The meaning of Sofya Vasilievna Kovalevskaya in a brief biographical encyclopedia. Biography of Sofia Kovalevskaya
Kovalevskaya Sofya Vasilievna (nee Korvin-Krukovskaya) (1850-1891), mathematician.
Born on January 15, 1850 in Moscow in the family of an artillery general. When Sophia was six years old, her father retired and settled on the family estate of Palibino, Vitebsk province.
A teacher was hired for the girl's classes. The only subject in which the future scientist showed neither special interest nor ability in the first classes was arithmetic. However, gradually she developed serious abilities for mathematics.
In 1868, Sofya Vasilievna married V. O. Kovalevsky, and the newlyweds went abroad. For two years she attended lectures in mathematics at the University of Heidelberg (Germany).
In 1874, the University of Göttingen, after defending her dissertation, awarded her a doctorate.
In 1881, Kovalevskaya was elected a member of the Moscow Mathematical Society. After the death of her husband, she moved with her daughter to Stockholm (1884) and received the chair of mathematics at Stockholm University, with the obligation to lecture in German for the first year, and in Swedish from the second.
Kovalevskaya quickly mastered the Swedish language and published her mathematical works in it.
In 1888, the Paris Academy of Sciences awarded her a prize for her research into rotation. solid near a fixed point.
In 1889, for two essays in connection with previous work, Kovalevskaya received the Stockholm Academy Prize and became a corresponding member of the St. Petersburg Academy of Sciences.
In April 1890, Sofya Vasilievna returned to Russia in the hope that she would be elected as a member of the academy in place of the mathematician V. Ya. Bunyakovsky, who died in 1889, and that she would gain financial independence, which would allow her to engage in science in her homeland. But when Kovalevskaya wished, as a corresponding member, to attend the scientific meetings, she was told that the participation of women in them was “not in the customs of the Academy.”
In September she went to Stockholm again.
1. Biography
Sofya Vasilievna Kovalevskaya is the greatest female mathematician, university professor. Although her work took place in areas of science that are very far from not only school course mathematics, but also from higher courses educational institutions, however, the life and Personality of S.V. Kovalevskaya’s works are very interesting and instructive, and her name represents the pride of Russian science.
Sofya Vasilievna Kovalevskaya was born on January 3 (15), 1850 in Moscow, in the family of General V.V. Korvin-Krukovsky, who soon retired and settled on his estate in. Vitebsk province. In the metric book of the Moscow Ecclesiastical Consistory of the Nikitsky Forty, Znamenskaya Church outside the Petrovsky Gate, for 1850 there is an entry:
Born on January 3, Sofia was baptized on January 17; her parents are Artillery Colonel Vasily Vasilyevich, son of Krukovskaya and legal wife his Elizaveta Fedorovna; the husband is of the Orthodox confession, and the wife is of the Lutheran confession. Receiver: retired Artillery second lieutenant Semyon Vasilyevich, son of Krukovskaya, and provision master Vasily Semyonovich, son of Krukovsky, daughter, maiden Anna Vasilyevna. The sacrament of baptism was performed by local priest Pavel Krylov with deacon Pavel Popov and sexton Alexander Speransky ]
The general's daughters, the younger Sophia and the eldest Anna, were brought up under the supervision of governesses, studied foreign languages and music to become well-mannered noble ladies. Sophia's first years were spent under the exceptional influence and care of a nanny, who replaced both her mother and father. The father, who had lost a large sum of money, had no time for the children, and the mother, upset by the birth of a daughter and not a son, did not even want to look at her. When Sophia grew up, the upbringing and education of the “savage” passed into the hands of Malevich’s home teacher and the strict English governess Mrs. Smith. Since childhood, Sophia was distinguished by a rich imagination and fantasies, as well as increased nervous excitability, she even had nervous attacks, and in mature age she suffered from nervous diseases.
Sophia also had such a sign of great nervousness as an aversion to deformities reaching the point of horror, for example, stories about pets being born with five legs or three eyes, as well as fear of all kinds of cruelty. Even the sight of a broken doll filled her with panic. One day, it was just such a doll, with a knocked-out black eye dangling from its head, that brought her to convulsions. As is known, due to her “female gender,” she could neither receive a full-fledged higher education in her time, nor have the opportunity to freely realize herself as a mathematician. And only her colossal hard work, will and talent, combined with the help and support of friends, helped her overcome all life's obstacles and obstacles.
Hardening began in childhood. Considering herself “unloved” and striving to somehow earn her parents’ love, Sonya studied diligently. And she soon became the pride of the family, realizing that everyone considered her very knowledgeable for her age. She showed signs of perseverance, discipline and strong will, so inherent in Capricorns.
Her teacher Joseph Malevich describes the beginning of his studies with Sophia as follows: “At the first meeting with my gifted student, I saw in her an eight-year-old girl, quite strong built, sweet and attractive appearance, in whose eyes a receptive mind and spiritual kindness shone. In the very first training sessions, she discovered rare attention, quick assimilation of what was taught, perfect complaisance, precise execution of what was required and a constantly good knowledge of the lessons.”
In turn, the strict governess created almost Spartan conditions for the girl: early rise, dousing cold water, tea, music lessons, homework, at noon - breakfast and a short walk, then more homework and completing assignments for tomorrow. A strict daily routine for Capricorn is not a difficult matter - it is the education of the individual and the development of a value system in harsh conditions.
Interest in mathematics did not appear immediately; the stimulus was the most ordinary conversation between the girl and her father, who one day at dinner asked his daughter: “Well, Sofa, have you fallen in love with arithmetic?” “No, daddy,” was her answer. To which the teacher reacted with some excitement: “So love it, and love it more than other scientific subjects!” Less than four months had passed when Sofa said to her father: “Yes, daddy, I like to do arithmetic: it gives me pleasure.”
Kovalevskaya is the first woman mathematician to become a professor. In her scientific research, Kovalevskaya went through all possible solutions to the problem, simultaneously analyzing and improving the already existing solutions of other mathematicians, and made a tangible contribution to the development of mathematics in the 19th century.
As soon as Kovalevskaya was carried away into the world of mathematics, she was completely forgotten; from that moment on, all troubles, difficulties and everyday problems faded into the background and had no meaning.
“I just have to touch mathematics,” she said, “and I’ll forget about everything in the world again.”
How great is the power of the inspiration that embraces you! - a feeling that cannot be described verbally...
Mathematics is, first of all, logic. And also a strict structure and system. The main scientific works of S.V. Kovalevskaya are devoted to mathematical analysis, mechanics and astronomy. In July 1874, on the basis of three works by Kovalevskaya presented by Weierstrass - “On the theory of partial differential equations” (ed. 1874), “Additions and comments to Dallas’s study on the shape of the ring of Saturn” (ed. 1885), “On the reduction of one class of Abelian integrals of the third rank to elliptic integrals" (ed. 1884) - the University of Göttingen awarded in absentia to S.V. Kovalevskaya degree of Doctor of Philosophy. IN analytical theory 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 completely symmetrical gyroscope, when the solution is completed.
The student turned out to be understanding and diligent. In the fifth year of study, a 13-year-old student, when finding the ratio of the circumference to the diameter (number ) showed her mathematical abilities: she gave her independent conclusion of the required ratio. When Malevich pointed out the somewhat roundabout way of deduction used by Sophia, she began to cry. As is known, in scientific research Kovalevskaya was accompanied by her teacher, a German mathematician and professor at the University of Berlin, Karl Weierstrass, without consulting with whom, she was afraid to bring her mathematical research to court.
Even herself, having become great and famous, she considered herself only a student of the Weierstrass school, for which her colleagues constantly reproached her for not being independent and even doubted whether these were her works. Which is completely wrong! The great Weierstrass, having raised and educated Kovalevskaya the mathematician, subsequently only reviewed the student’s works, but did not participate in any way in their development. If Kovalevskaya had not had her own mathematical talent and innate natural diligence, she would never have become what she became!
