Chapter 29 What an aching anguish, What a misfortune befell! Mandelstam All evil chances have armed themselves with me!.. Sumarokov Sometimes you need to have embittered people against yourself. Gogol It is more profitable to have another among the enemies,

Chapter 30. CONFUSION IN TEARS The last chapter, farewell, forgiving and compassionate I imagine that I will soon die: sometimes it seems to me that everything around me is saying goodbye to me. Turgenev Let's take a good look at all this, and instead of indignation, our heart will be filled with sincerity.

Chapter 10. Apostasy - 1969 (First chapter about Brodsky) The question of why IB poetry is not published in our country is not a question about IB, but about Russian culture, about its level. The fact that it is not printed is a tragedy not for him, not only for him, but also for the reader - not in the sense that he will not read it yet.

CHAPTER 47 CHAPTER WITHOUT A TITLE What title should I give this chapter?.. I think out loud (I always speak loudly to myself out loud - people who don't know me shy away). "Not my Bolshoi Theater"? Or: “How did the Bolshoi Ballet die”? Or maybe such a long one: “Lord rulers, do not

LOBACHEVSKII, Nicolai Ivanovitch. "O nachalakh geometrii", in: Kazanskii vestnik, Part XXVI (Feb. & Mar. 1829), Part XXV (April 1829), Part XXVII (Nov. & Dec. 1829); Part XXVIII (Mar. & Apr. 1830); Part XXVIII (July & Aug. 1830). Kazan: University Press, 1829-30. Extracted by the Author himself from a discourse entitled: "Exposition succinete des principles de la Geometrie etc., read by him at the meeting of the Department of Physical and Mathematical Sciences on February 11, 1826. "Kazan Herald, published at the Imperial Kazan University". 5 articles placed in parts XXV, XXVII, XXVIII. Kazan, printed at the university printing house, 1829-1830.

1829: part XXV, February-March, pp. 178-187, April, pp. 228-241; part XXVII, November-December, pp. 227-243, cl. tab. I, fig. 1-9 geometric diagrams.

1830: part XXVIII, March-April, pp. 251-283, cl. tab. II, fig. 10-17 Geometric Diagrams, July-August, pp. 571-636.

Some bibliographies also describe the 3rd folding sheet of geometric diagrams. But at the same time, in the very text of the famous work of Lobachevsky, only those 17 figures placed on 2 folding tables are described. In semi-coloured binding of the era with worn embossing on the spine. The publisher's covers for part XXV have been retained. Format: 21x13 cm. Rarity! PMM 293a.

Bibliographic description:

1. PMM, No. 293a.

2. The Haskell F. Norman library of science and medicine. Part III, Thursday 29 October 1998, Chistie's, New York.

3. Jeremy M. Norman and Diana H. Hook. The Haskell F. Norman library of science and medicine. San Francisco, 1991, 2 vols., No. 1379.

4. Harrison D. Horblit. One hundred books famous in science. New York, 1964, no. 69a.

5. M. Kline. Mathematical thought from Ancient to Modern Times. New York, 1972, p.p. 873-81.

6. Biographical dictionary of figures of natural science and technology. Moscow, 1959. Vol. 1, pp. 524-527.

7. Dictionary of scientific biography (famous DSB), vol. VIII, New York, 1973, p.p. 428-434.

8. Bolkhovitinov V., Buyanov A., Zakharchenko V., Ostroumov G. Stories about the Russian championship. Under the general editorship of V. Orlov. Moscow, ed. "Young Guard", printing house Red Banner, 1950, pp. 47-51.

9. People of Russian science. Essays on outstanding figures of natural science and technology. V.1, Moscow-Leningrad, OGIZ, 1948, pp. 90-98.

10. Creators of world science from antiquity to the 20th century. Popular biobibliographic encyclopedia. Moscow, 2001, pp. 302-304.

"The enduring glory of Lobachevsky is that he solved for us a problem that remained unsolved for two thousand years." S. Lee.

The essay “On the Principles of Geometry” was still published in 1830 in a separate print and in the “Complete Works on Geometry”, published by Kazan University in 1883. T.1-2, in 4 °, T.1, p. 1- 67. In 1998, the world's most famous science and medicine library, The Haskell F. Norman library of science and medicine, sold out for most of the year at Christie's in New York. Under lot No. 1174, there was a modest convoy of 5 articles pulled from the Kazan Bulletin for 1829-30. The final price is amazing - huge for that time! For anyhow that such money is not paid ... Since ancient times, mathematics has been recognized as the most perfect, most accurate of all sciences. And geometry was considered the crown of mathematics, both for the inviolability of its truths and for the impeccability of its judgments. And now the Russian scientist, professor of Kazan University Nikolai Ivanovich Lobachevsky (1792-1856) creates a new geometric system, which he himself called "imaginary". On December 14, 1825, the best representatives of Russian society rose up to fight against serfdom and autocracy. The news of the uprising reverberated like a thunderous echo throughout the empire, stirred the minds, found a response in every honest heart, and determined the direction of revolutionary thought for a long time. For the purpose of secrecy, the Decembrists called their revolutionary constitution - "Russian Truth" "Logarithms". Professor Lobachevsky was preparing the same revolution in geometry. These days I worked with special rapture. Nikolai Ivanovich persistently prepared his "revolt" in science, his unprecedented revolution in mathematics, which was destined to transform the face of the whole of natural science, to become a turning point in the development of the exact sciences. Armed with formulas, the geometer built a stronghold, a fortress, and by February 1826 the work was completed. And in the Euclidean university "swamp" things went on in their usual, illogical order. Ironically, the trustee of Magnitsky was recorded as a Decembrist! Say, opposed the Emperor Nikolai Pavlovich! Enraged, Nicholas I ordered an investigation into the case of the "former trustee of the Kazan educational district." A gendarme was assigned to Magnitsky. The investigation was led by Lieutenant-General Zheltukhin and the former rector of the university, once expelled by Magnitsky, and now Kazan provincial prosecutor Gavriil Ilyich Solntsev. Magnitsky was already doomed. Especially after the investigators discovered the theft of large government sums... A document has been preserved in the archives of the university - Lobachevsky's accompanying note to the report that he submitted to the Physics and Mathematics Department. The note began with the words: “I am forwarding my essay entitled “A Concise Exposition of the Principles of Geometry on Parallel Lines.” I want to know the opinion of scientists, my associates, about this. On the document, the date is "February 7, 1826", at the bottom - "Suschano 1826 February 11". So, on February 11, 1826 in Kazan, for the first time in the world, the birth of a completely new geometry, called non-Euclidean, was publicly reported; ... For over two thousand years, Euclid's geometry dominated mathematics. But in this geometry there is the so-called fifth postulate of parallels, which is equivalent to the statement that the sum of the angles in a triangle is equal to two right angles. This postulate did not seem to mathematicians as obvious as others, and they stubbornly tried to prove it. Here is a partial list of the names of scientists who have worked on this problem; Aristotle, Ptolemy, Proclus, Leibniz, Descartes, Ampère, Lagrange, Fourier, Bertrand, Jacobi. Gauss summed up the sad result of his searches. He wrote: “There are few things in the field of mathematics about which so much has been written as about the problem at the beginning of geometry in substantiating the theory of parallel lines. Rarely does a year go by without a new attempt to fill this gap. And yet, if we want to speak honestly and openly, then we must say that, in essence, in 2000 years we have not gone further in this matter than Euclid. Such a frank and open confession, in our opinion, is more in line with the dignity of science than vain attempts to hide this gap, which we are unable to fill with an empty interweaving of ghostly evidence. In a word, the desire to prove the fifth postulate is compared with a frenzied desire to find a "philosopher's stone" in the Middle Ages or with countless attempts to create a "perpetual motion machine". Geometers were not satisfied with the "dark spot" in Euclid's "Principles", and there was no solution. Analyzing the reasons for the numerous failures of his predecessors, Lobachevsky came to the conclusion that all attempts to prove the fifth postulate are doomed to failure. After a long search, the Russian scientist came to an amazing discovery: in addition to Euclid's geometry, there is another, built on the denial of the fifth postulate. Lobachevsky called it "imaginary geometry". The usual geometric representations, the laws of ordinary geometry are replaced by new ones. There are no such figures in Lobachevsky's geometry; the sum of the angles of a triangle is less than two straight lines, there is a relationship between the angles and the length of the sides of the triangle, the perpendiculars to the straight line diverge, etc. And the fifth postulate of Euclid about parallels is replaced by an anti-postulate: through the indicated point, it is possible to draw a set of lines that do not intersect the given one. This day, February 11, 1826, marked the beginning of a new era in the development of world geometric thought, it became the birthday of non-Euclidean geometry. The professors present at the meeting listened inattentively to the speaker. They were more interested in the story of the fall of the almighty Magnitsky. Each trembled for his place, anxiously awaiting a call to the formidable Zheltukhin and the caustic Solntsev. Even Nikolsky felt involved in the December uprising and was afraid of arrest and exile. They smoked a lot. It seemed strange and absurd to everyone that in such a shaky, hectic time one could still deal with some postulates and theorems, create a new geometry when the old one might not be useful either.

For our sins ... - muttered colleague Nikolsky and cautiously looked sideways at Nikolai Ivanovich. In the guise of Lobachevsky, he now seemed to have something satanic. Here Nikolai Ivanovich stopped at the blackboard, some kind of alien, unearthly smile crept across his lips. He knitted his sharp arched eyebrows, pulled a cap of dark blond hair almost over his eyes, tilted his head. He stands, shielding the drawing with his back, and, looking around at everyone with a gloomy thoughtful look, says:

The main conclusion that I came to with the assumption of the dependence of lines on angles admits the existence of geometry in a more extensive sense than as it was presented to us by the first Claim. In this extended form, I gave science the name Imaginary Geometry, where, as a special case, the commonly used geometry enters with the restriction in the general position that measurements really require ... What is the essence, the hidden meaning of the non-Euclidean geometry discovered by Lobachevsky? Why did the great geometer call it Imaginary? Why is Euclidean geometry a particular - or rather, limiting - case of Lobachevsky's geometry? Is Lobachevsky's geometry real in the sense of correspondence to physical space, is there a surface on which the new geometry is valid, or is it a useless figment of fantasy, an idle fiction, a play of the imagination, a formal proof of the independence of the fifth postulate from other Euclidean axioms? Which of the two geometries best describes the real world? Step by step, we traced how Lobachevsky approached the discovery of new geometry, traced, to the extent that it is possible to tell about the secret, subtle work of a brilliant mind, where from the chaos of fleeting observations based on experience and intuition, an unprecedented truth is born, gradually crystallizing in the form of a clear formulas. Lobachevsky's first significant discovery was to prove the independence of the fifth postulate of Euclid's geometry from other positions of this geometry. The second discovery was the logically consistent system of the new geometry itself. He looked at his geometry precisely as a theory, and not as a hypothesis. Having come to the logical conclusion that in world space, and possibly in. microcosm, the sum of the angles of a triangle must be less than two straight lines, Lobachevsky boldly put forward his original axiom, his postulate and built an unusual geometry, just like the Euclidean one, devoid of internal contradictions. He called it imaginary, not because he considered it a formal construction, but because so far it remained accessible only to the imagination, and not to experience. The thought did not leave him to return to the measurement of cosmic triangles and establish the truth. Without changing anything in the "absolute" geometry, he only replaced the fifth postulate with an anti-postulate, an anti-Euclidean axiom: through the indicated point, one can draw a set of straight lines that do not intersect the given one. On the drawing it looks like this:

Lobachevsky changed the very understanding of parallel lines. For Euclid, non-intersecting and parallel ones are the same, for Lobachevsky: of all those that do not intersect a given line AB (see drawing), only two lines are called parallel - this is K1RK. and LPL1. All the rest, which are in the beam between the parallel ones, are not considered as such (in modern literature they are called superparallel). Therefore, the postulate is refined: if a line AB and a point P not lying on it are given, then two lines can be drawn through the point P in the plane ABR, parallel to the given line AB. Lobachevsky, therefore, calls parallel those that separate AB that do not intersect from that that intersect a given line. The distance between the straight line AB and each of the parallel ones does not remain constant - it decreases in the direction of parallelism and increases in the opposite direction. Parallel lines can come close to each other, but they cannot intersect. The plane in which such parallels exist is commonly called the Lobachevsky plane. This plane is not at all "flat" in the Euclidean sense. In the Euclidean plane, the angle of parallelism is constant and always equal to 90°; in Lobachevsky geometry it can take all values ​​- from 0 to 90°. Therefore, Euclidean geometry is a particular (limiting) case of Lobachevsky's geometry, in which the angle of parallelism is variable. Geometrically, the magnitude of the angle of parallelism depends on the length X of the perpendicular PE; that is, if the perpendicular decreases, the angle of parallelism increases, gradually approaching 90°. It could be represented very conditionally in the drawing as follows:

In other words: when point P tends to coincide with point E, that is, when X tends to zero, then the angle of parallelism tends to 90°. Thus, in the new geometry there is an interdependence of angle and segment. When the angle of parallelism of a straight line, i.e. equal to 90°, the interdependence disappears. It does not exist in Euclidean geometry. In non-Euclidean it represents the most significant moment. From this interdependence, the basic formula of the entire geometry of Lobachevsky is derived. Lobachevsky introduces the so-called linear constant into the formula. In modern science, a linear constant is understood as the radius of curvature of the Lobachevsky space; the value of the constant depends on the specific physical conditions in a given part of the world space. The exceptionally large value of the constant indicates that our space has a huge radius of curvature and, consequently, a rather small, close to zero, curvature, that is, the space in our part of the universe has a flat, Euclidean character. But if we assume that the linear constant can have different values, then each of these values ​​will correspond to its own, special geometry. Therefore, an infinite number of different geometries can take place. For Kant, space is an unchanging entity; for Lobachevsky - it is a form of existence of matter. Space is capable of changing along with matter. Yes, yes, Lobachevsky created a strange geometry. There are no such figures here; the sum of the angles of a triangle is always less than two right angles, and as the triangle increases, it tends to zero. Try to imagine a triangle whose sum of angles is equal to nothing! And triangles of an arbitrarily large area in this amazing geometry cannot exist at all. There is a direct relationship between the angles and the length of the sides of the triangle, which is not in Euclidean. There are no rectangles. The relations for the circle are also different. The plane and Lobachevsky space have constant negative curvature, and so on. “Newton is the greatest genius and the happiest of all, because there is only one system of the world and it could only be discovered once,” said Lagrange. Rejecting the Newtonian concept of space and time, Lobachevsky created a new world - the grandiose “Lobachevsky world”, in which the Euclidean world familiar to us is only an extreme case, an infinitely small region of space where we crawl like ants. This infinitely small part of space contains all our joys, hopes, tragedies, our past and present, the whole meaning of our existence.

