved to Berlin, where she wanted to listen to the lectures of the famous mathematician Weierstrass. However, she did not succeed, as women were not allowed in Berlin University. But Weierstrass agreed to give her private lessons. This was the brilliant success of Sofia Vasilievna. It was very difficult to attract the attention of such a major scientist as Weierstrass and to become his first student. Weierstrass himself held conservative views on female education and was opposed to the admission of women to German universities. In addition, according to Felix Klein, being a student of Weierstrass was not easy, because "his intellectual superiority rather suppressed his listeners than pushed them on the path of independent creativity." However, S. Kovalevskaya’s brilliant abilities very soon forced Weierstrass to acknowledge his student’s mathematical talent: “As for Kovalevskaya’s mathematical education, I can assure,” he wrote, “that I had very few students who could be compared to her by diligence, ability, zeal and passion for science. "

Four years later, in 1874, Weierstrass filed a petition with the University of Gottingen to award S.V. Kovalevskaya with a Ph.D. in absentia (i.e., in absentia) without examinations. In letters to professors at the University of Göttingen, Weierstrass gives a description of the three works submitted by Kovalevskaya, of which each, in his opinion, was sufficient to obtain the desired degree. The first of these works - "On the theory of partial differential equations" - refers to the very foundations of the theory of these equations and is a generalization of the corresponding studies of Weierstrass to a much more complicated case. Before Weierstrass, a large French mathematician, Cauchy, dealt with the same question. The theorem proved by Kovalevskaya is one of the classical ones and is currently presented under the name of the “Cauchy-Kovalevskaya theorem” in all basic university courses.

The second work presented by S.V. Kovalevskaya relates to an interesting cosmological problem - the question of the shape of the ring of Saturn. Here S.V. Kovalevskaya develops Laplace's research, considering the ring to be liquid (at present, however, the hypothesis that the ring consists of solid particles is considered more plausible).

In the third of the presented works (“On the reduction of a certain class of Abelian integrals to elliptic integrals”), S. V. Kovalevskaya finds a thorough acquaintance with the most difficult theories of mathematical analysis.

With the degree of Doctor of Philosophy, the five-year period of the wandering life of Sofya Vasilyevna was completed. During this period, she made several trips, was in London, as well as in Paris - during the period of the Paris Commune - where she and her husband took part in the release of Jacquard from prison. In 1874, S.V. Kovalevskaya returned with her husband to Russia and began to live in St. Petersburg. For a rather long time, Sofya Vasilyevna moved away from studying mathematics. The circumstances of Russian life of that time contributed to this estrangement from science. S.V. Kovalevskaya, who received a brilliant mathematical education, could not find application for her knowledge in her homeland. She could only teach arithmetic in the lower grades of the gymnasium. She could not get close to Russian mathematicians on the basis of scientific work, as she belonged to a different mathematical direction. Only subsequently, Russian scientists - A. M. Lyapunov, N. E. Zhukovsky and others - became seriously interested in Kovalevskaya’s work on the rotation of a rigid body, but this was a completely different period of her life.

In 1878, S.V. Kovalevskaya moved with her family to Moscow. In 1879, she, at the suggestion of the largest Russian mathematician P. L. Chebyshev, made a report at the congress of natural scientists about her work. She is bothering about permission to take master's exams at Moscow University, but she is denied this, despite the support of professors. In 1881, Sofia Vasilyevna decided to return to Berlin to Weierstrass, taking her daughter Sofia, born in 1878, with her. The main work written by S.V. Kovalevskaya from 1881 to 1883 was an article on the refraction of light in crystalline media.

In 1883, V.O. Kovalevsky was tragically killed. An outstanding scientist committed suicide under the pressure of a number of circumstances, including material ones. Sofya Vasilyevna very seriously suffered the news of her husband’s death. She finally accepted the offer to move to Stockholm from the Swedish mathematician Mittag-Leffler, who had already tried several times to attract her to work at Stockholm University. Since that time, the flowering of the scientific and literary activity of S.V. Kovalevskaya began. Her penchant for literature manifested itself even in the Petersburg and Moscow periods of her life, when she wrote essays and theater reviews in newspapers. In Stockholm, this tendency was supported thanks to her friendship with the Swedish writer A. Sh. Edgren-Leffler, Mittag-Leffler's sister. Together with her, Sofya Vasilievna wrote the drama “The Fight for Happiness,” which was staged several times in Russia. In addition, S. V. Kovalevskaya wrote “Memoirs of Childhood”, the novel “The Nihilist”, the essay “Three Days at a Peasant University in Sweden”, “Memoirs of George Ellist” and other essays and articles published in Swedish, Russian and other languages . In literary works, the lively and deep mind of Sophia Vasilievna and the breadth of her interests are manifested.