The question about love for mathematics was asked so often by Kovalevskaya that she herself gave a very definite answer: “I owe the initial systematic teaching of mathematics to I.I. Malevich. Malevich taught arithmetic in particular well and in a unique way. However, I must confess that at first, when I began to study, arithmetic did not particularly interest me. Only after becoming somewhat familiar with algebra did I feel such a strong attraction to mathematics that I began to neglect other subjects. My love for mathematics manifested itself under the influence of my uncle Pyotr Vasilyevich Korvin-Krukovsky... from him I first heard about some mathematical concepts that made a particularly strong impression on me. My uncle talked about the squaring of the circle, about asymptotes - straight lines to which the curve gradually approaches without ever reaching them, and about many other things completely incomprehensible to me, which, nevertheless, seemed to me something mysterious and at the same time especially attractive."
Sofya Vasilievna herself says in her memoirs that her uncle had a great influence on awakening her interest in mathematics with his stories about the squaring of a circle (an unsolvable problem of constructing a square with a compass and a ruler, having an area equal to the area of a given circle) and other fascinating mathematical questions. These stories influenced the girl’s imagination and created in her an idea of mathematics as a science in which there are many interesting mysteries. Sofya Vasilievna talks about another incident that strengthened her interest in mathematics. By luck, even the walls of the children's room were covered with notes on differential and integral calculus. It turns out that when the Korvin-Krukovskys moved from St. Petersburg to their Palibino estate, they re-furnished and wallpapered the rooms of the house. There wasn’t enough wallpaper for one of the children’s wallpapers, it was difficult to order them from St. Petersburg, so we decided to cover the wall with plain paper until the opportunity was right. In the attic they found sheets of lithographed lectures by Ostrogradsky on differential and integral calculus. Sonya became interested in the strange signs that dotted the sheets, and stood in front of them for a long time, trying to make out individual phrases. From daily examination, the appearance of many formulas, although they were incomprehensible, was imprinted in my memory. When, at the age of fifteen, she began to take lessons in higher mathematics with the solution of differential equations, from the very famous teacher A.N. Strannolyubsky and listened to the presentation of the same questions that she had read about on the “wallpaper” without understanding the meaning, then the new concepts communicated to her by the teacher seemed old, familiar, and she learned them, to the surprise of the teacher, very easily, amazing the teachers - “as if she knew about this before."
Despite the prohibitions on higher “female” education, she obtained permission to listen to I.M.’s lectures. Sechenov and study anatomy with V.L. Gruber at the Military Medical Academy. Kovalevskaya's path in mathematics was thorny like no other, for the simple reason that she was... a woman. But even before that, fourteen-year-old Sophia surprised her father’s friend, physics professor N.P. Tyrtova, with his abilities. The professor brought Sophia his physics textbook. It soon turned out that Sophia, who had not yet taken a course in school mathematics, independently understood the meaning of the mathematical (trigonometric) formulas used in the textbook. After this, the general, proud of his daughter’s successes, allowed her to take mathematics and physics lessons during her winter stays in St. Petersburg, which fifteen-year-old Sofa was quick to take advantage of.
However, this was not enough for her. Sofya Vasilievna strove to receive a full higher education. The doors of higher educational institutions in Russia were closed to women at that time. The only option left, which many girls of that time resorted to, was to seek opportunities for higher education abroad. To travel abroad, permission was needed from the father, who did not want to hear about such a trip for his daughter. Then Sofya Vasilievna, who was already eighteen years old, fictitiously married Vladimir Onufrievich Kovalevsky, a later famous natural scientist, and as his “wife” she left with her sister for Germany, where she managed, not without difficulties, to enter the University of Heidelberg, where studied mathematics and attended lectures by German scientists Kirchhoff, Helmholtz and Dubois-Reymond. The university professors, among whom were famous scientists, were delighted with the abilities of their student. It became a landmark of the small town. Meeting her on the streets, mothers pointed her out to their children as an amazing Russian girl who was studying mathematics at the university.
In 1870 she moved to Berlin, where she worked for four years with the great mathematician Weierstrass, who agreed to give her private lessons (women were also not allowed at the University of Berlin). For three years, Sofya Vasilyevna, with very intensive studies, completed a university course in mathematics, physics, chemistry and physiology. She wanted to improve in the field of mathematics with the largest mathematician in Europe at that time, Karl Weierstrass in Berlin. In July 1874, the University of Geltingen awarded her the degree of Doctor of Philosophy in Mathematics and Master of Fine Arts "with the highest praise" for her defense of the thesis "Zur Theorie der partiellen Differentialgleichungen" ( rus . "Towards the theory of differential equations"). Three excellent works were enough for the University of Geltingen to forgive, in the words of Weierstrass, “Sonia’s belonging to the weaker sex.”
Since women were not admitted to the University of Berlin, Weierstrass, admiring Sofia Vasilievna’s exceptional abilities, studied with her for four years, repeating to her the lectures he gave at the university. In his submission, Weierstrass indicated that among his many students who came to him from all countries, he did not know anyone whom he “could place above Mrs. Kovalevskaya.” With a diploma of “Doctor of Philosophy with the highest praise,” twenty-four-year-old Sofya Vasilievna and her husband returned to Russia. Inspired by success, the “certified” Kovalevskaya rushed to her homeland to teach mathematics at St. Petersburg University. However, not only could she not get a place at the university, but she was not even involved in teaching at the Higher Women’s Courses that had opened by that time, after which she withdrew from scientific work for almost 6 years, taking an active part in the political and cultural life of her homeland. In 1879, at the suggestion of the mathematician P.L. Chebyshev, at the VI Congress of Russian Naturalists and Doctors, Kovalevskaya read a report on Abelian integrals. In the spring of 1880, she moved to Moscow in search of work, but Moscow University also did not allow her to take the master's exams. The attempt of Professor Mittag-Leffler of the University of Helsingfors to arrange Sofya Vasilievna as a teacher at this university was also unsuccessful.
Kovalevskaya’s attempts to get a professor’s position at the Higher Women’s Courses in France were also unsuccessful. In 1881 a new university was opened in Stockholm, the chair of mathematics of which was given to Professor Mittag-Leffler. After very difficult efforts, he managed to persuade the liberal circles of Stockholm to the decision to invite Sofya Vasilievna to the position of assistant professor at the new university. In 1883 she returned to Russia again. At the VII Congress of Russian naturalists and doctors in 1883, Kovalevskaya reported her work “On the refraction of light in crystals,” which was met with a bang, but again there were no job offers... Sofya Kovalevskaya received an invitation to take the position of privatdozent at the Stockholm University and in November 1883 she left for Sweden. A little later, in the summer of 1884, she was appointed professor at Stockholm University and over the course of eight years she gave twelve courses of lectures, including a course in mechanics.
Sofya Kovalevskaya received enormous assistance in this matter from her longtime friend, also a student of Karl Weierstrass, the Swedish mathematician Mittag-Leffler. The Democratic newspaper greeted her arrival with the words: “Today we are announcing the arrival of not some vulgar prince... The Princess of Science, Mrs. Kovalevskaya, honored our city with her visit and will be the first female associate professor in all of Sweden.”
Conservative layers of scientists and the population greeted Sofya Vasilyevna with hostility, and the writer Strindberg argued that a female professor of mathematics is a monstrous, harmful and inconvenient phenomenon. However, the talent of a scientist and the talent of a teacher that Sofya Vasilievna possessed silenced all opponents. Sophia met the Helsingfors professor back in 1876. And from the first minute of their acquaintance, he, a great supporter of women's education, passionately wanted to open up the opportunity for her to teach at the university. He immediately tried to obtain an assistant professorship for her at the University of Helsingfors, but without success. A year later, she was elected a full-time professor, and she was assigned, in addition to mathematics, temporary lectures on mechanics.