It is impossible not to be carried away by the opinion of Laplace, - the thick voice of Lobachevsky sounded, - that the stars we see belong to only one collection of celestial bodies, like those that we see as faintly flickering spots in the constellations of Orion, Andromeda, Capricorn and others. And so, not to mention the fact that in the imagination space can be extended indefinitely, nature itself shows us such distances, in comparison with which even the distances of our earth to the fixed stars disappear for smallness ... The hair moved on Nikolsky's head. He furtively crossed himself and muttered:

For our sins, Lord have mercy! ..

It seemed to him that Nikolai Ivanovich was subtly mocking everyone, deliberately talking nonsense, while he himself laughed sullenly. Imaginary! .. And in this case, how is it better than the imaginary geometry of Grigory Borisovich, where the hypotenuse is a symbol of the meeting of the heavenly with the valley? You can reward whatever you want ... And try to object! They say that instead of Magnitsky, Lobachevsky's old friend Musin-Pushkin is appointed to the post of trustee ... Do not wait for good. So Nikolai Ivanovich is spitting out in anticipation of a complete triumph. Musin-Pushkin is fierce. Nikolsky, as the favorite of Mikhail Leontievich (damn him with his fraud!), the first to the nail ... "People are crucifying ..." Simonov almost did not delve into the meaning of the report. Ivan Mikhailovich's face expressed frank boredom. During trips abroad, he met the "king of mathematicians" Gauss, met with Littrow, who already has twelve children. Littrow's wife sniffs tobacco and smokes a pipe. “Like a Turk,” says Littrov. I saw Ivan Mikhailovich and the famous Frenchmen Laplace, Legendre, Cauchy. Now Lobachevsky is trying to compete with celebrities, and this is a pity. Lobachevsky presented the report in French in the hope that it would be published in the scientific notes of the Physics and Mathematics Department. What good, the report will be given for review to him, Simonov ... Not only in French, but also in Russian, all this sounds wild, unnatural. Metaphysical nonsense ... Has Nikolai Ivanovich's mind gone beyond reason from the incessant labors and vigils? .. He is thin, pale, his eyes burn like those of a hungry wolf. In what only the soul keeps ... The muscles and the scalp are unusually mobile, the hair moves up to the face, then rolls down to the shoulders. Reminds me of a recent incident. The Latinist Professor Alfons Jobar jokingly punched Nikolai Ivanovich in the stomach. Lobachevsky suffocated and almost gave his soul to God. Nikolsky, of course, immediately reported to the trustee: “Recently, Mr. Lobachevsky, who was sick, barely getting out of bed, Jobar jokingly hit his belly with his fist so hard that it came under his spoon.” For bad antics, Jobar was expelled from Russia. And Lobachevsky tried to stand up for him. A strange man!.. When the speaker fell silent, Grigory Borisovich frankly and widely crossed himself. Amen! Lobachevsky asked the professors to express their opinion on the new geometry. There was an oppressive silence. They sat with their heads down, afraid to meet Nikolai Ivanovich's eyes. In the days of Cardano, in the 16th century, tournaments of mathematicians were organized, the most noble and enlightened persons became judges. The winners received large cash prizes. That is why the solution of any intricate problem mathematicians kept in the strictest confidence. Each such dispute became an event. Mathematical secrets are kept even in modern times. The descriptive geometry of Gaspard Monge, whom Lagrange called the "devil of geometry", was declared a military secret. Lobachevsky has no professional secrets. On the contrary, he wants everyone to understand his discovery, to appreciate it. But in vain, apparently, he threw beads. The professors filled their mouths like water. Finally, Nikolsky invites Professors Simonov, Kupfer, and Adjunct Brashman to consider Lobachevsky's essay and report their opinion separately. Simonov absently takes the Concise Exposition of the Beginnings, rolls it up into a tube, and puts it in his pocket. Whether on the street, or in another place, the manuscript fell out of his pocket. Ivan Mikhailovich never missed her. The "Compressed Statement of the Beginnings" is considered to be irretrievably lost. Fascinated by thoughts of marriage, the end of Magnitsky's career, and the appointments that would be under the new trustee, Simonov completely forgot both Lobachevsky's report and the order of the academic council. He did not attach any importance to the report. You never know when they read all sorts of nonsense at the meetings of the academic council! Only the reports of the famous astronomer Simonov are of significance for science. Ivan Mikhailovich did not recognize any fantasies, nothing imaginary. Having done absolutely nothing for the prosperity of the university, he everywhere put himself in the forefront, looked forward to the election of a new rector and had no doubt that he would be the rector. Lobachevsky's first manuscript, Geometry, was lost by Magnitsky. The second manuscript, Algebra, was lost by Nikolsky. The last manuscript perished in the same silent manner. And yet the opening of a new era in the history of mathematical thought has taken place! Well, what about Mikhail Leontievich Magnitsky? He was exiled to Revel. The bitter cold persisted, but Magnitsky did not have a fur coat. Prosecutor Solntsev gave him his. Old friends met: Lobachevsky and Musin-Pushkin. Mikhail Nikolaevich was appointed trustee of the Kazan educational district. In recent years, it has expanded in breadth, hung with crosses and medals. Musin-Pushkin spent many years in the Cossack regiments, participated in the Patriotic War, got used to severe discipline and categoricalness. Contemporaries describe his appearance as follows: "His appearance was ferocious: thick, frowning eyebrows, a protruding hooked nose and an angular chin indicated some strength of character and stubbornness." The character of Mikhail Nikolaevich was really not distinguished by softness. The experienced campaigner loved order and obedience, was somewhat despotic, but at the same time honest and fair. He especially appreciated the last two qualities in others. At the very first dance evening in the Noble Assembly, Mikhail Nikolaevich asked Nikolsky why there were no students here, and ordered several people to be brought. Nikolsky brought three, the most daring. Entering the dance hall, the students began to make the sign of the cross and make obeisances. Musin-Pushkin cursed them as fools and kicked them out. Then Mikhail Nikolayevich wished to hear how lectures were given at the university. I went to the lesson of the adjunct of philosophy and Russian literature Khlamov. The adjunct read listlessly, and Musin-Pushkin fell asleep. Noticing this, Khlamov paused. "What are you, brother, do not continue?" asked the trustee, startled by the silence. "I was afraid to disturb your excellency." - “Well, your lectures must be good! Musin-Pushkin remarked reproachfully. - I will suffer from insomnia, I will definitely visit you. You’re already lulling me to sleep ... "-" That's right, Your Excellency! A simple, natural, poorly educated man, Musin-Pushkin treated people of science with great respect and did not tolerate hypocrisy. He was well aware of all the works and behavior of Lobachevsky. He liked the direct, decisive and independent Lobachevsky. Gathering the professors, Musin-Pushkin said: - The post of director is now abolished. I propose to elect Nikolai Ivanovich Lobachevsky as the rector! Who has a different opinion, let him speak. Nobody wanted to express their opinion. Even Simonov. He hoped that in a secret ballot Lobachevsky would be given a ride, and he, the famous astronomer Simonov, would be elected. To the surprise of Ivan Mikhailovich, Lobachevsky flatly refused to be rector. Musin-Pushkin was not angry. He began to persuade the obstinate professor, spent evenings with him, went hunting, patiently explained that Nikolai Ivanovich was the only one who could establish a university. Simonov is too busy with his special, his fame, besides, he is lazy, capricious, boasts of high acquaintances. However, voting will show. He, as a trustee, will give the rector complete freedom of action. The word "freedom" always produced an irresistible effect on Nikolai Ivanovich - he agreed. Elections have taken place. On May 3, 1827, the thirty-four-year-old Lobachevsky became the rector of Kazan University. Simonov was hurt. He simply refused to understand professors who verbally flattered him, predicted even greater glory in science, and when it came to election, they preferred another. Lobachevsky was elected by eleven votes to three. Musin-Pushkin left for St. Petersburg, and Lobachevsky became the full master of the university. Only now did he realize what a burden he had taken on. The rector was elected for three years. But Lobachevsky was destined to remain the rector for nineteen years! The English geometer Clifford called Lobachevsky the Copernicus of geometry. Just as Copernicus destroyed the age-old dogma about the immobility of the Earth, so Lobachevsky destroyed the delusion about the immobility of the only conceivable geometry. An even higher assessment of the feat of the Russian mathematician was given by the Soviet scientist V. Kagan. He wrote: "I take the liberty of asserting that it was easier to move the Earth than to reduce the sum of the angles in the triangle, reduce the parallels to convergence and push the perpendiculars to the straight line to diverge." ... As we have already seen, it was Lobachevsky who reported his innermost thoughts about the new geometry to his "comrades". But the world did not shudder, did not come in surprise, did not admire. The report was listened to inattentively, there was no discussion; the audience did not understand. Moreover, the listeners - and they were lucky enough to learn about the birth of a new science from the mouth of its discoverer - did not even try to understand anything. But it was about an extraordinary, almost fantastic structure of the world. We decided that this is nonsense, devoid of any meaning. As a matter of form, three professors were assigned to study the report to determine its significance. The commission did not give any response, and the work itself - the world's first document of non-Euclidean geometry - was lost and has not been found to this day. From that moment until the end of his life, Lobachevsky did not meet with understanding in his homeland. All his works were subjected to sharp criticism, ridicule and bullying. In Russia, he forever remained an unrecognized scientist, "an eccentric who is going out of his mind", "a famous Kazan madman." And despite this, throughout his life, Lobachevsky tirelessly improved "imaginary geometry." Already in 1829-30, Nikolai Ivanovich set out his new wonderful ideas - complex and unexpected - in print. His memoir "On the Principles of Geometry" appeared in the Kazan Vestnik magazine. About a third of this work, as noted by Lobachevsky, was “extracted by the writer from the reasoning” read at the meeting of the department on February 11, 1826. The memoir was presented extremely concisely, concisely, so it was not easy to understand the essence of new ideas. And the essay not only did not find recognition, but was met with undisguised irony. The secretary of the Academy, Fuss (son of Academician Fuss), handed over the memoir to Ostrogradsky. Mikhail Vasilievich Ostrogradsky has already become the first mathematical figure, an ordinary academician. His Mathematical Star was blazing with blinding light. Everyone understood both in the fatherland and abroad: the genius Ostrogradsky came to science! He is destined to become the founder of analytical mechanics, one of the founders of the Russian mathematical school. His outstanding achievements will be recognized by the entire scientific world. He will drink the cup of glory to the end during his lifetime. He will be called "the luminary of mechanics and mathematics." Member of the American, Turin, Rome, Paris Academies ... All higher educational institutions will consider it a great honor to enlist him as a professor. The words "Become Ostrogradsky!" become the motto of the youth. When Lobachevsky's memoir was placed on the table for Mikhail Vasilyevich, the mathematician shuddered.

Again Lobachevsky!

The fact is that another mathematician, Lobachevsky, a distant relative of Nikolai Ivanovich, lived in St. Petersburg. This St. Petersburg Lobachevsky, Ivan Vasilyevich, was obsessed with the idea of ​​squaring the circle and bored Ostrogradsky. In the table at Ostrogradsky lay the work of Ivan Vasilievich "Geometric program containing the key to the quadrature of unequal holes (3:4) (1:4) and the segment in the composition of the half-difference of these being." Having opened the memoir "On the Principles of Geometry" by Kazan Lobachevsky, Ostrogradsky was horrified. What the hell?! The squaring of the circle is not enough for this Lobachevsky, now he has taken up the theory of parallels! He invented a new geometry - imaginary! .. It's hard to deal with crazy people ... Mikhail Vasilyevich wrote in a sweeping way: "This Lobachevsky is not a bad mathematician, but if you need to show the ear, then he shows it from behind, not from the front." Fuss kindly explained to Academician Ostrogradsky that this Lobachevsky was not at all the same Lobachevsky, but the rector of Kazan University.

Then another thing, - said Mikhail Vasilyevich and wrote:

“The author, apparently, set out to write in such a way that he could not be understood. He achieved this goal: most of the book remained as unknown to me as if I had never seen it...” Ostrogradsky's genius was not enough to understand the discovery of the Kazan geometer. The memoir "On the Principles of Geometry" provoked a fit of anger in Mikhail Vasilyevich. And such a person takes the place of the rector!.. Expose! So that he would not corrupt the youth with his chimeras... Having made such a decision, Ostrogradsky became Lobachevsky's secret sworn enemy for life. Even ten years later, when Mikhail Vasilyevich was again given a new work by Lobachevsky for review, he would say:

“One can outdo oneself and read a poorly edited memoir if the expenditure of time is redeemed by the knowledge of new truths, but it is more difficult to decipher a manuscript that does not contain them and which is difficult not by the loftiness of ideas, but by a bizarre turn of sentences, shortcomings in the course of reasoning and deliberately applied oddities. This last feature is inherent in the manuscript of Mr. Lobachevsky ... It seems to us that Mr. Lobachevsky's memoir on the convergence of series does not deserve the approval of the Academy.