At Stockholm University, S. V. Kovalevskaya read with great success twelve courses in various departments of mathematics, "guiding the intellectual life of youth with depth and clarity."

In Stockholm, S.V. Kovalevskaya wrote a scientific paper on the rotation of a rigid body, which, according to N.E. Zhukovsky, was mainly her scientific fame. For this work, on December 24, 1888, the Paris Academy awarded the S.V. Kovalevskaya Borden Prize, increasing it from 3,000 to 5,000 francs.

Let us dwell on this work. Euler and Poinsot investigated the case of rotation of a solid (in mechanics a rotating solid is called a top), subjected to gravity when the center of gravity of the body coincides with the fulcrum. Lagrange examined another case of the rotation of a rigid body around a fixed point of support, provided that the center of gravity of the top lies above the point of support. In both of these cases, thanks to the studies of Euler and Lagrange, one can completely solve the question of how any point of the body will move if the so-called initial conditions of motion are known. After the work of Euler, Poinsot, and Lagrange, there was a lull in research on the issue of rigid body rotation. The Borden Prize, appointed by the Paris Academy for further success in resolving this problem at some significant point, remained unconstrained or issued incompletely several times. Obviously, it was necessary to approach this task from some new point of view. S.V. Kovalevskaya, when considering it, approached her on the basis of the concepts of the theory of analytic functions, which she possessed well. She managed to make out to the end a new case of rotation of a rigid body discovered by her.

N.E. Zhukovsky illustrates the cases of Euler-Poinsot, Lagrange and Sophia Kovalevskaya with the images of three tops shown in the drawing attached here. The final solution to the problem for the case of S. V. Kovalevskaya has a very complex form, and only a thorough acquaintance with the theory of hyperelliptic functions allowed her to completely cope with the problem. S.V. Kovalevskaya proved that the cases of Euler, Lagrange and her are the only ones admitting a solution of a certain kind.

With the advent of the memoir of S. V. Kovalevskaya, which sets out the results of her research, a number of new questions arose for scientists related to the problem of the rotation of a solid body. Many mathematicians and mechanics, both Russian (A. M. Lyapunov, S. A. Chaplygin, N. E. Zhukovsky, etc.) and foreign (Levi-Civita and others), began to engage in the problem of the rotation of a solid with different points of view. The Russian scientist N. B. Delaunay constructed a device that reproduces the top (or, as it is sometimes called, a gyroscope) of Kovalevskaya. It should be noted that the problem of the rotation of a solid body, the solution of which eludes the hands of scientists and which was therefore called, in the words of S.V. Kovalevskaya, "a mathematical mermaid", is not yet completely solved. But whatever the results of further research, the name of Sofia Kovalevskaya will forever remain connected with this important task of mechanics.

In 1889, the Russian Academy of Sciences elected S.V. Kovalevskaya as its corresponding member. At that time, Sofya Vasilievna was in Stockholm and found out about her election from a telegram sent from St. Petersburg: “Our Academy of Sciences has just elected you a corresponding member, making this an innovation that has not yet had a precedent. I am very happy to see one fulfilled of my most ardent and just desires. Chebyshev. "

S.V. Kovalevskaya died on February 10, 1891 in Stockholm from pneumonia, which she received when she returned from Italy to Sweden after the winter holidays. She was only 41 years old, she was in the prime of her mind and talent.

S.V. Kovalevskaya was the first woman scientist in the field of exact sciences and aroused great interest in herself with her many-sided living nature and artistic talent. The name of Sofia Vasilievna Kovalevskaya will forever remain in the history of science crowned with deserved fame.

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