In 1888, the Paris Academy of Sciences announced the theme for one of its biggest prizes: “The problem of the rotation of a rigid body around a fixed point.” This problem was solved to the end only in two special cases. These solutions belonged to the greatest mathematicians of their time: the St. Petersburg academician L. Euler (1707-1783) and the French mathematician J. Lagrange (1736-1813). It was necessary to “improve the problem in some significant point.” Among the 15 works submitted to the competition, a work was submitted with the motto: “Say what you know, do what you must, let what be done.” This work was so superior to all others that the academic commission, consisting of the greatest mathematicians in France, awarded the author a prize increased from 3,000 to 5,000 francs. Its author turned out to be Sofya Vasilievna Kovalevskaya. She, as a French magazine of that time notes, who came to receive the prize, was the first woman to cross the threshold of the Academy.
The joy of Sofia Vasilyevna is understandable, as she wrote on this occasion: “The problem that had eluded the greatest mathematicians, the problem that was called the mathematical mermaid, turned out to be captured... by whom? Sonya Kovalevskaya!
The attempt made by Sofia Vasilievna’s friends to “return S.V. Kovalevskaya to Russia and Russian science” ended with a hypocritical reply from the Tsar’s Academy of Sciences that “in Russia, Mrs. Kovalevskaya cannot obtain a position as honorable and well-paid as the one she occupies in Stockholm.” " Only at the end of 1889 did academic mathematicians manage to achieve the election of Sofia Vasilievna as a corresponding member of the St. Petersburg Academy, and first the Academy had to resolve the fundamental issue of “admitting female persons to election as corresponding members.” Since this honorary title did not provide any financial means, Kovalevskaya’s return to her homeland remained impossible as before.”
At the beginning of 1891, Sofya Vasilievna, returning from the winter holidays, which she spent in Italy, caught a cold; On February 10, she died in Stockholm and was buried there.
S.V. Kovalevskaya, during her life, published nine scientific works, receiving another award from the Swedish Academy of Sciences for one of them. Her works relate to the field of pure mathematics, mechanics, physics and astronomy (about the ring of Saturn). In work on mechanics, she completed what the famous Euler and Lagrange began, in mathematics she completed Cauchy’s ideas, and in the question of the ring of Saturn she supplemented and corrected Laplace’s theory. Euler, Lagrange, Laplace, Cauchy are the greatest mathematicians of the late 18th and early XIX century. To supplement or correct the work of such luminaries of science, you need to be a very great scientist. Such a scientist was S.V. Kovalevskaya. New scientific results obtained by her are presented in large university courses.
Sofya Vasilievna at the same time was a wonderful fiction writer. Her autobiographical "Childhood Memories", the novel "Nihilist" and excerpts from unfinished or lost stories provide an interesting picture of social and political life Russia of the second half of the 19th century. Critics noted that from the pages of her stories “there is a whiff of Turgenev.” She also wrote, together with the Swedish writer Mittag-Leffler, an interesting drama “The Struggle for Happiness,” the only work in world literature written according to a mathematical plan.
S.V. Kovalevskaya, in addition to her scientific and literary merits, has an exceptional place in the history of the struggle for women's equality. She repeatedly says in her letters that her success or failure is not only her personal matter, but is related to the interests of all women. Therefore, she was extremely demanding of herself. In one of her poems she writes:
“A lot will be demanded from that person, to whom many talents were given!”
Sofya Vasilyevna realized that she had been given many talents, that she had invested them in the cause of all women, and that a lot would be asked of her. When Sofya Vasilievna in the eighties sought recognition of her academic rights in Russia, the Tsar’s minister replied that Mrs. Kovalevskaya and her daughter would not live to see the time when a woman in Russia would gain access to a professorial chair.
The royal ministers were not only bad politicians, but also bad prophets. Sofia Vasilievna’s daughter, doctor Sofya Vladimirovna Kovalevskaya, who died in 1952 in Moscow, lived for 35 years under Soviet rule, when all fields of activity were open to women.
Before Sofia Vasilievna Kovalevskaya, the history of mathematical sciences knows only a few women mathematicians. These are: the Greek Hypatia in Alexandria, torn to pieces in the year 415 by a crowd of Christians, excited by the agitation of monks who feared the influence of the beautiful and learned pagan Hypatia on the head of the city; Marquise du Chatelet (1706-1749), translator of Newton's works into French"; she studied historical sciences from Voltaire and taught Voltaire mathematical ones; her biography notes that for both of them this teaching turned out to be ineffective; professor of mathematics at the University of Bologna, Italian Maria Agnesi (1718 -1831). The name of which is borne in higher mathematics by the curved line of Agnesi's curl"; the Frenchwoman Sophia Germain (1776-1831), whose name is found in number theory and higher analysis, the Frenchwoman Hortense Lenot (1723-1788), a famous calculator, whose name is the name of the hydrangea flower, brought from on India.
There are many women professors of mathematics in the Soviet Union, among whom we can mention such outstanding professors as Vera Iosifovna Schiff (died in 1918), Nadezhda Nikolaevna Gernet (1876-1943), Ekaterina Alekseevna Naryshkina (1895-1940), a friend of S. V. Kovalevskaya Elizaveta Fedorovna Litvinova (1845-1918), and many living ones. At the same time, one cannot but agree with Corresponding Member of the USSR Academy of Sciences, Doctor of Physical and Mathematical Sciences Pelageya Yakovlevna Polubarinova-Kochina that “Kovalevskaya surpassed her predecessors in talent and the significance of the results obtained. At the same time, she determined general level women who strived for science in her time." S. V. Kovalevskaya remains for all times the pride of Russian science.
Scientific activity
The most important studies relate to the theory of rotation of a rigid body. Kovalevskaya discovered the third classical case of solvability of the problem of the rotation of a rigid body around a fixed point. This advanced the solution of the problem begun by Leonhard Euler and J.L. Lagrange.
She proved the existence of an analytical (holomorphic) solution to the Cauchy problem for systems of partial differential equations, studied the Laplace problem on the equilibrium of the ring of Saturn, and obtained a second approximation.
Solved the problem of reducing a certain class of Abelian integrals of the third rank to elliptic integrals. She also worked in the field of potential, mathematical, and celestial mechanics.
In 1889 she received a major prize from the Paris Academy for her research on the rotation of a heavy asymmetrical top.
The most famous of Kovalevskaya’s mathematical works are: “Zur Theorie der partiellen Differentialgleichungen” (1874, “Journal f ü r die reine und angewandte Mathematik", volume 80); "Ueber die Reduction einer bestimmten Klasse Abel scher Integrale 3-ten Ranges auf elliptische Integrale” (“Acta Mathematica”, 4); "Zus ä tze und Bemerkungen zu Laplace s Untersuchung ü ber die Gestalt der Saturnsringe" (1885, "Astronomische Nachrichten", vol. CXI); “Ueber die Brechung des Lichtes in cristallinischen Medien” (“Acta mathematica” 6.3); "Sur le probl è me de la rotation d un corps solide autour d un point fixe" (1889, "Acta mathematics", 12.2); "Sur une propri é t é du syst è me d equations differentelles qui definit la rotation d un corps solide autour d un point fix e" (1890, "Acta mathematica", 14.1). ABOUT mathematical works abstracts were written by A. G. Stoletov, N. E. Zhukovsky and P. A. Nekrasov in the “Mathematical Collection”, volume XVI published and separately (M., 1891).
A system of partial differential equations with unknown functions u1,u2,...,uN of the form
Niui(x,t)?tni=Fi(t,x,ui,...,uN,...,?auj?ta0?xa11...?xann,...),
where x=(x1,...,xn) , a=a0+a1+...+an , a?nj , a0?nj?1 , i,j=1,...,N , that is, the number of equations equal to the number of unknowns, is called the Kovalevskaya system. The independent variable t is distinguished by the fact that among the derivatives of the highest order ni of each function of the system there is a derivative with respect to t of order ni and the system is resolved with respect to these derivatives.