Everything is turned upside down here. Sublime ideas, new truths, impeccable reasoning... Not envy, but outright misunderstanding - that's what it was! Even when Lobachevsky, having found the manuscript of his textbook "Algebra" in dusty cabinets, finally published it, Ostrogradsky, leafing through the textbook, exclaimed: "The mountain gave birth to a mouse!" But Nikolai Ivanovich did not find out anything: Secretary Fuss did not want to upset the rector of Kazan University, to whom the tsar himself favors, Nikolai Ivanovich did not wait for a response to his work. Well... Don't get used to it! Ostrogradsky decided to strip Lobachevsky "naked", to compromise before the public. The very idea that a maniac was leading the upbringing of young people was unbearable to Ostrogradsky. He summoned two crooks, whom, due to a misunderstanding, he considered his friends - S.A. Burachek and S.I. Green. Burachek and Zeleny taught in the officer classes of the Naval Cadet Corps, where Ostrogradsky also lectured. In addition, Burachek was listed as an employee of the Son of the Fatherland magazine. The editors of this journal, Grech and Bulgarin, were closely connected with the Third Department, and any review in Son of the Fatherland was regarded as a political denunciation. Ostrogradsky decided to “turn over” Lobachevsky to Grech and Bulgarin. The tsar, in any case, reads the magazine, pay attention to who is entrusted with the leadership of Kazan University.

Write! Ostrogradsky ordered shortly. Soon a sharp pamphlet on the work of the Kazan geometer appeared in the press. In 1834, an anonymous article was published in the journal Son of the Fatherland: “On the Principles of Geometry, Op. Lobachevsky. Once Simonov looked into the rector's office, put two magazines on the table - "Son of the Fatherland" and "Northern Archive".

Here you are remembered...

Lobachevsky opened the page carefully laid by Simonov - and could not believe his eyes: “There are people who, having sometimes read one book, say: it is too simple, too ordinary, there is nothing to think about in it. I advise such lovers of thinking to read the geometry of Lobachevsky. Here's something to really think about. Many of our first-class mathematicians (a hint of Ostrogradsky!) read it, thought, and did not understand anything ... It would even be difficult to understand how Mr. Lobachevsky, from the easiest and clearest in mathematics, what kind of geometry, could do such a heavy, so obscure and impenetrable teaching, if he himself had not somewhat advised us, saying that his Geometry is different from the common one, which we all studied and which, probably, we can no longer unlearn, but is only imaginary. Yes, now everything is very clear. What the imagination, especially lively and at the same time ugly, cannot imagine! Why not imagine, for example, black - white, round - quadrangular, the sum of all angles in a rectilinear triangle is less than two lines and the same definite integral is equal to either π / 4 or ∞? Very, very possible, although for the mind all this is incomprehensible. But they will ask: why write, and even print such ridiculous fantasies? I confess that it is difficult to answer this question ... At the same time, yes, let us be allowed to touch on personality a little. How can one think that Mr. Lobachevsky, an ordinary professor of mathematics, would write a book for any serious purpose that would bring a little honor even to the last parish teacher? If not scholarship, then at least common sense should be in every teacher, and in the new Geometry this latter is often lacking. Considering all this, I conclude with a high probability that the true purpose for which Mr. Lobachevsky composed and published his Geometry is simply a joke, or, better, a satire on learned mathematicians, and perhaps even on learned writers of the present day. Praise be to Mr. Lobachevsky, who took it upon himself to explain, on the one hand, the arrogance and shamelessness of false new inventors, and, on the other hand, the simple-hearted ignorance of the admirers of their new inventions. But, realizing the full value of Mr. Lobachevsky's work, I cannot, however, but blame him for the fact that, without giving his book a proper title, he made us think for a long time in vain. Why not write, for example, a satire on geometry, a caricature of geometry, or something similar, instead of the title "On the Principles of Geometry"? showed the true point of view from which one should look at his work. S.S. The authors cowardly concealed their names, signing with the initials “S. FROM.". Bulgarin and Grech spared no space in their journals for a libelous review: the result was a very voluminous article with long excerpts from the memoir "On the Principles of Geometry". Lobachevsky sat for a long time in mournful thought. Bulgarin and Grech care about everything: not only literature, but also geometry. Whoever hides under the pseudonym "S. S., it is felt that this person carefully read the memoir. But why such wild anger? Who is he? A mathematician, no doubt. Why didn't you want to understand? Or he simply did not want to accept ... One thing is clear: the main goal of “S. FROM." - influence the public, belittle, ridicule the Kazan geometer, make him look almost crazy. For some reason, Newton's words came to his mind: "Genius is the patience of thought concentrated in a certain direction." Patience of thought... When d'Alembert, in his youth, asked his aunt what a philosopher is, she replied: "A madman who torments himself all his life only to be talked about after death." Auntie was wise. Making a discovery is not enough. It still needs to make its way into the minds of the people. You can't retreat. Why do these people not want to understand a simple truth: even if the real case - Euclidean geometry - is contained as a special case (albeit speculatively) in a more general case - new geometry, then it is still more profitable to study the latter, at least some combinations turned out to be never used ? It is very probable that Euclidean propositions alone are true, although they will forever remain unproved. Be that as it may, the new geometry, if it does not exist in nature, nevertheless can exist in our imagination and, remaining unused for measurement in reality, opens up a new vast field for the mutual applications of geometry and analytics. Why, in this case, does Ostrogradsky's proposal, according to which the symbol denoting the solution of an equation of any degree, be considered as a completely explicit function, over which we can perform any actions, is not ridiculed? Why don't the "radicalists" raise a howl? The response to the publishers has been written and sent. But Lobachevsky labored in vain: the “robber brothers” Bulgarin and Grech only laughed at the helpless indignation of the Kazan geometer. They threw his answer into the basket. When Musin-Pushkin read the libel in The Son of the Fatherland, he became furious and immediately turned to the Minister of Public Education, Uvarov, who had replaced Shishkov. “In the 41st book of The Son of the Fatherland, criticism is placed on the work of Mr. Lobachevsky. Leaving aside the dignity of the work itself, which can and should be analyzed like any other, it seems to me, however, that Mr. Reviewer should not have touched on personalities; either to put the writer below the parish teacher, or to call his composition a satire on geometry, etc. ... Is there another, hidden goal here? To humiliate a scientist who has served with honor for more than twenty years, who has published many very good textbooks and who, for the benefit of the university, has taken up an honorable and laborious duty for the eighth year ... ”But Uvarov does not at all intend to quarrel with Bulgarin and Grech. It was the same Uvarov who made the words "Autocracy, Orthodoxy, Nationality" his motto. He also does not want to quarrel with Musin-Pushkin. “I drew the attention of the censors to the above expressions and ordered the publisher of the journal to place in it objections to criticism, which the writer of Geometry would make.” However, Lobachevsky's refutation was never published. Lobachevsky is 40 years old. He decides to drastically change his fate and on October 13, 1832, he marries for love the young Varvara Alekseevna Moiseeva. If Newton did not leave a single offspring to the human race, then Lobachevsky has five of them; sons Alexey, Nikolay; daughters Nadezhda, Varvara, Sophia. In this respect he is destined to surpass all the great geometers put together; in twenty-four years of married life, Nikolai Ivanovich and Varvara Alekseevna would have fifteen children! The house is large, provincially cozy, spacious and important. Here is his wife, children, mother Praskovya Alexandrovna. Lobachevsky takes off his uniform, puts on a dressing gown and immediately turns into a kind family man. Severely shifted eyebrows diverge, eyes warm. Behind the bluish glass patterns - evening, loose snowdrifts, crimson chimes of bells. Children sit at the table wary and quiet, with round eyes. Waiting for fairy tales. For the umpteenth time I have to read "Ruslan and Lyudmila" - the most interesting. Then - the fables of Krylov, "Evenings on a farm near Dikanka" by Gogol, the novels of Walter Scott. Nikolai Ivanovich loves a joke, laughter. Sometimes he composes fairy tales himself: about Ivanushka the Fool, who entered Kazan University, studied to be a prince and married a beautiful princess. He laughs so contagiously that everyone grabs their stomachs. He idolizes his young wife. She is jealous of him for everyone and everything: for Musin-Pushkin, and for the wife of the trustee Alexandra Semyonovna, for university comrades, for service, for eternal deeds and worries. He especially cannot stand it when he locks himself in his office and writes something by the light of two candles until morning. He has an aversion to lamps. Recognizes only candles. The handwriting is beaded, neat. He is careful in everything, even in small things. Each pencil, each pen is wrapped in paper. His whole life is calculated by the minute - even at home. And this tires Varvara Alekseevna. He gets up early, at seven o'clock, drinks tea at eight, never rests after dinner, but walks and walks from room to room with his hands behind his back, smoking his pipe or cigar. Alcohol is indifferent. Occasionally, for the sake of the guests, he will drink a glass of Madeira or sherry. He is hospitable, loves to eat, he orders the cook his favorite dishes, explains how much and what to put in each dish; and that everything must be on almond milk and olive oil. Yes, he has a manic craving for work, yes, he has his own little quirks and quirks. Who doesn't have them? A young wife is bored in a deserted three-story house. She loves the sparkle of lights and dresses, courtship, worship. I have to give up "New Beginnings of Geometry with a Complete Theory of Parallels", go to the theater, masquerade, balls to the governor or to the Assembly of Nobility. And in the Lobachevsky house itself, which is considered aristocratic, it is rarely without guests. Having married, Nikolai Ivanovich acquired a bunch of relatives. They are along all lines: along the line of the Wielkopolskys, and along the line of the Moiseevs, and along the line of the Musin-Pushkins. The wife's sister Praskovya Ermolaevna Velikopolskaya is married to the manufacturer Osokin, whose factory is leased by Alexei Lobachevsky. One of the brothers of Varvara Alekseevna is a diplomat, a dragoman in Persia. Everyone has to be accepted, return visits take a lot of time. Musin-Pushkin is an inveterate hunter and fisherman, every time he calls Nikolai Ivanovich to the Abyss. All relatives call Lobachevsky "beech", "a man not of this world." And indeed, this stern man, busy thinking about unearthly geometry, looks strange against the backdrop of noisy Kazan society. He is like a resident of another planet, accidentally brought here by cosmic storms, to a provincial city, where even the most inveterate aristocrats and Voltaireans are well versed in the prices of lard, fish, cattle, where to lose entire estates at cards, to go wildly reveling is considered the highest valor, where everyone is valued. not according to the mind, but according to the ranks. For everyone, even for his wife, Lobachevsky is just a high-ranking official, head of the university, state councilor, holder of the orders of St. Vladimir 4th degree, St. Stanislav 3rd degree, St. Anna 2nd degree. He was awarded the insignia of impeccable service for twenty-five years, was awarded a full pension - two thousand rubles a year. The Tsar himself awarded him a diamond ring, and the Minister of Education showered him with thanks. Why is he called "a man not of this world"? They just don't understand him, they can't understand him. According to the existing rules, the Vladimir Cross already gives the right to nobility. That is why everyone is at a loss: why is Nikolai Ivanovich not bothering about restoring him to the rights of a hereditary nobleman? Aren't all of the bureaucratic people striving to break out into the nobility? Simonov has been walking among the nobility for a long time ... It is not so easy to dismiss relatives. Some are sophisticated in the history of science. The son of a poor farmer, Newton, did not renounce his nobility and knighthood; the son of a Norman peasant Laplace became a count. Didn't Gaspard Monge become a count through his service? Humboldt is said to have given himself the title of baron. Or, perhaps, the great Mikhail Lomonosov did not receive from the Tsaritsa an estate for a glass factory as a gift? .. Lobachevsky is sullenly silent. How to explain to all of them that now there is no time to bother about the nobility; in the midst of work on "New Beginnings", what is more important than ranks and titles? .. It is more difficult to cope with his wife. The tantrums start right away.

Think about the future of children! she screams. - Your children should be listed as nobles, so that after your death no one dares to push them around. Varvara Alekseevna's character is rather heavy. There's nothing to be done: the liver! Strong in appearance, Varvara Alekseevna is actually distinguished by very fragile health. She has many ailments. Even doctors helplessly give up. “My wife, naturally weak in constitution,” writes Nikolai Ivanovich to Velikopolsky, “experienced attacks of female illness, then fever, liver disorder, again uterine disease, and finally another fever. The complexity of the disease in her frail body led the doctors to a dead end.