The following notation is used:
Yes? ?ki(x)=?a?? ki(x)?xa11...?xann,
where a?=a0+a1+...+an , ai?0 , i=1,...,N
Formulation:
If all functions ?ki(x) are analytic in a neighborhood of the point x0=(x01,...,x0n), and the functions Fi are defined and analytic in a neighborhood of the point (t0,x01,...,x0n, ?ki(x0),...,Da? ?ki(x0),...), then the Cauchy problem has an analytical solution in a certain neighborhood of the point (t0,x01,...,x0n), which is unique in the class of analytical functions.
Kovalevskaya's theorem on the existence of analytical (that is, representable in the form of power series) solutions of partial differential equations finds numerous applications in all the most important sections of the modern theory of differential equations and related areas of mathematics. Its use is essential in the proofs of many important and difficult theorems.
Formulation of the Cauchy-Kovalevskaya theorem for the simplest ordinary differential equation with the initial condition (0) = 0.
If the function f (x, y) is an analytic function of x and y in a neighborhood of the point (0, 0), then there is a unique analytic solution y(x) of equation (1) in some neighborhood of the point x = 0, satisfying the initial condition (2) .
The proof of a similar theorem for a differential equation of any order and for a system of such equations was carried out by O. Cauchy using the majorant method. Using the example of problem (1), (2), the majorant method is as follows. The function f (x, y) in equation (1) is replaced by a majorant, that is, an analytical function F (x, y), the expansion coefficients of which in power series are non-negative and not less than the absolute values of the corresponding coefficients of the power series expansion of the function f (x, y). The majorant is chosen as simple as possible so that equation (1) can be integrated explicitly, that is, from the explicit form of the solution y(x) of the problem, the convergence of the corresponding power series would follow, which is obviously a majorant for solving problem (1), (2 ). Cauchy used majorants of the form, which led to cumbersome calculations. S.V. Kovalevskaya, apparently, did not know these works by Cauchy; there are no references to them in her works (it is interesting to note that Cauchy is the author of 789 published works, not counting several voluminous monographs). At the beginning of her work, she gives formulations of theorems for the existence of analytical solutions of ordinary differential equations and notes that they are taken from the lectures of “the respected teacher Mr. Weierstrass.” S.V. Kovalevskaya in her work proved the existence theorem analytical solution, satisfying given initial conditions, first for a quasilinear system of first-order partial differential equations, and then for a general nonlinear system of any order of normal form by reducing it to a quasilinear system. The famous French mathematician A. Poincaré (1854-1912) wrote: “Kovalevskaya significantly simplified the proof and gave the theorem its final form.” To prove S.V. Kovalevskaya applied the majorant method using majorants of the form.
Kovalevskaya's theorem is used where it is necessary to construct asymptotic solutions, that is, solutions that satisfy the equation only with a certain accuracy. Such solutions are used, for example, in establishing the necessary conditions for the correctness of the Cauchy problem for hyperbolic equations with multiple characteristics - this is an issue that has attracted the attention of many researchers in recent years. The Cauchy-Kovalevskaya theorem and its modifications play a major role in questions in the theory of hyperfunctions related to solvability linear equations with partial derivatives. Any hyperfunction can be represented as a sum of boundary values of analytical functions. The basic scheme for solving equations in hyperfunctions is as follows: 1) the right-hand sides, initial and boundary functions are represented as sums of boundary values of analytical functions; 2) in analytical functions the solution is found by applying the Cauchy-Kovalevskaya theorem; 3) to obtain a solution in hyperfunctions, the boundary values of the obtained analytical solution are taken. 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 regarding the dissertation of S.V. Kovalevskaya: “In the dissertation in question, I (apart from correcting numerous grammatical errors) did not take any other part than setting the task for the author. And in this regard, I should also note that I, in fact, , did not expect a different result compared to what is known from the theory of ordinary differential equations. I was, in order to remain in the simplest case, of the opinion that a power series in many variables, formally satisfying a partial differential equation, must also always be convergent within a certain region and must, therefore, represent a function that actually satisfies the differential equation. That this is not the case, as you can see from the example of an equation considered in the dissertation, was discovered, to my great amazement, by my student completely independently, and, moreover, first for much more complex differential equations , than given, so that she even doubted the possibility of obtaining a general result; seeming like this simple means which she found to overcome the difficulty thus arising, I highly valued as proof of her correct mathematical instincts." Kovalevskaya's theorem finds important and significant applications in research on the theory of partial differential equations carried out until recently, and subtle modern studies are all in to a greater extent reveal its deep and complete character.
Memory of S.V. Kovalevskaya
· Kovalevskaya (lat. Kovalevskaya) - lunar crater; The name was approved by the International Astronomical Union in 1970.
· In memory of S. Kovalevskaya, the minor planet (1859) Kovalevskaya, discovered by the astronomer of the Crimean Astrophysical Observatory Lyudmila Zhuravleva on September 4, 1972, was named.
· Gymnasium named after S.V. Kovalevskaya - educational institution in the city of Velikie Luki (Russia), founded in 1958. It has had the honorary name “named after S.V. Kovalevskaya” since 2000.
· Secondary school named after Sofia Kovalevskaya in Vilnius (lit. Vilniaus Sofijos Kovalevskajos vidurin? mokykla ) - 49th high school in Vilnius (Lithuania) opened on September 1, 1980. In 1998, the school was named after Sofia Kovalevskaya.
· Sofia Kovalevsky School (Swedish: Sonja Kovalevsky-skolan) is the former name of the Metapontum secondary school (gymnasium) (Swedish: grundskolan Metapontum) in Stockholm (Sweden), founded in 1996
· Kovalevskaya Street and Sofia Kovalevskaya Street are street names in many cities of the former USSR.
Kovalevskaya mathematician scientist professor
Literature
1.Polubarinova-Kochina P.Ya. Sofya Vasilievna Kovalevskaya. 1850-1891: Her life and work. - M.: Gostekhizdat, 1955. - 100 p. - (People of Russian science).
2. “Mathematicians, mechanics” - biographical reference book. M., 1983.
Malinin V.V. Sofia Kovalevskaya is a female mathematician. Her life and scientific activities. - CIT SSGA, 2004.
When writing this article, material from Encyclopedic Dictionary Brockhaus and Efron (1890-1907).
Kochin P.Ya. Sofya Vasilievna Kovalevskaya. - Moscow: Science, 1981. - P. 7.8. - 312 s.
L.A. Vorontsova. Sofya Kovalevskaya: Life of wonderful people. Young Guard, 1959. Pp. 266.
7.Kovalevskaya S.V. “Memoirs and Letters” - M.: Publishing House of the USSR Academy of Sciences, 1951.
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She became the world's first woman to study mathematics, a real woman professor, but her homeland rejected her. Her home teacher called her Pascal in a skirt, but her father flatly forbade her to study abroad. Her husband gave her the freedom to study, and she accepted this gift with pleasure. She saved the wounded at the barricades and wrote books, but she could not fit into the ideological framework of her country. Therefore, Sofya Vasilievna Kovalevskaya received recognition in her homeland only after her death. Let's understand who she was and what achievements made her immortal, without applying gender divisions.
Sofya Kovalevskaya: a short biography of Pascal in a skirt
At one time there were many rumors and conversations about Sofya Kovalevskaya. Gray-haired, elderly professors and academics laughed at her, believing that a woman’s place could be in the kitchen, bedroom or nursery, but definitely not at the university department. She easily proved the opposite and during her short life she achieved considerable success in the field of science, but was never recognized in her homeland. The personality and fate of this unusual woman cannot be uninteresting, because at least after death, she overcame prejudice and became the real pride of Russia.
It is interesting that, according to Sofia Kovalevskaya herself, she received her first acquaintance with mathematical formulas in early childhood. After her father retired, their house was being renovated, but there wasn’t enough wallpaper for her room, so one wall was left unfinished, only preparatoryly covered with sheets from Professor Ostrogradsky’s book of lectures on differential and integral calculus. Mysterious symbols, similar to ancient spells, amazed the little girl and forever sunk into her memory.
Nature generously rewarded this thin, slightly awkward girl; she was interested not only in mathematics, although it was in this that she achieved the greatest success in her career. short life. She wrote a detailed study related to the rotation of a rigid body around a fixed point, proved the possibility of a holomorphic solution to the Cauchy problem, easily worked with elliptic and Abelian integrals, and carried out research in terms of air (celestial) mechanics, potential theory, and mathematical physics.