It is better not to argue with her - she will still insist on her own. And only when the hysteria passes, he, calmly smoking his pipe, briefly and impressively points out to his wife the imprudence of her speeches. Guests, guests... endless guests! The ceilings and walls of a three-story building are trembling. Nikolai Ivanovich sits in his office, covering his ears with his hands. Varvara Alekseevna is in charge in the hall. Diseases are instantly forgotten. Varvara Alekseevna is a hospitable hostess. The smile never leaves her lips. Her passion is card games. The cards puff up until dawn. Nikolai Ivanovich enters, looks anxiously at his wife: her face is distorted with a grimace, her eyes shine feverishly, her fingers tremble. She learned to play cards from her brother Ivan Velikopolsky. When Ivan Ermolaevich arrives in Kazan, the Lobachevskys' house turns into a players' salon. Lobachevsky does not play cards, the players make him feel disgusted. Whether business chess! If you really can’t leave the guests to their fate, it’s better to play chess than to join the top five. The theory of chess is akin to mathematics. Perhaps someday this theory will become the starting point for a complex geometric or other system; the game will turn into a powerful method of learning. After all, the theory of probability was also born out of a game of dice... There is nothing superfluous in Lobachevsky's office. Table, armchair, books, manuscripts. There is no comfort here. Fuchs instilled an interest in collecting beetles and butterflies, in collecting herbaria and minerals. Collections on the table, under the table, on the walls. The office is like a laboratory. The rector sends expeditions to Siberia, to Asian countries, to Persia, Mesopotamia, Syria, Egypt, Turkey, and from there various curiosities are brought as gifts. There is a whole group of orientalists at the university: Kazembek, Berezin, Sivilov, Vasily Vasiliev, Osip Kovalevsky - professor of Mongolian literature. Kovalevsky was exiled to Kazan for belonging to a secret society. He has special supervision. Mirza Kazembek Alexander Kasimovich, professor at the Department of the Turkish-Tatar language, is the closest friend of Nikolai Ivanovich. With him, they fight in chess. This is how it is between them: Lobachevsky asks in Tatar, Kazembek answers in Turkish or French. A practice that brings many fun minutes. Kazembek dedicated one of his first works “On the Capture of Astrakhan in 1660” to Lobachevsky. Sometimes Alexander Kasimovich reads something from the "Shah-name" of the great Ferdowsi. Reads in Persian. Nikolai Ivanovich listens attentively to someone else's speech and thinks about incorruptibility, human thought. It is much more interesting with Kazembek than with the entire Kazan noble society. In 1835, at the initiative of Lobachevsky, "Scientific Notes of the Kazan University" began to appear. Here, in the very first volume, Nikolai Ivanovich publishes his "Imaginary Geometry" and the answer to critics from "Son of the Fatherland". “In one of the issues of the journal Son of the Fatherland for 1834, criticism was published that was very offensive to me and, I hope, completely unfair. The reviewer based his review on the fact that he did not understand my theory and considers it erroneous, because in the examples he encounters one absurd integral. However, I do not find such an integral in my work. In November last year I sent a reply to the publisher, which, however, I don’t know why, has not yet been published for five months. Stone slabs remained in the university yard after construction; they lay down here for centuries. One of the slabs cracked: a soft green sprout poked out through the crack. It was he, so defenseless in appearance, who split a multi-pood slab and climbed, climbed up to the sun ... - Imaginary geometry ... - said the rector and smiled tiredly. He firmly believes that with the discovery of "imaginary geometry" the monopoly of Euclid's geometry, which for more than twenty centuries was considered the only possible one, ended. Lobachevsky showed that Euclid's geometry is a special case of the "imaginary" geometry discovered by him. With the discovery of non-Euclidean geometry, fruitless attempts to prove Euclid's fifth postulate, a problem over which mathematicians struggled for two thousand years, ended. Subsequently, Lobachevsky called his geometry "pangeometry" (universal geometry). Only scientific experience could reveal which of the geometries is realized in real physical space. Lobachevsky's work received a negative assessment from the Academy of Sciences. Despite the lack of understanding of scientists and criticism in the press, the scientist continued to defend his views. He published a number of works - "Imaginary Geometry" (1835), "The Application of Imaginary Geometry to Certain Integrals" (1836), "New Beginnings of Geometry with a Complete Theory of Parallels" (1835-38). In 1840 Lobachevsky's book "Geometric Studies" was published in Germany in German. Karl Gauss, who came to non-Euclidean geometry independently of Lobachevsky, was delighted with his work and suggested that he be elected a corresponding member of the Göttingen Scientific Society for his scientific merits. This happened in 1842. Gauss himself, having discovered non-Euclidean geometry, did not publish the results, fearing misunderstanding. In contrast to him, the Hungarian mathematician J. Bolyai, in his work "Appendix" ("Appendix"), published in 1832 (separate reprints appeared in 1831), gave a concise presentation of the foundations of the new geometry. When Gauss wrote to him that he himself had come to this system of geometry long ago, Bolyai decided that he wanted to give himself the priority of discovery. Later, having become acquainted with the works of Lobachevsky and learning that the first publication appeared two years earlier than The Appendix, Boyai at first decided that Gauss was hiding under Lobachevsky's pseudonym. However, after studying the text, he saw the originality of the work and refused further research on non-Euclidean geometry. Only Lobachevsky fought for his ideas until the end of his life. Lobachevsky also obtained important results in other branches of mathematics - algebra (Lobachevsky's method), in mathematical analysis, etc. And now there is turmoil in Kazan: the tsar himself is coming here! Musin-Pushkin literally rages. It seems to him that not everyone shows due zeal. Cleanliness, order... Mikhail Nikolayevich appears with his cambric handkerchief now in the new building of the clinic, now in the library, now. in laboratories and offices, then in the observatory. For some reason, kings first of all rush to the latrine. Here - not a speck. In all cases, mahogany, varnish, parquet, glass. Yes, yes, the best in the Empire!.. Mikhail Nikolayevich involuntarily admires the slender architectural ensemble, created in just five years. Lobachevsky even. managed to save fifty thousand rubles. A lot of money. Korinfsky, of course, is a talented architect, but he does not have such a scope as Lobachevsky's. I studied architecture on my own - and now I beat everyone. Even in St. Petersburg and Moscow. Musin-Pushkin looks at the geometer as if he were some kind of miracle. Where does a person have so many talents? Why so many for one? The tsar must appreciate... Nicholas I is accompanied by the chief of gendarmes, Benkendorf, and the commandant of the Peter and Paul Fortress, Skobelev. The Tsar surveys the university absent-mindedly. He can't wait to get into the latrine. But the ceremony, even for kings, has the force of law. Finally it's all over! Nikolai wipes his sweaty forehead with a handkerchief. And while the tsar is in the closet, the chief of gendarmes and the commandant of the Peter and Paul Fortress stand at attention at the door. It was not by chance that Nicholas I came to the university. Not so long ago, a new charter of Russian universities was published. The charter gave broader powers to the trustee and the rector, democracy was curtailed. But the main task of the reform was to strengthen the role of the nobility in the government of the country, to make it difficult for people from the people to enter higher educational institutions, "to attract children of the upper class in the Empire to the university and put an end to the perverse education of them by foreigners." The tsar wanted to see with his own eyes how his orders were carried out by the authorities of Kazan University. The autocrat was unpleasantly surprised to learn that the rector of the local university was not a nobleman. Casting a cold look on Nikolai Ivanovich's colorless eyes, he said:

You, Lobachevsky, still wear civilian clothes? And still not in the nobility. Your work is known to us. Why did it happen? Submit to valid! And the wheel began to spin ... “Recognizing the above evidence of the hereditary nobility of State Councilor Nikolai Ivanov Lobachevsky as sufficient and consonant with the force of laws, the Kazan noble deputy assembly determines to include him, Lobachevsky, and his sons Alexei and Nikolai in the third part of the noble genealogy book.” They handed over a diploma for hereditary noble dignity, a “letter of honor” from the tsar on parchment and a noble coat of arms. “And we know that our loyal State Councilor Nikolai Lobachevsky, after completing the course of sciences at our Kazan University and after being awarded the 3rd title of master in August 1811, entered our service in March 1814, 26th, as an adjunct in physics mathematical sciences ... ”The coat of arms of the nobility caused a convulsive fit of laughter in the geometer. Before that, it was not necessary to see what the coat of arms is. I thought: something like a diploma or an order. And they brought a huge shield into the house. Immediately smelled of the Middle Ages, knightly times. The coat of arms is decorated not without hints. In the upper red field - a bee, a symbol of industriousness, and a six-pointed golden star, made up of two triangles; in the lower blue - a horseshoe of happiness and a flying arrow.

That's better! Musin-Pushkin said.

There was the son of a poor official who died of consumption, Kolya Lobachevsky. I did not think about honors, titles. Tried to avoid administrative dokuku. Hidden work was going on in the depths of the brain, which raised it above the Euclidean world, above the galaxies. But the stream of life picked it up, carried it to other heights. Crosses, nobles, ministers, kings, own stone house, estates, wife-landowner, nobility, eminent relatives, children ... As if with someone else. And who is growing and growing ... Wait now for a real civilian, new royal favors. And no one cares about non-Euclidean geometry. They consider it a miracle. “Whatever the child amuses himself ...” The tsar himself orders Lobachevsky to examine the higher educational institutions of St. Petersburg, Dorpat, and Moscow. He is back in Petersburg. Examines the Academy of Sciences, the University, the Pedagogical Institute, the Corps of Communications, Corps of Pages. Dreams of meeting Pushkin and Gogol. In St. Petersburg, Lobachevsky is waiting for heavy news: Pushkin was killed in a duel! Nikolai Ivanovich wanders aimlessly along the granite embankments of the Neva, chained with ice; Petersburg seems deserted. The most resonant string in the universe has been broken... Homeless and cold. When the news of Pushkin's death reached Kazan, Professor Surovtsev shed a tear and exclaimed: “The sun of Russian poetry has set: Pushkin is dead!.. Can we give a lecture? Let's go to church and pray for him..." At home, Lobachevsky found Varvara Alekseevna unconscious: it turns out that while he was away, his daughter Nadezhda died. This summer, Nikolai Ivanovich met the famous poet Vasily Zhukovsky, whose poems he knew. A tall, ruddy man in a tailcoat, the poet Zhukovsky accompanied the heir to Tsarevich Alexander Nikolaevich (the future Alexander II), who was traveling around Russia. The Tsarevich wished to inspect the university, to meet with its rector Lobachevsky. The meeting took place in the so-called "yellow hall" and did not make much of an impression on Nikolai Ivanovich. But then, after the departure of the Tsarevich, Lobachevsky still thought a lot about the poet Zhukovsky. Zhukovsky and Pushkin... They were friends. But how far apart are they! The irreconcilable enemy of the throne Pushkin and the courtier Zhukovsky, the educator of the royal children ... Interest in the work of Zhukovsky was forever lost. And you would bend your neck before His Majesty, serve his children? .. After all, even Euler ... Lobachevsky always put himself direct questions and answered them. He was a man of unusually sensitive and bashful soul. For himself, he never demanded anything, not even what was rightfully his. Only once ... and then for the sake of mischief, when he decided to leave the university, he decided to mock them. And they believed, took him for "their", demanding a legitimate share of the common pie. Since then, he no longer joked with them - because they do not have a sense of humor. Before the tsar had time to sneeze, Lobachevsky was already a real civilian!.. They always wanted to make him an accomplice. And now Nicholas has issued a new charter for the universities. Lobachevsky must implement this charter, which limits the access of the children of the people to higher educational institutions, to life. After all, Lobachevsky is now a nobleman, and what does he care about the raznochintsy? .. But what about Mably with his people's rights to revolution, Bacon, enlighteners, encyclopedists? Perhaps, after all, it is necessary to educate the people, as Pushkin did, and not the royal offspring? And Lobachevsky acts in a way that only he alone could do. Announcements are pasted all over the city: the rector of the university will give public lectures on certain days of the week "to spread the taste for learning." And he reads "people's physics, for the artisan class," that is, for the workers. No matter how busy he is, he never misses these lectures. The doors of the university are open to everyone. The cycle of public lectures of the rector is called "On the chemical decomposition and composition of bodies by the action of an electric current." He knows how to explain the most complex issues in a fascinating, intelligible way. Sets up experiments. He fights with the weapon most accessible to him - enlightenment. Students, masters, adjuncts help. And now the reading of public lectures becomes obligatory for everyone, by law. Even the sick Nikolsky, who knows how to make up for all the troubles, teaches the peasants arithmetic. Kotelnikov, Kazembek, old Ivan Ipatievich Zapolsky, former teacher of Lobachevsky, teacher of mathematics at the gymnasium, Alexander Popov, recently graduated from the university with a silver medal, chemist Zinin, botanist Eduard Eversman, son - Musin-Pushkin Nikolai - there are not so few of them, people's educators! Musin-Pushkin, of course, is true to himself: he secured a special reward for Nikolai Ivanovich "for the successful and very useful delivery of public lectures." The ministry did not figure out what it was about, the remuneration was paid. In the memorandum, the trustee noted: "Professor Lobachevsky captivated the audience, presenting them in poetic pictures the marvelous structure of the world with its various phenomena." When the minister later scolded Mikhail Nikolaevich for such an "innovation", Musin-Pushkin was sincerely surprised:

And what? It is necessary to educate... And Professor Lobachevsky says so! Years passed. July 1846 marked the 30th anniversary of his service at the university. According to the charter, the scientist had to leave, despite the fact that he was in his prime - he was only 53 years old. Soon the eldest son of Lobachevsky died, which undermined his health. He became sullen and began to go blind. A year before his death, sick and blind, Lobachevsky dictated his last work, Pangeometry. On February 24, 1856, the scientist died unrecognized, and above all in his homeland. As always, the case helped. After the death of Gauss, his diaries and correspondence were published, containing enthusiastic reviews of the work of Lobachevsky. They started talking about the scientist, began to look for his works. The first interpretation of its geometry, followed by recognition, was given by the Italian mathematician E. Beltrami. In 1895, the Lobachevsky International Prize was established for outstanding discoveries in the field of geometry. Its first laureates were the German scientists D. Hilbert and F. Klein, who developed the ideas of Lobachevsky and made important discoveries in the field of substantiation of Euclidean and non-Euclidean geometries. In 1896, a monument to Lobachevsky was opened in Kazan with funds raised by international subscription. The great discovery of the Kazan scientist expanded our geometric ideas. Along with Euclidean, scientists began to consider non-Euclidean spaces. “... The creation of Lobachevsky's geometry,” wrote Academician A.N. Kolmogorov, - was a turning point that determined to a large extent the entire style of mathematical thinking of the 19th century, which was so opposite to the style of thinking of mathematicians of the previous 18th century. The main scientific merit of N.I. Lobachevsky lies in the fact that for the first time he fully saw the logical unprovability of the Euclidean axiom of parallels and made all the main mathematical conclusions from this unprovability. The axiom of parallels, as you know, says: in a given plane to a given line, it is possible to draw only one parallel line through a given point not lying on this line. Unlike the rest of the axioms of elementary geometry, the axiom of parallels does not have the property of immediate evidence, at least for one thing, which is a statement about the entire infinite line as a whole, while in our experience we are faced only with larger or smaller "pieces" (segments ) straight lines. Therefore, throughout the history of geometry, from antiquity to the first quarter of the last century, there have been attempts to prove the axiom of parallel, i.e. derive it from the rest of the axioms of geometry. N.I. began with such attempts. Lobachevsky, who accepted the assumption opposite to this axiom that at least two parallel lines can be drawn to a given line through a given point. N.I. Lobachevsky sought to reduce this assumption to a contradiction. However, as he unfolded from his assumption and the totality of the rest of Euclid's axioms a longer and longer chain of consequences, it became more and more clear to him that no contradiction not only could not be obtained, but could not be obtained. Instead of contradiction, N.I. Lobachevsky received, although peculiar, but logically completely harmonious and impeccable system of sentences, a system that has the same logical perfection as ordinary Euclidean geometry. This system of sentences constitutes the so-called non-Euclidean geometry or Lobachevsky geometry. Having received the conviction of the consistency of the geometric system he built, N.I. Lobachevsky did not and could not give a rigorous proof of this consistency, since such a proof went beyond the limits of the methods of mathematics in the early 19th century. The proof of the consistency of Lobachevsky's geometry was given only at the end of the last century by Cayley, Poincare and Klein. Without giving a formal proof of the logical equality of his geometric system with the usual system of Euclid, N.I. Lobachevsky, in essence, fully understood the undoubtfulness of the very fact of this equality, expressing with complete certainty that, given the logical impeccability of both geometric systems, the question of which of them is implemented in the physical world can only be resolved by experience. N.I. Lobachevsky was the first to look at mathematics as an experimental science, and not as an abstract logical scheme. He was the first to set up experiments to measure the sum of the angles of a triangle; the first who managed to abandon the millennial prejudice of a priori geometric truths. It is known that he often liked to repeat the words: “Let work in vain, trying to extract all wisdom from one mind, ask nature, it keeps all secrets and your questions will be answered without fail and satisfactorily.” In the point of view of N.I. Lobachevsky, modern science introduces only one amendment. The question of what kind of geometry is realized in the physical world does not have that immediate naive meaning that was attached to it in the time of Lobachevsky. After all, the most basic concepts of geometry - the concepts of a point and a straight line, having been born, like all our knowledge, from experience, are, nevertheless, not directly given to us in experience, but arose only by abstraction from experience, as our idealization of experimental data, idealizations, which alone make it possible to apply the mathematical method to the study of reality. To clarify this, we will only point out that the geometric line, by virtue of its infinity alone, is not - in the form in which it is studied in geometry - the subject of our experience, but only an idealization of very long and thin rods or light rays directly perceived by us. . Therefore, the final experimental verification of the axiom of parallel Euclid or Lobachevsky is impossible, just as it is impossible to establish the sum of the angles of a triangle absolutely exactly: all measurements of any physical angles given to us are always only approximate. We can only assert that Euclid's geometry is an idealization of real spatial relationships, which satisfies us completely as long as we are dealing with "pieces of space not very large and not very small", i.e. as long as we do not go either way too far beyond our usual, practical scales, as long as we, on the one hand, say, remain within the solar system, and on the other, do not plunge too deep into the atomic nucleus. The situation changes when we move on to cosmic scales. And there, beyond the horizon of our most advanced telescopes, such a curvature of space and its super-total compression occurs that the problem disappears by itself. The modern general theory of relativity considers the geometric structure of space as something dependent on the masses acting in this space and comes to the need to involve geometric systems that are "non-Euclidean" in a much more complex sense of the word than that which is already associated with the geometry of Lobachevsky himself. The significance of the very fact of the creation of non-Euclidean geometry for all modern mathematics and natural sciences is colossal, and the English mathematician Clifford, who named N.I. Lobachevsky "Copernicus of Geometry", did not fall into exaggeration. N.I. Lobachevsky destroyed the dogma of "immovable, the only true Euclidean geometry" in the same way as Copernicus destroyed the dogma about the immovable, constituting the unshakable center of the Universe - the Earth. N.I. Lobachevsky convincingly showed that our geometry is one of several logically equal geometries, equally flawless, equally complete logically, equally true as mathematical theories. The question of which of these theories is true in the physical sense of the word, i.e. most adapted to the study of this or that circle of physical phenomena, there is precisely a question of physics, and not of mathematics, and, moreover, a question whose solution is not given once and for all by Euclidean geometry, but depends on what kind of circle of physical phenomena we have chosen. The only, indeed significant, privilege of Euclidean geometry remains that it continues to be a mathematical idealization of our everyday spatial experience and therefore, of course, retains its basic position both in a significant part of mechanics and physics, and even more so in all technology. But the philosophical and mathematical significance of N.I. Lobachevsky, of course, cannot belittle this circumstance.

List of works by Lobachevsky:

1. 1823. Geometry. Published in 1909 by the Kazan Physical and Mathematical Society. The "Geometry" is accompanied by two proofs of Euclid's postulate, which Lobachevsky expounded in his lectures of 1815-17.

2 1828 Extract from Wheatstone's memoir: "On the resonances or reciprocated vibrations of columns of air" ("Quarterly Journal of Science, Literature and Arts". New Series I, 175-183, London, 1828).

3. 1829-1830. On the Principles of Geometry (Kazan Vestnik, part 25, February and March 1829, pp. 178-187; April 1829, pp. 228-241; part 27, November and December 1829, pp. 227-243, tab. I, figs 1-9; part 28, March and April 1830, pp. 251-283, pl. II, figs 10-17; July and August 1830, pp. 571-636). Reprinted in the complete collection of works on geometry, vol. I, Kazan, 1883, pp. 1-67.

4. 1828. Speech on the most important subjects of education, read. July 5, 1828 (Kazanskiy Herald, part 35, August 1832, pp. 577-596).

5. 1834. Algebra or calculation of finite. Kazan, university printing house (Censored permission given by Sergei Aksakov, February 18, 1832 in Moscow), pp. X and 528. 8°.

6. 1834. Reducing the degree in a two-term equation, when the exponent without a unit is divided by 8 ("Scientific Notes", 1834, I, pp. 3-32).

7. 1834. On the disappearance of trigonometric lines ("Scientific Notes", 1834, II, pp. 167-226).

8. 1835. Conditional equations for the motion and position of the main axes of circulation in a solid system ("Scientific Notes" of Moscow University. February 1835, No. VIII, pp. 169-190).

9. 1835. Imaginary geometry ("Scientific Notes", 1835, I, pp. 3-83, tables with figs. 1-8). Almost identical to No. 13. Reprinted in the Complete Works, Vol. I, pp. 71-120.

10. 1835. A way to ensure the disappearance of infinite lines and to approach the value of functions of very large numbers (Scientific Notes, 1835, II, pp. 211-342).

11. 1835-1838. New beginnings of geometry with a complete theory of parallels ("Scientific Notes", 1835, III. pp. 3-48. Introduction and chapter I, І table, figs. 1-20; 1836, II, pp. 3-98, chapters II - V, 3 pl., figs 21-41, 42-60, 61-75; 1836, III, pp. 3-50, chapters VI-VII, 2 pl., figs 76-91, 92-106; 1837 , I. pp. 3-97, chapters VIII-XI, 2 tables, figs 107-120, 121-134; 1838, I, pp. 3-124, chapter XII; 1838, III, pp. 3-65 , chapter XIII). Reprinted in Complete Works, vol. I, pp. 219-486.

12. 1836. Application of imaginary geometry to some integrals ("Scientific Notes", 1836, I, pp. 3-166, 1 table, figs. 1-20). Reprinted in the Complete Works, Vol. I, pp. 121-218.

13. 1837. Géométrie imaginaire par Mr. N. Lobatschewsky, recteur de l "Université de Cazan. (Crelle's Journal. T. 17, volume 4, pp. 295-320, 1 tab., figs. 1-8. Berlin, 1837; sent in 1834 or 1835 .) Reprinted in the Complete Works, vol. II, pp. 581-613.

14. 1840 russ. wirkl. Staatsrathe und ord. Prof. der Mathematik bei der Universität Kasan. Berlin. 1840. In der F. Finckeschen Buchhandlung (Weidle "sche Buchdruckerei) 61 pp. small octave, 2 tables, figs. 1-15, 16-35. Reprinted fac simile by Mayer und Müller in Berlin 1887. Reprinted in the Complete Works , vol. II, pp. 553-578.

15. 1841. Ueber die Convergenz der unendlichen Reihen The appendix has a special pagination and Lobachevsky's article occupies the first 48 pages).

16. 1842. Sur la probabilité des résultats moyens, tirés des observations répétées. (Par Mr. Lobatschefsky, recteur de l "université de Cazan. Journal der reinen und angewandten Mathematik von Grelle. Bd. 24. Heft. 2, pp. 164-170). Translation of some pages from chapter XII of New Beginnings. Complete collected works, pp. 428-438.

17. 1842. Total eclipse of the sun in Penza on June 26, 1842 (“Scientific Notes”, 1842, III, pp. 51-83; also reprinted in the “Journal of the Ministry of National Education”, 1843, vol. XXXIX, section II, pp. 65-96).

18. 1845. Detailed analysis of the reasoning presented by master A.F. Popov under the title: “On the integration of differential equations of hydrodynamics reduced to linear form”, for the degree of Doctor of Mathematics and Astronomy. Appendix to Popov's doctoral dissertation. Kazan, 1845.

19. 1852. The value of some definite integrals ("Scientific Notes", 1852, vol. IV, issue I, pp. 1-26; issue II, pp. 27-34). This work also appeared in German in the "Archiv für wissenschaftliche Kunde von Russland" published by G. A. Erman. Berlin 1855. Bd. 14, pp. 232-272, under the title: "Ueber den Werth einiger bestimmten Integrale. Nach dem Russischen von Herrn Lobatschefskji, Prof. emer. in Kasan.

20 1856 University, in memory of its fifty years of existence, vol. I. Kazan, 1856, pp. 279-340. Reprinted in the Complete Collected Works, vol. II, pp. 617-680).

21. 1855. Pangeometry, Honored Professor N.I. Lobachevsky ("Scientific Notes", 1855, vol. І, pp. 1-56; Kazan, 1856. Coincides with No. 20. Reprinted in the Complete Collected Works, vol. І, pp. 489-550).

/ P.S.Aleksandrov // Advances in Mathematical Sciences. - 1946. - V.1. - No. 1(11). - C.11-14. but

Kolesnikov M.S. Lobachevsky / M.S. Kolesnikov. - M., 1965. - 319 p. 51-K603 to/x

Smogorzhevsky A.S. On the geometry of Lobachevsky / A.S. Smogorzhevsky. - Moscow: Gostekhteoretizdat, 1957. - 67 p. - (Popular lectures on mathematics; issue 23) 513-C51 to/x

1. Aleksandrov A.D. Significance of Lobachevsky geometry/ A.D. Aleksandrov // In memoriam N.I. Lobatschevskii. - Kazan, Kazan University Publishing House. - 1995. - V.3. - N 1. - P.4-9.
2. Aleksandrov I.A. On the works of N.I. Lobachevsky in the field of mathematical analysis / I.A. Aleksandrov // 2 Sib. geom. Conf., Tomsk, November 26-30, 1996. - Tomsk, 1996. - P.8-12. G97-2512 kh4
3. Aleksandrov P.S. N.I. Lobachevsky - the great Russian mathematician [To the 100th anniversary of his death]. Public lecture transcript. / P.S. Aleksandrov. - M., 1956. - 24 s. 51-A464 to/x
4. Bespamyatnykh N.D. Scientific and methodological significance of the algebraic works of N.I. Lobachevsky: author. diss. ... / N.D. Bespamyatnykh. - Grodno, 1949. - 6 p. A-7079 to/x
5. Bonola R. Non-Euclidean geometry: a critical and historical study of its development / R. Bonola; per. from Italian. and foreword. A.R. Kulisher; foreword G. Libman. - M.: URSS, 2010. - 216 p. - (Physico-mathematical heritage: mathematics (history of mathematics): FMN). - From the appendix: N.I. Lobachevsky's attitude to the theory of parallel lines until 1826: article / A.V. Vasiliev. V18-B815 but
6. Buchstaber V.M. History of the Prize N.I. Lobachevsky (on the occasion of the 100th anniversary of the first award in 1897)/ V.M. Buchstaber, S.P. Novikov // Advances in Mathematical Sciences. - 1998. - T.53. - No. 1 (319). - P.235-238. but
7. Vasiliev A.V. The value of N.I. Lobachevsky for the Imperial Kazan University: Speech, delivered. on the day of the opening of the monument to N.I. Lobachevsky 1 Sept. 1896 prof. A. Vasiliev - Kazan: Tipo-lit. Imp. University, 1896.
8. Vakhtin B.M. The great Russian mathematician N.I. Lobachevsky / B.M. Vakhtin. - M., 1956. - 55 p. 51-B.226 to/x
9. Vishnevsky B.V. The contribution of Boyai, Gauss and Lobachevsky to the discovery of non-Euclidean geometry (to the 200th anniversary of the birth of Janos Boyai) / VV Vishnevsky // Izvestiya vysshikh uchebnykh zavedenii. Maths. - 2002. - N 11. - S.3-7. but
10. Vishnevsky V.V. The creative heritage of N.I. Lobachevsky and his role in the formation and development of Kazan University / V.V. Vishnevsky. - Kazan: Kazan Publishing House. un-ta, 2006. - 65 p. G2007-7213 V1d/W555 b/w1
11. Gaiduk Yu.M. Additional materials on the history of the dissemination of N.I. Lobachevsky's ideas in Russia / B.V. Fedorenko // Historical and mathematical research. - Issue 9. - M., 1956. - S.215-246. 51-I902/N9 to/x
12. Gerasimova V.M. Index of literature on the geometry of Lobachevsky and the development of its ideas / V.M. Gerasimova. - M., 1952. - 192 p. 513-G361/N7 to/x
13. Glukhov A. "To keep the fire of life": Nikolai Ivanovich Lobachevsky (1792-1856) / A. Glukhov // University book. - 2000. - N 5. - C.24-28. С4921 b/w11
14. Delaunay B.N. Elementary proof of the consistency of Lobachevsky's planimetry / B.N. Delone. - M., 1956. - 139 p. 513-D295 to/x
15. Dulsky P.M. The builder of Kazan University, the great Russian mathematician N.I. Lobachevsky and his iconography / P.M. Dulsky // Kagan V.F. Lobachevsky. - M.-L., 1948. - S.273-487. 51-K129 to/x
16. Evtushik L.E. Influence of Lobachevsky's ideas on the development of differential geometry / L.E. Evtushik, A.K. Rybnikov // Vestn. Moscow university Ser. 1, Mathematics, mechanics. - 1994. - N 2. - S.3-14. but
17. Kadomtsev S.B. Geometry of Lobachevsky and physics / S.B.Kadomtsev. - 2nd ed., corrected. - M., 2007. - 63 p. B18/K136 but
18. Koveshnikov E.V. Incompleteness and uncertainty of the classical geometry of Euclid and the history of their overcoming in the geometries of Lobachevsky, Riemann, Hilbert and Mandelbrot / E.V. Koveshnikov, V.N. Savchenko // Actual problems of the humanities and natural sciences. - 2011. - N 5. - S.77-83. but
19. Kurashov V. Lessons of N.I. Lobachevsky / V. Kurashov // Higher education in Russia. - 2005. - N 5. - S.124-126. C4528 to/x
20. Litsis N.A. Philosophical and scientific significance of the ideas of N.I. Lobachevsky / N.A. Litsis. - Riga, 1976. - 396 p. G76-14673 to/x
21. Lishevsky V.P. Geometry Copernicus / V.P. Lishevsky // Science in Russia. - 1996. - N 5. - S.57-60. but
22. Lunts G.L. Analytical works of N.I. Lobachevsky/ G.L.Lunts // Advances in Mathematical Sciences. - 1950. - V.5. - No. 1(35). - P.187-195. but
23. Manturov O.V. Nikolai Ivanovich Lobachevsky (on the occasion of his 200th birthday)/ O.V. Manturov // Advances in Mathematical Sciences. - 1993. - T.48. - N 2 (290). - P.5-16. but
24. Markov N.V. N.I. Lobachevsky - the great Russian scientist / N.V. Markov. - M., 1956. - 55 p. 51-M272 to/x
25. Mednykh A.D. Mathematics: a three-dimensional world in which we do not live / A.D. Mednykh // Science first hand. - 2006. - N 2 (8). - P.86-97. but
26. Nagaeva V. Pedagogical ideas and activities of N.I. Lobachevsky: abstract of diss. … / V. Nagaeva. - M., 1949. - 16 p. A-7091 to/x
27. Natural mathematics: the ideas of Napier and Lobachevsky in modern times. science: (collection) / [Ed. Vereshchagin I.A.]. - Berezniki, 1995. - 174 p. - (Connection of times; issue 2). G94-3436/N2 kx
28. Norden A.P. The legacy of N.I. Lobachevsky and the activities of Kazan geometers/ A.P.Norden, A.P.Shirokov // Advances in Mathematical Sciences. - 1993. - T.48. - N 2 (290). - P.47-74. but
29. On the theory of parallel lines by N.I. Lobachevsky// Mathematical collection. - 1868. - V.3. - N 2. - S.78-120.
30. Non-Euclidean spaces and new problems in physics = Non - Euclidean spaces and new problems in physics: Sat. Art., dedicated. To the 200th anniversary of N.I. Lobachevsky / Editorial Council: D.D. Ivanenko (prev.) and others - M .: Belka, 1993. - 72 p. G93-8771 kh4
31. Pont Jean-Claude. Theory of parallel and non-Euclidean geometry: an epistemological question in the work of N.I. Lobachevsky / Jean-Claude Pont. - Kazan: Kazan Publishing House. un-ta, 2003. - 47 p. G2004-18691 W181/P567 chz1
32. Celebration by Kazan University of the centenary of the discovery of non-Euclidean geometry by N.I. Lobachevsky, 11/24/1826-11/25/1926. - Kazan. 1927. - 112 p. DH-4475 to/x
33. Application and development of Lobachevsky ideas in modern physics = Application and development of Lobachevsky ideas in modern physics: tr. intl. seminar dedicated to 75th anniversary of N.A. Chernikov, Dubna, 25-27 Feb. 2004 - Dubna: JINR, 2004. - 206 p. G2005-14051 W311/P764 chz1
34. Rukavitsyn I.N. N.I. Lobachevsky: on the centenary of the discovery of non-Euclidean geometry / I.N. Rukavitsyn. - Irkutsk, 1926. - 32 p. B86-956 to/x
35. Severikova N.M. Scientific feat N.I. Lobachevsky / N.M. Severikova // Historical sciences. - 2008. - N 2. - S. 85-89. Т3137 b/w8
36. System hypercomplex physics: Lobachevsky's ideas in the science of the XXI century: (collection) / [Ed. Vereshchagin I.A.]. - Berezniki, 1996. - 238 p. - (Link of Times; issue 3) B31-C409/3 but
37. One Hundred and Twenty Five Years of Lobachevsky's Non-Euclidean Geometry. 1826-1951. Celebration of Kazan. state un-vol. V.I. Ulyanov-Lenin and Kazan Phys.-Mat. Society of the 125th anniversary of the discovery of non-Euclidean geometry by N.I. Lobachevsky. - M.-L., 1952. - 208 p. 513-C81 to/x
38. Khilkevich E.K. Lectures on the course "Fundamentals of Geometry. Geometry of Lobachevsky and Experience. The Philosophical Significance of Lobachevsky's Creativity" / E.K. Khilkevich. - Tyumen, 1956. - 16 p. 513-X458 to/x
39. Chusov A.V. On changing the ontology of understanding space in the 19th century / A.V. Chusov // Bulletin of the Moscow University. Series 7: Philosophy. - 2010. - N 4. - S.64-74. but
40. Shestakov A. Leonard Euler and N.I. Lobachevsky / A. Shestakov, A. Kiryukov // Leonhard Euler - a great mathematician. - M.: MIKHiS, 2008. - P.138. G2009-3643 V.d/E322 b/w1
41. Yushkevich A.P. N.I. Lobachevsky. Scientific and pedagogical heritage. Leadership of Kazan University. Fragments. Letters (review) / A.P. Yushkevich // Advances in Mathematical Sciences. - 1978. - T.33. - No. 3(201). - C.217-221. but
42. Yaglom I.M. Galileo's principles of relativity and non-Euclidean geometry: monograph / I.M. Yaglom. - M.: Editorial URSS, 2004. - 303 p. (revised Nov 2018) In memoriam N. I. Lobatschevskii (revised Nov 2018)

Nikolai Ivanovich Lobachevsky - an outstanding Russian mathematician, for four decades - rector, activist of public education, founder of non-Euclidean geometry.

This is a man who was several decades ahead of his time and remained misunderstood by his contemporaries.

Biography of Lobachevsky Nikolai Ivanovich

Nikolai was born on December 11, 1792 in a poor family of a petty official Ivan Maksimovich and Praskovia Alexandrovna. The birthplace of the mathematician Nikolai Ivanovich Lobachevsky is Nizhny Novgorod. At the age of 9, after the death of his father, he was transported by his mother to Kazan and in 1802 was admitted to the local gymnasium. After graduating in 1807, Nikolai became a student at the newly founded Kazan Imperial University.

Under the tutelage of M. F. Bartels

A special love for the physical and mathematical sciences was able to instill in the future genius Grigory Ivanovich Kartashevsky, a talented teacher who deeply knew and appreciated his work. Unfortunately, at the end of 1806, due to disagreements with the leadership of the university, "for displaying a spirit of disobedience and disagreement," he was dismissed from the university service. Bartels, a teacher and friend of the famous Carl Friedrich Gauss, began to teach mathematics courses. Arriving in Kazan in 1808, he took patronage over a capable but poor student.

The new teacher approved of the progress of Lobachevsky, who, under his supervision, studied such classic works as "The Theory of Numbers" by Carl Gauss and "Celestial Mechanics" by the French scientist Pierre-Simon Laplace. For disobedience, stubbornness and signs of godlessness in his senior year, the likelihood of expulsion hung over Nikolai. It was the patronage of Bartels that contributed to the removal of the danger hanging over the gifted student.

in the life of Lobachevsky

In 1811, upon graduation, Nikolai Ivanovich, whose brief biography is of sincere interest to the younger generation, was approved as a master in mathematics and physics and left at the educational institution. Two scientific studies - in algebra and mechanics, presented in 1814 (earlier than the deadline), led to his elevation to adjunct professor (associate professor). Further, Nikolai Ivanovich Lobachevsky, whose achievements would later be correctly assessed by descendants, began teaching himself, gradually increasing the range of courses he read (mathematics, astronomy, physics) and seriously thinking about the restructuring of mathematical principles.

The students loved and highly appreciated the lectures of Lobachevsky, who a year later was awarded the title of extraordinary professor.

New orders of Magnitsky

In order to suppress freethinking and revolutionary mood in society, the government of Alexander I began to rely on the ideology of religion with its mystical-Christian teachings. Universities were the first to undergo drastic checks. In March 1819, M. L. Magnitsky, a representative of the main board of schools, arrived in Kazan with an audit, taking care exclusively of his own career. According to the results of his check, the state of affairs at the university turned out to be extremely deplorable: the lack of scholarship of the pupils of this institution entailed harm to society. Therefore, the university needed to be destroyed (publicly destroyed) - with the aim of an instructive example for the rest.

However, Alexander I decided to correct the situation with the hands of the same inspector, and Magnitsky, with particular zeal, began to “put things in order” within the walls of the institution: he removed 9 professors from work, introduced the strictest censorship of lectures and a harsh barracks regime.

The wide activity of Lobachevsky

The biography of Nikolai Ivanovich Lobachevsky describes the difficult period of the church-police system established at the university, which lasted for 7 years. The strength of the rebellious spirit and the absolute employment of the scientist, which did not leave a single minute of free time, helped to withstand difficult tests.

Nikolai Ivanovich Lobachevsky replaced Bartels, who left the walls of the university, and taught mathematics in all courses, also headed the physics room and read this subject, taught students astronomy and geodesy, while I. M. Simonov was on a trip around the world. Enormous work was invested by him in putting the library in order, and especially in filling its physical and mathematical part. Along the way, mathematician Nikolai Ivanovich Lobachevsky, being the chairman of the construction committee, supervised the construction of the main building of the university and for some time served as dean of the Faculty of Physics and Mathematics.

Non-Euclidean geometry of Lobachevsky

The colossal number of current cases, extensive pedagogical, administrative and research work did not become an obstacle to the creative activity of the mathematician: 2 textbooks for gymnasiums came out from his pen - Algebra (convicted for use and Geometry (not published at all). Magnitsky for Nikolai Ivanovich was placed under strict supervision, due to the manifestation of insolence and violation of established instructions. However, even under these conditions, acting humiliatingly on human dignity, Lobachevsky Nikolai Ivanovich worked hard on the strict construction of geometric foundations. The result was the discovery of new geometry by scientists, committed on the path of a radical revision of the concepts of the era of Euclid (3rd century BC).

In the winter of 1826, a Russian mathematician carried out a report on geometric principles, which was submitted for review to several eminent professors. However, the expected review (neither positive nor even negative) was not received, and the manuscript of the valuable report has not survived to our times. The scientist included this material in his first work "On the Principles of Geometry", published in 1829-1830. in the Kazan Bulletin. In addition to presenting important geometric discoveries, Nikolai Ivanovich Lobachevsky described a refined definition of a function (clearly distinguishing between its continuity and differentiability), undeservedly attributed to the German mathematician Dirichlet. Also, the scientists made careful studies of trigonometric series, evaluated several decades later. A talented mathematician is the author of a method for the numerical solution of equations, which over time was unfairly called the “Greffe method”.

Lobachevsky Nikolai Ivanovich: interesting facts

The auditor Magnitsky, who for several years inspired fear with his actions, was expected by an unenviable fate: for many abuses revealed by a special audit commission, he was removed from his post and sent into exile. Mikhail Nikolaevich Musin-Pushkin was appointed the next trustee of the educational institution, who managed to appreciate the active work of Nikolai Lobachevsky and recommended him to the post of rector of Kazan University.

For 19 years, starting in 1827, Lobachevsky Nikolai Ivanovich (see photo of the monument in Kazan above) worked hard in this post, achieving the dawn of his beloved offspring. On Lobachevsky's account - a clear improvement in the level of scientific and educational activities in general, the construction of a huge number of office buildings (physics office, library, chemical laboratory, astronomical and magnetic observatory, mechanical workshops). The rector is also the founder of the strict scientific journal "Scientific Notes of the Kazan University", which replaced the "Kazan Vestnik" and was first published in 1834. In parallel with the rector's office for 8 years, Nikolai Ivanovich was in charge of the library, was engaged in teaching activities, and wrote instructions to mathematics teachers.

Lobachevsky's merits include his sincere cordial concern for the university and its students. So, in 1830, he managed to isolate the educational territory and conduct a thorough disinfection in order to save the staff of the educational institution from the cholera epidemic. During a terrible fire in Kazan (1842), he managed to save almost all educational buildings, astronomical instruments and library material. Nikolai Ivanovich also opened free access to the university library and museums to the general public and organized popular science classes for the population.

Thanks to the incredible efforts of Lobachevsky, the authoritative, first-class, well-equipped Kazan University has become one of the best educational institutions in Russia.

Misunderstanding and rejection of the ideas of the Russian mathematician

All this time, the mathematician did not stop in ongoing research aimed at developing new geometry. Unfortunately, his ideas - deep and fresh, went so against the generally accepted axioms that contemporaries failed, and perhaps did not want to appreciate the works of Lobachevsky. Misunderstanding and, one might say, bullying to some extent did not stop Nikolai Ivanovich: in 1835 he published "Imaginary Geometry", and a year later - "The Application of Imaginary Geometry to Some Integrals". Three years later, the world saw the most extensive work, New Principles of Geometry with a Complete Theory of Parallels, which contained a concise, extremely clear explanation of his key ideas.

A difficult period in the life of a mathematician

Having not received understanding in his native land, Lobachevsky decided to acquire like-minded people outside of it.