However, few people know that in addition to her scientific mathematical research, she also did completely opposite things. If you understand thoroughly who Sofya Kovalevskaya is, it is worth mentioning her literary experience. Comprehensively developed and gifted, she could not choose what she would do all her life. She wrote memoirs before reaching old age, for example, the diary “Childhood Memories” published in the ninetieth year of the nineteenth century in the “Bulletin of Europe”, composed odes and poems, and even wrote a full-fledged human drama, again based on differential equations, in which I wanted to show that each person decides his own destiny by choosing certain steps and actions.
The birth of Sofia Kovalevskaya and her family
Many of her contemporaries shrugged their shoulders in surprise, and when asked who Sofya Kovalevskaya was, they did not know what to answer. However, her work and passion made her famous. Therefore, it wouldn’t hurt to tell how it all happened and why a girl from a decent family, instead fashionable outfits and hats was interested in integrals and differentials. The girl had truly outstanding ancestors who bore the surname Schubert. Grandfather of the baby a real general from infantry, Fedor Fedorovich, was indeed considered an outstanding mathematician in his time, and his father, that is, Sophia’s great-grandfather, became famous for his geodetic and astronomical research. Moreover, both men were full members of the St. Petersburg Academy of Sciences.
On Sophia’s father’s side, heredity was also normal, since she was born on January 15, 1850, in the city estate of the guild Alexei Streltsov, in a family also well educated, a descendant of the ancient Hungarian king Matthew Corvin, Vasily Vasilyevich Corvin-Krukovsky, an artillery colonel. He had an excellent education and a wonderful wife, Elizaveta Feodorovna, née Schubert. No one could even imagine what fate was in store for this tiny girl, who was destined not for a simple and understandable female destiny, but for a difficult and even somewhat masculine path.
Childhood and youth of the future mathematician
Her parents thought that for Sophia and her sister, family would become the main thing in the future, so they planned to limit themselves to a modest education at home, as was customary then. Marriage, children, occasional receptions and balls, that’s all that should have happened, but it didn’t happen. Sophia and her sister Anna grew up as rebellious rebels, with a purely boyish mindset. They ran around in the fields and forests all day long, horrifying and infuriating their first mothers, nannies and governesses.
Worth knowing
It is interesting that the father, who was always traveling on business, never had any special hopes for Sophia, relying on the eldest Anna and the younger Fedenka. However, the only son did not live up to his father’s hopes, which fortunately he no longer saw. The guy simply squandered all the inheritance he received aimlessly, and devoted the end of his life to writing memoirs about his illustrious sister, with whom he didn’t really get along in his youth.
When Sophia was eight years old, a new teacher was taken into the house, the son of a small noble landowner, who graduated from the university, but never found a use for himself, Joseph Ignatievich Malevich. It was this young man who instilled in the Korvin-Krukovsky children a love for the exact sciences and an irresistible craving for research. He immediately noticed that Sophia definitely had inclinations, inclinations, abilities and even talent, which he repeatedly told Vasily Vasilyevich. However, he only waved it off and grinned through his thick mustache. The girl completed the male gymnasium course taught by Malevich in eight years.
A close friend of Korvin-Krukovsky, a real professor of physics from the Maritime Academy, named Nikolai Tyrtov, who often visited his house, was delighted with the success of his youngest sixteen-year-old daughter. He predicted fame and a career for her, called her the new Pascal in a skirt and recommended that she continue her studies. But dad was completely adamant, he had no intention of letting his daughters go abroad, and in Russia, according to the rules, a woman could not go to university, she had no right.
In 1966, Sophia finally went abroad, but on her father’s orders she had to return to St. Petersburg. However, she could no longer stop, so she still tried to enroll. They laughed at her, but not everyone, for example, the famous Russian teacher and public figure Alexander Strannolyubsky immediately saw the potential of this fragile girl and agreed to teach her privately.
Education and the formula of love
The moment came when she could no longer learn anything new, but a woman could only obtain a foreign passport with the permission of her father or husband, and then she and her sister decided to choose the second. Then a new acquaintance turned up on her way - a young scientist, paleontologist and geologist named Vladimir Onufrievich Kovalevsky. He was handsome, pleasant, intelligent, but did not have the analytical skills of his wife. But he was of noble birth and could replace his father to write permission to travel abroad. True, the man managed to love his fictitious wife with all his heart, but she did not want to hear anything like that.
In the sixty-eighth year of the nineteenth century, they got married and almost immediately went abroad, where he took up his favorite paleontology, and she joined the University of Heidelberg, which is under Koenigsberger, in the sixty-ninth. In the seventies, Sophia entered the University of Berlin, according to the rules of which no woman could come to lectures. However, even here there was a person who immediately recognized the girl’s talent. This was the German mathematics professor and “father of modern analysis,” as he was then called, Karl Theodor Wilhelm Weierstrass, who began to personally supervise Sofia Kovalevskaya’s studies.
Revolutionary views of Sophia
While Sophia was studying mathematics, her sister Anna managed to go to Paris, where she married the French Blanquist revolutionary Victor Jacqulard. He was a talented journalist and took part in the first Paris Commune. To help her sister, and also completely sharing and sympathizing with the views and ideas of utopian socialism, Sophia could not stay away from the events. She rushed to help, without even thinking about how it could end for her.
Sophia came to Paris and subsequently helped rescue Jacqular from prison, along with her husband and Anna, and first looked after the wounded Communards during the siege of the city. This was a huge, simply colossal risk for her future scientific career, but she could not do otherwise, and her fictitious husband, with whom they were becoming closer, also participated in this. He shared and supported her in everything, and in his eyes she saw understanding and love. She thought that she could rely on him in difficult times, which soon came, and the unfortunate woman had to catch air with her hands, since he was no longer around, but more on that in turn.
Meanwhile, the first female mathematician turned into simply a woman who wanted her own personal happiness, which she rightfully deserved. Kovalevskaya’s friends, who advocated emancipation, constantly scolded her for her overly warm relationship with her husband. However, it was no longer possible to stop the “process”; the girl also fell in love with the man who laid his own destiny at her feet. Despite sidelong glances, they settled together and a few years later they even had a daughter. In the same seventy-four year, the University of Göttingen, based on the results of the dissertation “Zur Theorie der partiellen Differentialgleichungen,” awarded the honorary title of Doctor of Philosophy.
Magnificent but short-lived career as a scientist Kovalevskaya
After this kind of political upheaval that France, and with it her sisters Anna and Sophia, experienced, she decided to return to her homeland in order to return to the interesting, mysterious and calm and confident world of formulas and equations. It seemed, and indeed was, more familiar to her than the world of shooting and pain, even if it was for the freedom of all mankind. In seventy-four she completed her work “On the Theory of Partial Differential Equations,” for which she received a doctorate and a Master of Fine Arts.
In the seventy-ninth she made a report at the sixth congress of natural scientists, held in St. Petersburg, and by the eighty-first she had become a private assistant professor of the Moscow Mathematical Society. Sophia's husband, Vladimir Kovalevsky, meanwhile, decided to completely abandon his academic career and devote himself entirely to business in order to somehow provide for the family, which, roughly speaking, lived on bread and water and lived on the help of parents and other relatives.
This became his last and fatal mistake. He fails several cases in a row, leaving his wife and child without any means at all, after which he cannot stand it and shoots himself in the forehead in the eighty-third year of the nineteenth century. Sophia herself, not having time to recover from the shock, is trying to find a teaching position for herself, but the maximum that her homeland can offer her is to teach arithmetic to female students.
Step by step: on the career ladder
Then she packs up the baby and goes to Berlin to visit her old friend Professor Weierstrass, who has already helped her more than once. It was he who, having launched the complex machine of his connections, finally secured a place for her at Stockholm University. The main condition was to teach only the first two years in German, and then switch to Swedish. This period was more than enough for the woman and she learned Swedish even before the mandatory period ended. She even began to write literary works in this language and publish them as if in her native language, which amazed those around her even more.