In 1840, Lobachevsky Nikolai Ivanovich (see photo in the review) published his work with clearly stated main ideas in German. One copy of this edition was handed to Gauss, who himself was secretly engaged in non-Euclidean geometry, but did not dare to speak publicly with his thoughts. Having familiarized himself with the works of the Russian colleague, the German recommended that the Russian colleague be elected to the Gottingen Royal Society as a corresponding member. Gauss spoke laudatory about Lobachevsky only in his own diaries and among the most trusted people. The election of Lobachevsky nevertheless took place; this happened in 1842, but it did not improve the position of the Russian scientist in any way: he had to work at the university for another 4 years.

The government of Nicholas I did not want to evaluate the many years of work of Nikolai Ivanovich Lobachevsky and in 1846 suspended him from work at the university, officially naming the reason: a sharp deterioration in health. Formally, the former rector was offered the position of assistant trustee, but without a salary. Shortly before his dismissal and deprivation of the professorial department, Lobachevsky Nikolai Ivanovich, whose brief biography is still being studied in educational institutions, recommended instead of himself the teacher of the Kazan Gymnasium A.F. Popov, who perfectly defended his doctoral dissertation. Nikolai Ivanovich considered it necessary to give the right path in life to a young capable scientist and found it inappropriate to occupy the chair under such circumstances. But, having lost everything at once and finding himself in a position that was completely unnecessary for himself, Lobachevsky lost the opportunity not only to lead the university, but also to somehow participate in the activities of the educational institution.

In family life, Lobachevsky Nikolai Ivanovich since 1832 was married to Varvara Alekseevna Moiseeva. In this marriage, 18 children were born, but only seven survived.

last years of life

Forced removal from the work of his whole life, rejection of the new geometry, the rude ingratitude of his contemporaries, a sharp deterioration in the financial situation (due to ruin, the wife's estate was sold for debts) and family grief (the loss of the eldest son in 1852) had a devastating effect on physical and spiritual health Russian mathematician: he noticeably haggard and began to lose his sight. But even the blind Nikolai Ivanovich Lobachevsky did not stop attending exams, came to solemn events, participated in scientific disputes and continued to work for the benefit of science. The main work of the Russian mathematician "Pangeometry" was written by students under the dictation of the blind Lobachevsky a year before his death.

Lobachevsky Nikolai Ivanovich, whose discoveries in geometry were appreciated only decades later, was not the only researcher in the new field of mathematics. The Hungarian scientist Janos Bolyai, independently of his Russian colleague, brought to the court of his colleagues in 1832 his vision of non-Euclidean geometry. However, his works were not appreciated by contemporaries.

The life of an outstanding scientist, wholly devoted to Russian science and Kazan University, ended on February 24, 1856. They buried Lobachevsky, who was never recognized during his lifetime, in Kazan, at the Arsky cemetery. Only after a few decades did the situation in the scientific world change dramatically. A huge role in the recognition and acceptance of the works of Nikolai Lobachevsky was played by the studies of Henri Poincare, Eugenio Beltrami, Felix Klein. The realization that Euclidean geometry had a full-fledged alternative had a significant impact on the scientific world and gave impetus to other bold ideas in the exact sciences.

The place and date of birth of Nikolai Ivanovich Lobachevsky are known to many contemporaries related to the exact sciences. In honor of Nikolai Ivanovich Lobachevsky, a crater on the Moon was named. The name of the great Russian scientist is the scientific library of the University in Kazan, to which he devoted a huge part of his life. There are also Lobachevsky streets in many cities of Russia, including Moscow, Kazan, Lipetsk.

480 rub. | 150 UAH | $7.5 ", MOUSEOFF, FGCOLOR, "#FFFFCC",BGCOLOR, "#393939");" onMouseOut="return nd();"> Thesis - 480 rubles, shipping 10 minutes 24 hours a day, seven days a week and holidays

240 rub. | 75 UAH | $3.75 ", MOUSEOFF, FGCOLOR, "#FFFFCC",BGCOLOR, "#393939");" onMouseOut="return nd();"> Abstract - 240 rubles, delivery 1-3 hours, from 10-19 (Moscow time), except Sunday

Starshinov Nikolay Ivanovich Organizational and pedagogical activity and pedagogical views of N. I. Lobachevsky: Dis. ... cand. ped. Sciences: 13.00.01: Kazan, 2001 229 p. RSL OD, 61:02-13/734-8

Introduction

Chapter I Organizational and pedagogical activity of I.I. Lobachevsky .

1.1. Formation of N.I. Lobachevsky as a scientist and teacher 12

1.2. Organizational and pedagogical activity of N.I. Lobachevsky at Kazan University 29

1.3. Pedagogical activity of N.I. Lobachevsky on the leadership of the Kazan educational district 44

Conclusions on the first chapter 72

Chapter II. Pedagogical activity. Pedagogical views of N. I. Lova .

2.1. N.I. Lobachevsky as a teacher, his pedagogical views 75

2.2. Pedagogical views of N.I. Lobachevsky on the problems of educating students 94

2.3. On the continuity and prospects of the scientific and pedagogical heritage of N.I. Lobachevsky at Kazan University 1.19

Conclusions on the second chapter 141

Conclusion 145

Bibliographic list of used literature 150

Appendix 1. Materials for the biography of N.I. Lobachevsky 166

Annex 2. Didactic complex for the special course "Scientific and pedagogical heritage of N.I. Lobachevsky". 172

Annex 3. The way of recognition of the ideas of N.I. Lobachevsky

Introduction to work

On the eve of the 200th anniversary of Kazan State University, pedagogical views, the results of the organizational, pedagogical and scientific activities of N.I. they are especially relevant, and his pedagogical system is not only not outdated, but continues to develop.

In the process of modernization of modern education, the diversity of ideas, theories, concepts of its development is growing, at the same time new problems arise, including the loss of value orientations in education and a noticeable decrease in the prestige of pedagogical science as the basis for the professional and pedagogical training of future teachers. the need to comprehend and generalize everything valuable that has been accumulated in the history of domestic pedagogical science, is said in a number of studies conducted in recent years (N.D. Nikayadrov, V.A. Slastenin, B.S. Gershunsky, V.I. Andreev, L.G. Vyatkin, E.G. Osovsky, A.I. Piskunov and others).

Back in the middle of the 19th century, K.D. Ushinsky pointed out the need to systematize the facts and patterns of anthropological sciences, on which "the rules of pedagogical theory are based." Means of optimal

The most important solution to pedagogical problems has long been considered their study and analysis in the historical aspect, taking into account the prospects for the future.

The merits of N.I. Lobachevsky in the field of development of education in Russia are enormous. Significant work on the study of his heritage was done by specialists in various fields of knowledge: mathematicians, historians, teachers, philosophers:% - as the largest figure in university education (V.V. Aristov,

V.A.Bazhanov, A.V.Vasiliev, M.T.Nuzhin, B.L.Laptev, V.V.Morozov and others); as a great Russian mathematician, creator of non-Euclidean geometry (A. V. Vasiliev, V. V. Kuzmin, B. L. Laptev, A. P. Norden, B. V. Fedorenko and others); as an excellent subject teacher (A. V. Vasilyev, V. M. Verkhunov, E. D. Dneprov, B. L. Laptev, V. V. Morozov, A. I. Markushevich, A. P. Norden and others); as a teacher-educator (P.S. Aleksandrov, B.L. Laptev, B.V. Fedorenko, A.V. Vasiliev and others).

A number of dissertations are devoted to various aspects of the scientific and pedagogical heritage of N.I. Lobachevsky; V.M. Nagaeva (1949), B.V. Bolgarsky (1955), and a teacher in the encyclopedic dictionary is defined as a person who conducts practical work on the upbringing, education and training of children and youth and has special training in this area, as well as developing theoretical problems of pedagogy. We are interested in these concepts in relation to N.I. Lobachevsky. In the future, we will consider the stages of his formation as a scientist in the era of the formation of Kazan University, as well as as a specialist in the natural sciences and as a teacher, who was a highly erudite person in various fields of knowledge.

We will trace the following stages of the life of N.I. Lobachevsky - childhood, student years and independent scientific and pedagogical activity.

The stages of the life of any person are important not only for revealing their meaning and value for later life, but also in themselves. Researchers such as L. de Moz, Bodo von Borris, Ralph Frenken rightly believe that it is also necessary to analyze childhood from the point of view of "the subsequent problems of adult life, the propensity to make certain decisions, the strengthening or weakening of social tension in society, whose members lived a certain childhood" [P2, p.49]. We believe that this approach is also applicable to the study of the youth of a certain personality. From such positions, we will try to consider the above-mentioned periods of the life of N.I. Lobachevsky.

Teachers, psychologists, historians have established that the immediate environment in which they lived - family, neighbors, place of residence (city, suburb, village), school - had a strong impact on the lives of children. The family performs many functions - educational, cultural, regulating, reproducing. The family is a special microcosm, with its own traditions and attitudes. They are quite stable over time, manifest themselves throughout a person’s life, and are reproduced in the nature of raising children. Family relationships and cultural traditions lay the "script" of a person's adult life. In the family, important factors in upbringing were "not only the professions of parents, but also the religious beliefs of family members, their personal characteristics, education, relationships with each other and with distant relatives, family size, and much more."

The childhood years of the future geometer were spent in Nizhny Novgorod in a family consisting of parents and two brothers. A number of assumptions have been made regarding the personality of the father in historiography. An end to this discussion was put by the study of the outstanding mathematician D.A. Gudkov. After analyzing the sources published by a number of researchers (L.B. Modzalevsky, A.A. Andronov, B.F. Fedorenko), he pointed out errors in publications that led to incorrect conclusions. DA. Gudkov convincingly, in our opinion, proved that the father of Alexander, Nikolai and Alexei Lobachevsky was the Makaryevsky district surveyor, Captain Sergei Stepanovich Shebarshin. N.I. Lobachevsky spent his childhood in his house on Alekseevskaya Street near the Black Pond.

S.S.Shebarshin was born in 1748/49, came from "soldier's children". Thanks to his abilities, he was accepted and studied at the gymnasium at Moscow University, and then at the university itself. After graduating from the university, Shebarshin was enrolled in 1771 by the Senate as a surveyor of the Survey Office, in 1775 - a land surveyor. As T.I. Kovaleva and N.F. Filatov rightly note, “the very fact of involving him in land surveying, which required special knowledge in mathematical calculation, geography and geometry, as well as in drawing and drawing, gives reason to believe that within the walls of the Moscow University S.S. Shebarshin showed due interest not only in the exact sciences, but also in the arts. The documents published by D.A. Gudkov allow us to conclude that S.S. Shebarshin was a conscientious official, a decisive and principled person. This did not go unnoticed by the authorities and he quickly moved up in the service. In June 1893, he was appointed to be a land surveyor at the Makarievsk district court. Makariev, at that time was a major trading center in Russia. Service in this city was considered not only prestigious, but also profitable. By 1797 he owned in Nizhny Novgorod two houses, three plots of land, two serfs, etc.

The mother of Nikolai Ivanovich was Praskovya Alexandrovna Lobachevskaya (1765-1840) - "a woman of dramatic and mysterious fate", as D.A. Gudkov writes. So far, her maiden name has not been established, although a number of assumptions have been made. She came from landless nobles and owned a house in Makaryev and six serfs, bought by her in 1793 from S.S. Shebarshin. Approximately between the spring of 1787 and the first half of 1789, she married the poorest official - the registrar Ivan Maksimovich Lobachevsky, who then already suffered from "suffocation and scurvy disease." For unknown reasons, this marriage broke up. However, there was no official divorce. Not later than the end of 1790, Praskovya Alexandrovna joined her fate with S.S. Shebarshin. She was then 24/25 years old, he was 40/41 years old. S.S. Shebarshin favorably differed from I.M. Lobachevsky both in terms of the level of education (he let know the encyclopedic knowledge he received at Moscow University, great life experience), and in terms of his position in the bureaucratic world, and in material well-being. They had three sons. In the autumn of 1797, S.S. Shebarshin died and Lobachevsky had to raise the children herself and settle property matters.

There are conflicting opinions about the level of education of P.A. Lobachevskaya in the literature. A.V. Vasiliev, for example, believed that she was a woman "energetic, towering in her education above the then level of wives of petty officials." VF Kagan claimed that she "was a poorly educated, but very reasonable and energetic woman." It seems that, after all, A.V. Vasiliev is right, since, as follows from the documents published by L.B. Modzalevsky, Lobachevsky not only correctly wrote petitions and letters without resorting to the help of clerks, but also knew the rules for compiling them. This is one of the indicators of her education.

The level of well-being of the family also determines its capabilities. The main source of existence for the family of N.I. Lobachevsky was the salary of S.S. Shebarshin. From 1792 it was 300 rubles. Is it a lot or a little for a family of three, and then five people? Comparable with the salaries of other officials. Thus, the director of the Main Public School in Nizhny Novgorod received a salary of 500 rubles, teachers of the 4th and 3rd grades - 400 rubles, 2nd - 200 rubles, 1st - 150 rubles. . I.A. Vtorov, who served in the viceroyal board of the city of Simbirsk as a clerk, received "meager funds of 150 rubles." M. M. Speransky in 1795 received "the highest salary of a seminary professor" in St. Petersburg - 275 rubles a year. But this salary provided only the modest living needs of Speransky (who was not yet married) and he was looking for additional income. Thus, a salary of 300 rubles in Nizhny Novgorod provided only the minimum needs of the family of an official of the "middle hand", as they said then. Bribery was a fairly common phenomenon at that time. She-barshin left his children a small fortune. This indicates that he was not only smart, but also an honest person and did not take bribes.

After Shebarshin's death, his property was valued at 337 rubles. It is noteworthy that there is not a single book in the inventory, and from the dishes there are only two teapots and three porcelain tea pairs. Without a doubt, Praskovya Alexandrovna had a significant part of the property and was not subject to an inventory.