In 1880, Sonya Kovalevskaya, a beautiful young widow with a tiny child in her arms, smart, educated, with a high position and a good income, became intimate with a relative of her late husband, Maxim Kovalevsky. He left his homeland due to government persecution and was happily received at the house of a relative. Moreover, she even found him a job - lecturing to students, but after a joint vacation on the Riviera and an offer that she completely rejected, the young people finally broke up.
In 1988, Sofya Vasilyevna Kovalevskaya was named among the laureates of the Borden Prize from the Paris Academy of Sciences for her achievements in mathematics. This was not just any achievement, but a real breakthrough, especially if you remember that girls were not even allowed to listen to lectures. The following year, the second work was also highly noted by the Swedish Academy, after which Sophia was also elected a corresponding member of the physics and mathematics department of the Russian Academy of Sciences.
Sophia's scientific activities
Kovalevskaya’s most significant achievements in the field of mathematical analysis are her study of the theory of rotation of solid bodies. She completed the research in place of Joseph Louis Lagrange and Euler, who left this world early, and discovered the third classical case of the solvability of the problem of the rotation of a rigid body around a fixed point. It was this woman who proved the existence of a holomorphic solution to Cauchy problems and worked hard in the area of research into potential theory and celestial mechanics. Her scientific works are numerous and varied; we will present only a few of them.
- Journal für die reine und angewandte Mathematik.
- Zur Theorie der partiellen Differentialgleichungen.
- Zusätze und Bemerkungen zu Laplace's Untersuchung über die Gestalt der Saturnsringe.
- Sur le problème de la rotation d'un corps solide autour d'un point fixe.
- Sur une proprieté du système d’equations differentielles qui definit la rotation d’un corps solide autour d’un point fix e.
- Ueber die Reduction einer bestimmten Klasse Abel'scher Integrale 3-ten Ranges auf elliptische Integrale.
In 1989, she even received a prize in Paris for her study of the rotation of a heavy top with an asymmetrical shape. Sofia Kovalevskaya's discoveries will pave the way for new research, so her contribution to science is simply invaluable.
Literary experiments of mathematician Kovalevskaya
It is interesting that, having a purely analytical mindset, Sofya Vasilievna also had considerable literary potential. Not only did she know how to learn and explore new things, but she also knew how to present it all in an understandable and in simple language, and was fluent in more than a dozen different grammars, including Swedish, German, English, French, in addition to her native one. True, she wrote mainly in Swedish and Russian.
- "The Vorontsov Family" (published in Swedish in the 1860s).
- Kampen för Lyckan, tvänne paralleldramer of K. L. (1887).
- Vae victis (1892).
- "Memories of George Elliot" (1886).
- "Three days at a peasant university in Sweden" (1890).
- "Memories of Childhood" (1890).
Kovalevskaya was a follower of the idea of predetermined fate and even fatalism, but not without a bit of common sense. She believed that all words and actions are predetermined for everyone, but there are turning points when a person is given a choice as to which path to follow next.
Personal life and death of the first female mathematician: memory through the ages
Understanding what the scientist Sofya Kovalevskaya discovered, somehow we often simply forget to find out how her personal life turned out. While still a young girl, she no longer dreamed of a rich and loving husband, beautiful dresses and a bunch of kids who brought joy, but they were burning only with science, they wanted and thirsted for knowledge more than any good in the world. Therefore, her family life is unlikely to be happy, although she still managed to experience family happiness, albeit short-lived.
Marriage and children
Sofya Vasilyevna could not go to university in her homeland, but there was no way she could go abroad without her dad’s permission. Then she finds a young scientist Vladimir Onufrievich Kovalevsky, who decides to help her. The couple entered into a fictitious marriage in 1868, after which they almost immediately went abroad. The wife entered the university, and the husband began to conduct his paleontological research. They didn’t even live together, but the man turned out to be so patient and his feelings were enough for two. Over time, Sofya Vasilyevna understood herself and allowed her husband to approach her, became inspired and even fell in love.
From this union, which began as a fiction, a daughter was born, who was decided to be named Sophia in honor of her mother. She was born on October 5, 1878. After she grew up, she followed in her mother’s footsteps, although she did not achieve much success in the field of science. She studied at the St. Petersburg Women's College medical institute, and then long time worked as a doctor. It was she who translated many of her mother's works from Swedish.
Death of a scientific star and naming in memory of Sofia Kovalevskaya
In the ninety-first year of the nineteenth century, Sofya Kovalevskaya left Berlin, intending to get to Stockholm, where another report and scientific work awaited her. However, at the same time, a smallpox epidemic begins in Denmark and the scientist decides to return so as not to catch the infection. There were few options and she had to travel in an open carriage, despite the bitter cold around her. Sofya Vasilyevna caught a bad cold, after which a protracted and complex pneumonia began, which was then very difficult to treat. On January 29, 1891, she died, brought to Stockholm, where she had been so eager, with a diagnosis of pleurisy and cardiac paralysis. She was buried there, in the Northern Cemetery, her grave can still be seen today.
In the seventieth year of the last century, the International Astronomical Union decided to name one of the lunar craters in honor of Sophia Kovalevskaya, which they successfully did, now it will forever bear the name Kovalevskaya. There is a gymnasium named after this great woman, who is in her fifties, in the city of Velikiye Luki, and an award has also been awarded annually since 1992 under her name. Also, many streets in Russia, Sweden, Germany and Denmark are named after her.
There is even a personal museum of this woman, which is located in the village of Polibino, in the Pskov region, where she spent her childhood. In 2014, Alice Monroe published a book about Kovalevskaya, entitled “Too Much Happiness,” and films using her image were released in fifty-six, eighty-three, eighty-five, and even two thousand and eleven.
Name: Sofiya Kovalevskaya
Age: 41 years old
Place of Birth: Moscow
A place of death: Stockholm, Sweden
Activity: mathematics professor
Family status: was married
Sofya Kovalevskaya - biography
Sofya Vasilyevna Kovalevskaya (nee Korvin-Krukovskaya) is a brilliant woman mathematician, the first in the world to become a professor. Unfortunately, nowadays she is rarely remembered, but her biography is interesting and fascinating.
Sofya Kovalevskaya - childhood biography
Largely on mathematical development Sophia was influenced by her parents who gave her good upbringing and education. Sophia was born into a wealthy and rich family January 3, 1850. Then her family still lived in Moscow. The girl’s father, Corwin-Krukovsky, was an artillery general at that time, and her mother, Elizaveta Schubert, was involved in housekeeping and raising children.
Sophia also had an older sister, Anna. When little Sophia was barely six years old, her father left his place of service and decided to settle with his family on a family estate near Moscow. Realizing that the children needed a good education, a teacher was immediately hired.
Sofia Kovalevskaya - Education
Primary home education also included the study of arithmetic, but the future brilliant mathematician did not show any interest in this subject, nor did she show her extraordinary abilities. But an in-depth study of this subject, which lasted more than 4 years, provided the basis for the further development of Sophia’s mathematical talents.
After 10 years, the girl very quickly mastered the basics of arithmetic, learned to solve problems, and soon her teacher Malevich allowed her to study Bourdon’s arithmetic, which was designed for 2 years of study at the University of Paris. People around her began to notice the girl's extraordinary mathematical abilities, and one day her father was advised to hire another teacher - Strannolyubsky, a naval lieutenant. Already in the first lesson, Sophia amazed him with her talent for instantly mastering a new topic.
In 1863, Sophia entered pedagogical courses at the Mariinsky Gymnasium in the natural and mathematical department. Having received a matriculation certificate, Sophia, along with her husband and sister, moves to St. Petersburg and again returns to Strannolyubsky’s lessons. She also begins secretly attending math lectures. She is now absorbed in only one thing - mathematics, having decided to devote her whole life to it.
Continuing her education, Sofya Kovalevskaya and her husband travel abroad. But, not finding good teachers in Vienna, he moved to Heidelberg. With difficulty, scandals and conflicts, Sophia managed to ensure that she was allowed to listen to lectures on mathematics and physics. The most famous people In Germany, lectures were given to female students, which Sofya Kovalevskaya also listened to. At that time, she attended Könisberger’s course, lectures by the mathematician Kirchhoff, Dubois Reymond, Helmholtz, and carried out experiments in a chemical laboratory under the direction of Bunsen.
Her teachers were amazed at the abilities of their student, and each of Sophia’s works received only positive reviews her teachers.
In 1878, Sofya Kovalevskaya and her family moved to Berlin to study with Professor Weirstrass, but the girl was never admitted to the university, but she began to take private lessons from the professor, and sometimes even he could think while answering difficult questions from his student .
Sofya Kovalevskaya - Career
But a new page in the biography of the brilliant mathematician and mechanic Sofia Kovalevskaya begins when she decides to complete her first independent work. She tried to explore the ring of Saturn.
In 1873-1874, the famous mathematician began to engage in new research. This time the topic of her search was differential equations partial derivatives. This doctoral dissertation amazed scientists with its simplicity and accuracy, and later it began to be called the “Cauchy–Kovalevskaya Theorem.” Thanks to this work, Sofya Vasilievna was awarded the degree of Doctor of Mathematical Philosophy and Master of Fine Arts. In 1874, having completed her studies abroad, she returned to her homeland.
In 1884, Sofya Kovalevskaya gave her first lecture at Stockholm University. Soon she was appointed professor at this university for 5 years. But she continued her mathematical research. In 1886, together with her sister, who was ill at the time, she wrote her first book.
In 1888, the famous mathematician Sofya Kovalevskaya was awarded the Borden Prize, and soon received an award from the Swedish Academy.
Sofya Kovalevskaya - biography of personal life
In 1863, Sofya Vasilyevna, in order to enroll in pedagogical courses, entered into a fictitious marriage with Vladimir Kovalevsky, who was 8 years older than her. It was originally decided that he would become the groom older sister, but he chose Sophia.
After the training ended, an important event occurred in the biography of Sofia Kovalevskaya. Her fictitious marriage becomes a reality and soon a daughter is born into this union in 1878. Childbirth is difficult for her, and for some time she even remains bedridden. The doctors' forecasts were not reassuring: they were not sure that Sophia would ever get out of bed.
Sofia Kovalevskaya - illness and death
After her illness, Sophia continues to study science, but her relationship with her husband deteriorates. Taking her daughter, she leaves for Berlin, and her husband goes to Odessa, where his brother then lived. In 1883 he shot himself.
On January 29, 1891, Sofya Vasilievna died of heart paralysis. Unfortunately, she died in Stockholm, since her research was not given due attention in her homeland.
The apartment building of State Lady Buturlina, where the newlyweds Kovalevsky lived
Having learned that Kovalevskaya lived in this house, I decided to remember her biography. It turned out that Sophia was not only a mathematician, but also a mystic. She believed in signs of fate and prophetic dreams, often foreseeing future life events. Kovalevskaya's great-grandmother was a gypsy fortune teller, and Sophia believed that she had inherited her mystical gift.
Throughout her life, Sophia met reliable patrons who helped her move forward and open doors that remained closed to other women scientists in the 19th century. She had some special charm that influenced people.
Sophia saw no contradictions between her passions for science and mystical thoughts: “Many, who have never had the opportunity to learn more about mathematics, confuse it with arithmetic and consider it a dry science. In essence, this is a science that requires the most imagination... You cannot be a mathematician without at the same time being a poet at heart.”- she wrote.
From her great-grandfather Fyodor Schubert, a mathematician and astronomer, Sophia inherited a talent for the exact sciences, which brought her world fame.
Sophia's family included Germans, Austrians, Russians, Poles, and gypsies, and she was very proud of her “international blood.” But indeed, geniuses are born with such a “genetic mixture”.
Sophia in her youth
Great-grandfather scientist Fyodor Schubert, whose talent was inherited by Sophia
He came to her in a dream with tips
Sophia developed an interest in mathematics from an early age. During the renovation of the estate where the family lived, there was not enough wallpaper for the children's room; one wall had to be covered with sheets from a mathematics textbook.
Sophia recalled: “These sheets, covered with strange, incomprehensible formulas, soon attracted my attention. I remember how, as a child, I spent whole hours in front of this mysterious wall, trying to make out at least individual phrases and find the order in which the sheets should follow each other.”
The girl considered these signs magical and tried to unravel their meaning. She loved solitude and stayed away from her lively sister Anna and brother Fedya. The brownie, whom she saw with her own eyes, became her friend. Sophia believed that her “great-grandmother’s gypsy eye” allowed her to see what was hidden from others.
Her uncle Pyotr Vasilyevich helped Sophia unravel the meaning of the secret signs on the wall:
“My love for mathematics manifested itself under the influence of my uncle Pyotr Vasilyevich Korvin-Krukovsky... from him I first heard about some mathematical concepts that made a particularly strong impression on me. My uncle talked about the squaring of the circle, about asymptotes - straight lines to which the curve gradually approaches without ever reaching them, and about many other things completely incomprehensible to me, which, nevertheless, seemed to me something mysterious and at the same time especially attractive,” she recalled.
And another photo of the house
Young Sophia’s talent for science was noticed immediately; at the age of 15, she received permission to listen to lectures by mathematician I.M. Sechenov and study astronomy with Professor V.L. Gruber at the Military Medical Academy.
Sophia's relatives understood that the prediction was coming true.
When Sophia's mother was pregnant, Fyodor Schubert appeared to her in a dream and cheerfully said, “You will have a mathematician. My business will continue." When the girl Sophia was born, the mother considered the dream empty; she was afraid to even think that her daughter would join the “ugly women” who spent their entire lives “hunched over books.”
It should be noted that Sophia did not resemble the blue stocking stereotype.
Vladimir Kovalevsky, being Sophia’s fiancé, wrote to his brother: “Despite her 18 years, the “sparrow” is educated, excellent, knows all languages as if she were her own, and is still studying mainly mathematics. Works like; ant, from morning to night, and for all that she is alive, sweet and very pretty.”
Kovalevsky was 8 years older than Sophia.
Sophia wanted to continue her studies abroad, but according to the rules of the 19th century, she could only travel around Europe with relatives or her husband. Sister Anna advised her on a fictitious marriage that would help her achieve her plans.
“Sofia’s premature development was greatly influenced by the precocious and lively Anyuta, who was seven years older than her,” recalled Sophia’s friend.
In the mid-19th century, clubs spread in Russia where girls could meet future fictitious husbands in order to quickly begin their independent lives. Usually the grooms were from worthy families, and the parents of the young ladies had no reason to refuse. Seeing Sophia, Kovalevsky said that he was ready to get married even now.
Young scientist Kovalevskaya
According to the memoirs of Sophia’s friend: “She made a peculiar impression with her childish appearance, which earned her the affectionate nickname “little sparrow.” She was already 18 years old, but she seemed much younger. Vertically challenged, thin, but rather plump in the face, with short hair curly hair chestnut color, with an unusually expressive and mobile face, with eyes that constantly changed expression, now shining and sparkling, now deeply dreamy, she was an original mixture of childish naivety with deep power of thought... she did not pay the slightest attention to her appearance and her toilet ", which was distinguished by its extraordinary simplicity, with an admixture of some disorder that did not leave her all her life."
In 1869, Sophia and her husband went to the German city of Heidelberg, where they received permission to study at the university. The news quickly spread throughout the city. The townspeople, meeting Sophia on the street, looked at her with interest and told their children “The only learned woman!”
There were many talented women scientists in Europe, but it was Sophia who received such an honor. It was rumored that her “gypsy blood” helped her exert a magical influence on people and achieve what they wanted.
Sophia wrote poems that reflect her mysterious nature.
Have you ever been indifferent?
Walking aimlessly among the crowd
And suddenly some passionate song
Do you accidentally hear sounds?
An unexpected wave hits you
The memory of previous years smelled
And something sweet and dear
The soul responded in response.
It seemed to you that these sounds
As a child, you heard more than once,
So much happiness, bliss, torment
They were remembered for you.
You were in a hurry with your usual hearing
I can catch a familiar tune,
I wanted you behind every sound,
Follow every word.
Suddenly the song stopped
And the voice died away without a trace.
And without end and without beginning
The song remains forever.
How hateful it seemed
At that moment there is silence all around you.
It’s as if I was cut off with pain
There is a responsive string in my soul!
And how annoying and annoying
The song accompanied you all the time;
How is your hearing, disobedient to your will?
I repeated it to you forever!
The fictitious marriage with her husband gradually became real.
Sophia turned out to be a romantic person who dedicated poems to her husband and was very jealous of the ladies who preached “free love.” “Jealousy was one of the most powerful shortcomings of Kovalevskaya’s impetuous nature,” contemporaries noted.
The romantic “Sofya wanted her husband to constantly swear his love to her and show signs of attention, but Vladimir Kovalevsky did not do this,” which led to quarrels. The husband in return was jealous of Sophia’s science, wanting more reciprocal attention from his wife.
Vladimir Kovalevsky was a talented biologist who tried to engage in commerce to provide his wife with a decent life.
The gift of a fortuneteller helped Sophia restrain her husband from taking wrong steps. She often had terrible dreams, after which she persuaded her husband to leave commerce forever.
Envious women, watching the life of the Kovalevsky spouses, whispered: “She could not buy herself a dress, could not look after her things, could not find a way in the city... she was so impractical that all the small worries of life seemed unbearable to her,” “her husband follows her like a nanny”, “Kovalevskaya is poorly dressed as always.”
In 1870, 20-year-old Kovalevskaya went to Berlin to continue her studies at the University of Berlin, where she received the refusal “A woman cannot be listed as a legitimate student at the University of Berlin.”
She turned to the great mathematician Weierstrass for help; when they met, she could not find the words and handed over her sheets of notes. After viewing the young lady’s work, the admiring scientist agreed to give Sophia private lessons.
Again, unknown forces helped the woman mathematician move forward, bypassing rules and prejudices.
German mathematician Weirstrass, who helped Sophia's career
Kovalevskaya often dreamed of her great-grandfather scientist Fyodor Schubert, these dreams helped her in her work. One day, in a dream, his great-grandfather gave Sophia the idea of \u200b\u200b“celestial mechanics” and the study of the “rings of Saturn”.
“I feel that I am destined to serve truth - science and pave the way new way women, because it means serving justice. I am very glad that I was born a woman, as this gives me the opportunity to simultaneously serve truth and justice,” wrote Kovalevskaya.
After success in Europe, Kovalevskaya returned to Russia; in 1881 she was elected a member of the Moscow Mathematical Society, but her dream of teaching at the university has not yet come true.
Kovalevskaya said about envious people: “When Pythagoras discovered his famous theorem, he sacrificed 100 bulls to the gods. Since then, all animals have been afraid of new things.”
Kovalevskaya with her daughter Sonechka
Kovalevskaya did not lose hope; Emperor Alexander II was planning reforms that were supposed to change many social rules, but the emperor was killed. His son Alexander III took a tough position, and interrogations of revolutionary-minded citizens began. Vladimir Kovalevsky, Sophia’s husband, was a member of revolutionary societies. He persuaded his wife to leave Russia so that his reputation would not harm her. Having parted with Sophia, he lost her cautionary advice in commercial matters. Horrible dream Sophia's dream came true. Kovalevsky went bankrupt from an unsuccessful deal and committed suicide by poisoning himself with chloroform, he was 40 years old.
Before his death, he wrote to his brother: “Write to Sophia that my always thought was about her and how much I was to blame for her and how I ruined her life...”.
The death of her husband was a strong blow for Kovalevskaya; she could not eat for four days and fell ill from weakness.
Having slightly recovered from her grief, the widow went with her daughter to Berlin to visit the teacher Weierstrass, who, with the help of his Swedish colleague Mittag-Leffler, helped her get a position as a professor of mathematics at Stockholm University in 1884. Sophia is 34 years old, she is a young recognized scientist.
Swedish mathematician Mittag-Leffler, who helped Sophia get a professorship
Having received worldwide recognition, Sophia wrote: “My fame has deprived me of ordinary female happiness... Why can’t anyone love me? I could give more to my loved one than many women, why do they love the most insignificant, and only no one loves me?”
Fans and fashionable “free love” did not bring happiness.
According to the memoirs of contemporaries:
“That was her misfortune, that she could not get used to life in Stockholm, or anywhere else in the world, but she always needed new impressions for her mental activity, constantly demanded dramatic events from life...”
Fate turned out to be favorable; in 1880, Sophia met a relative of her late husband, Maxim Kovalevsky. He was not an elegant handsome man; the fat gentleman won over with his good nature and cheerful disposition. Sophia jokingly said about her fan, “he takes up too much space on the couch and in his thoughts.” Maxim was a world-respected sociologist who lectured in Paris, London, and Berlin. Maxim became an adherent of the Masonic lodge, about whose activities there are many legends; he was sympathetic to Sophia’s mystical views. Kovalevsky moved to Sweden, where he lectured at Stockholm University. The lovers spent the summer at Maxim's villa in Nice, but Sophia did not dare accept the marriage proposal.
Maxim Kovalevsky
In 1890 they separated, but soon became close again; Sophia celebrated the new year of 1891 with Maxim in Nice. She finally agreed to accept his proposal; the wedding was planned for the summer.
After the new year, bad feelings began to haunt Kovalevskaya. One night she heard a quiet cry, remembering the legends about the brownie, she asked “For better or worse?”, but there was no answer. In the morning, obeying an unknown force, she persuaded the groom to go to Genoa, where she headed to the ancient cemetery of Santo Campo. She wandered among the graves for a long time until she stopped at one of the mourning statues. After standing in silence, Sophia suddenly said to Maxim, “One of us will not survive this year!”
Sophia during the heyday of her fame
Returning to Sweden, Sophia caught a bad cold on the way. At home in Stockholm, she fell ill, sensing the imminent end of her life. “Some kind of change has occurred in me,” she said.
The day before her death, she told Maxim that she would write the story “When There Is No More Death.” And her last words were “too much happiness.”
Sofya Vasilievna Kovalevskaya died at the height of her fame; she recently turned 41 years old. Kovalevskaya was buried in Stockholm at the Northern Cemetery, the grave was covered with flowers on the day of the funeral. The woman scientist was mourned by the whole world.
The poet Franz Lefler dedicated a poem to Kovalevskaya:
Soul of flame and doom!
Has your airship arrived?
Obedient to the call of truth?
In that starry world so often you
Flew away on the wings of thought,
Where did you go in your dreams?
I was thinking about the universe...
Goodbye! We honor you sacredly,
Leaving your ashes in the grave;
Let the Swedish land be above him
Lays on easily without being overwhelming....
Goodbye! With your glory
You, having parted with us forever,
You will live in people's memory
With other glorious minds,
As long as the wonderful starlight
It will pour from heaven to earth
And in a host of shining planets
Saturn's ring will not be eclipsed.
Maxim Kovalevsky said at the funeral: “Sofya Vasilievna! Thanks to your knowledge, your talent and your character, you have always been and will be the glory of our homeland. It is not for nothing that all of learned and literary Russia mourns you. On her behalf, I bid you farewell for the last time!”
In her poems, Sofya Kovalevskaya left instructions for talented descendants - to move forward and never give up.
| If you are in life even for a moment I felt the truth in your heart, If there is a ray of truth through darkness and doubt Your path was illuminated with a bright radiance: So that in your unchangeable decision Fate has not ordained for you ahead, The memory of this sacred moment Keep it forever like a shrine in your chest. The clouds will gather in a discordant mass, It would have been better for you not to have been born, |
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