What kind of education did the Lobachevsky brothers receive before entering

The first Kazan gymnasium? It is known that when applying to the gymnasium, Praskovya Alekseevna attached three certificates: on property status, inspector with data on entrance exams and on the state of health.

The first showed that she could not pay for the education of her children and contribute money in favor of the gymnasium at a time. It is known that, according to the "Regulations on the establishment of a gymnasium", nobles and raznochintsy were accepted into it for state support, boarders with a fee (nobles at 150, and raznochintsy - 120 rubles per year), as well as children "without any fee for teaching" , The Lobachevsky brothers were enrolled among the latter by the Council of the gymnasium.

Organizational and pedagogical activity of N.I. Lobachevsky at Kazan University

Let us first consider the education system in Russia at the beginning of the 19th century, when N.I. Lobachevsky assumed the post of rector of Kazan University. As Z.I. Vasilyeva notes, “historians distinguish six milestone periods of reforming domestic education, including the 19th century: Peter the Great reforms, Catherine’s reforms, Alexander’s liberal educational reform of 1802-1S04, the Nikolaev counter-reform of 1828, the reforms of 1863- 1864, and counter-reforms of the 70-80s. The Russian state of the 17th and 19th centuries was characterized by building the educational system from above, maintaining a monopoly on the school, adapting education to the needs and political interests of the state, and using religious dogmas and clergy for protective purposes. The state, with the help of educational reforms, regulated and directed the development of education in a "reliable channel" .

It should be noted especially 1804, the year of foundation of Kazan University. For the first time in Russia, according to the Decree of 1804 signed by Alexander I, a coherent state education system was legalized, consisting of 4 links (steps): Stage I - parish school - 1 year. II level - county school - 2 years, in county towns. Its goal is to give a complete primary education to the children of urban residents who did not belong to the nobility and clergy. The school was supposed to prepare children for gymnasium education. Stage III - gymnasium - 4 years, in the provincial cities on the basis of the main public schools, for the nobility, officials. The purpose of the gymnasium is to prepare for university education. Stage IV - university education.

Those wishing to study at the university must first take a gymnasium course, those entering the gymnasium - the course of the county school, and the county school could only be entered after graduating from the parish school.

According to the charter of 1804, all schools were declared classless, accessible, free. For each stage, the content of education was determined. The university received the right to manage all the educational institutions that were in its district. And at that time in Russia there were 6 districts and, accordingly, 6 universities: Moscow, St. Petersburg, Kazan, Kharkov, Derpt, Vilnius.

Universities had the right of autonomy; could open their printing house and publish textbooks for educational institutions, have scientific associations and student societies. The election of the rector, deans and other positions was envisaged. But, as ZI Vasilyeva rightly notes, the implementation of this system was utopian: there was no necessary material base, there were not enough teachers, the city self-government and zemstvos in the villages were not prepared for this. Primary - (first) stage of education - parish schools remained without any support. In practice, this statute has not been universally implemented.

Nikolaev counter-reform of 1828-1835 largely localized the Alexander reform of 1802-1804. The “Charter of Gymnasiums and Colleges of Universities” (1828) restored the class, closed nature of the school system, canceled the previously introduced continuity of communication between different types of educational institutions. In educational institutions, police supervision is established, cane discipline is introduced.

At such a time - May 3, 827 - N.I. Lobachevsky was elected rector of Kazan University, when, after the suppression of the Decembrist uprising, any freedom-loving thought was subjected to the most severe persecution. But thanks to the high authority, seething energy and real civic courage of Nikolai Ivanovich Lobachevsky, this era became the heyday of the scientific activity of Kazan University.

With the dismissal of the trustee of the Kazan educational district ^ M.L. Magnitsky, a new era began in the formation and development of Kazan University. Temporarily, the administration of the district was taken over by the rector of the university, K.F. Fuks. The real streamlining of university life began only with the appointment on February 24, 1827 of a new trustee of the educational district - MN Musin-Pushkin. The personality of the person who had such a significant impact on the university requires a separate description, especially since almost immediately after his appointment, M.N. Musin-Pushkin begins to work in close contact with a young talented professor of mathematics, the future rector of the university the role of a trustee) by N.I. Lobachevsky.

Mikhail Nikolaevich Musin-Pushkin was born in Kazan in 1793. He belonged to an old noble family, received a good education at home. In 1810, he passed the exam for the gymnasium course and entered

among the students of Kazan University, but soon left for military service. Participated in the battles of the Patriotic War of 1812 and in the foreign campaign of the Russian army, quickly rose to the rank of colonel. But in 1817 he left military service and settled on his estate, in the famous peasant revolt of 1861. The abyss of the Spassky district of the Kazan province.

The memoirs of contemporaries depict him as a demanding and despotic boss, a rude and quick-tempered person. “Cursing, cutting off not only a student, but also a professor cost nothing for him,” recalls V.P. Vasiliev.

But, on the other hand, the memoirs paint Musin-Pushkin as a direct and fair person. He understood the importance of science for the state and took care of the university with all his heart and won general love for his readiness to always come to the aid of any good undertaking. "The university owed a lot to Musin-Pushkin and his concerns both about the staff of teachers and about the arrangement of classrooms, libraries, teaching aids." A particularly valuable advantage of an administrator is the ability to select people, Musin-Pushkin fully possessed this advantage. And therefore, in the reunion of the views and thoughts of two inextricably linked for almost 20 years, loving the University of the smartest people of their time, M.N. Musin-Pushkin and N.I. Lobachevsky, the key to that bright era for Kazan University, which over the years has grown in breadth and turned into the largest center of education and culture in Russia and Europe.

In general, Lobachevsky at first wanted to evade the honorary, but heavy duty of the rector, entrusted to him by the trust and respect of his comrades, and agreed only because he hoped for the trust and disposition of the trustee.

When Lobachevsky was elected rector, the university was going through a difficult time. In the preceding period, the level of teaching has dropped markedly, many professorships were not filled, and there was a shortage of the most necessary equipment, instruments, and books for either teaching or scientific activities.

N.I. Lobachevsky as a teacher, his pedagogical views

Many authors turned to the personality of N.I. Lobachevsky in order to find the secret of his genius. We fully share the opinion of V.I. Andreev that "to understand a person, his personal development is possible only through the holistic achievement of his motivational sphere, intellectual, volitional, moral and other spheres of life in their organic unity, taking into account biological capabilities and socio-cultural environmental conditions ". We believe that the pedagogical views and pedagogical activity of N.I. Lobachevsky were focused on the humanization of education. Here, by the humanization of education, we mean, as in V.I.

The formation of pedagogical views and pedagogical activity of N.I. Lobachevsky are closely connected with Kazan University - one of the oldest in Russia. Therefore, we consider it appropriate to recall what university education is.

As N.S. Ladyzhets notes, "the university is a product and achievement of European civilization" . Next, we present some, in our opinion, useful information from the author's monograph on university education. As N.S. Ladyzhets notes, "in the historiographical and pedagogical literature, the term "university", which was assigned to a new type of educational unit, along with the monastic vocational schools that took place, is most often associated with the universality of the content of education ",

At the same time, the foundation of university education and the substantiation of its social significance and industrial specificity, as the author rightly writes, is "the trinity of education, research and education" .

When analyzing, for example, the 18th century, V.B.Mironov notes that the economy, science, technology, politics are in great motion, become purposeful. “The economy cracks the patriarchal relations of production. Politics, having shaken the pillars of absolutism, overthrows feudalism and royal power. Science and technology are united in an alliance, the result of which was the industrial revolution.

We agree with the opinion that "university education since its inception has traditionally been the main mechanism for the transfer of culture, the level of knowledge achieved and constantly improved in accordance with historical possibilities. Another mechanism, not so obvious and stable for various stages of industrial development, is the possibility of changing social status in accordance with the socially certified assessment of acquired professional skills as a result of professional activity.However, the idea of ​​the comprehensiveness of university education, which implies the unity of teaching, research and education, turned out to be unrealized in this period. disciplinary knowledge, since the time of the humanists, education has remained as the development of mental abilities and character.The ideal of education itself correlates to a greater extent not with educational, but with moral values, The situation changes radically only in the era of romantic humanism, which was formed in Germany at the turn of the XVIII-XIX centuries. This time, the basis for the transition to a new type of education and the formalization of the classical idea of ​​the university were quite specific and associated with the unification of the University of Berlin with the Royal Academy. This new type of university education, which became a symbol of advanced education in the 19th century, radically influenced the further evolution of the world university system, is inextricably linked with the name of Wilhelm von Humboldt. It is also essential that it is with this model, which has received practical implementation, that a new stage in the analysis of university education begins, further represented by the tradition of theoretical reflection, terminologically entrenched in the “development of the idea of ​​the university” .

The views of N.I. Lobachevsky on the tasks and originality of university education are reflected in the following documents: 1) "Note on the educational institutions of St. Petersburg" (1836); 2) "Opinion on changes in tests for scientific degrees" (1839).

N.I. Lobachevsky singled out two systems of university education. The first one he called teaching. It has become widespread in German universities and is based on complete freedom to "acquire knowledge." The second system - "educational ... close in spirit to home parental education, ... to the people's spirit, even in a warlike spirit, received preference in France, especially in Russia." It is characterized by "the appointment of all occupations by the authorities with strict supervision of morality." Recall that when creating Russian universities, including Kazan, at the beginning of the 19th century. the German Protestant university system was taken as a model.

The purpose of education, according to the well-founded opinion of N.I. Lobachevsky, determined its content. In the gymnasium, the pupil received a "general education." Therefore, the gymnasium course is more extensive than the university course in terms of the number of subjects. Thus, the goal of the gymnasium is to equip pupils with a system of knowledge, skills and abilities necessary for life in society (to give "the necessary information for everyone", "knowledge acquired here (i.e. in the gymnasium - N.S.)" should be "sufficient for the ordinary needs of life"). Between elementary, secondary and higher schools, N.I. Lobachevsky believed there should be continuity: "Teaching in gymnasiums should be in agreement with teaching in district schools, to which it serves as a continuation, and at the university, to the beginning of which it must be brought up."

In higher educational institutions, according to N.I. Lobachevsky, "the highest degree of education" is acquired. “The highest degree of education, it seems, should be called that,” he writes, “which, with the information necessary for everyone, with the general concepts of all sciences, lies in those knowledge that can be acquired only with a special natural ability.” Consequently, the goal of university education is to give the student the opportunity, based on his inclinations, to devote himself "to the subject to which you should forever devote yourself to your favorite pastime in life and in order to remain among the scientists, among the representatives of education throughout the state ( by me - N.S), in all his estates and ranks ". Thus, a university graduate had to become a scientist, teacher, figure in the cultural life of Russia. N.I. Lobachevsky saw this as the purpose of universities and the goal of higher education. In this regard, he proposed to revise the numerous scientific disciplines that were read at the university, to delimit the university course. "University education", in his opinion, "should not ... have anything in common with the gymnasium" both in content and in teaching methods.

University education should have a practical orientation. “Here they teach what actually exists,” the rector of the university said in his speech “On the most important subjects of education,” and not what was invented by one idle mind. Exact and natural sciences are taught here, with the aid of languages ​​and historical knowledge” [FROM, p.323,324].

Let us compare the views of N.I. Lobachevsky with the government program, which was reflected in the "Charter of gymnasiums, county and parish schools, which are in the department of universities" (1828) and the university charter of 1835,

The purpose of primary and secondary educational institutions, according to the "Charter", was "to provide youth with the means to acquire the knowledge that is most necessary for the state of every state" . Thus, in the pedagogical concept declared by the government, moral education was in the first place, training should have been class-based, limited. Each stage provided a complete education, independent of the higher stage of education. Only the gymnasium had a dual purpose: to prepare young people both for the university and for entering the service immediately after the gymnasium. This should have been facilitated by the subjects of the gymnasium course.

Pedagogical views of N.I. Lobachevsky on the problems of educating students

The concept of "education" in Russian pedagogy began to stand out from the second half of the 18th century. In this specific meaning, in particular, it is mentioned in the “General Institution for the Education of Both Sexes of Youth” (1764) and in a number of other documents prepared by I.I. Betsky, a public figure and associate of Catherine II. Based on the ideas of J.A. Comenius, D. Locke, J. J. Rousseau, he called for observing the relationship between moral, mental and physical education. He also compiled the first guide for parents and educators, which outlines issues related to children's health, mental education (teaching), the role of play in the education and upbringing of children, and taking into account the individual psychological characteristics of children in the upbringing process.

Understanding the term "education" as a trinity: moral education, physical and mental was typical for E.R. Dashkova, N.I. Novikov, A.A. Prokopovich-Antonsky.

E.R. Dashkova, in her essay “On the Meaning of the Word Education”, published in 1783, wrote, summing up her thoughts: “Perfect education consists of physical education, moral and, finally, school, or classical. The first two parts are necessary for every person, but the third of a certain rank is necessary and decent for people. ..classical education is carried out by a perfect knowledge of the natural language, also Latin and Greek. Further, she lists items that are useful for some, but for others "may be considered superfluous" 19, pp. 287,288].

In 1783, N.I. Novikov published his pedagogical essay “On the Education and Instruction of Children”, in which for the first time in Russia the word “pedagogy” was used as a special and important science of “education of the body, mind and heart”. “Education,” according to N.I. Novikov, “has three parts; physical education, relating to one body; moral, having the object of education of the heart, i.e. education and management of the natural feeling and will of children; and intelligent education, concerned with enlightening or educating the mind." It is characteristic that the sequence of arrangement of the constituent parts of education in Dashkova and Novikov is the same - physical, moral, mental.

A follower of N.I. Novikov was a professor, director of the Noble Boarding School of Moscow University LA. Prokopovich-Antonsky. In his treatise "On Education" he wrote that "education is physical and moral. Its subject is the formation of the bodily and mental abilities of a person. The body makes it strong and slender, the mind enlightened and solid, and the heart arms against the ulcer of vices.

For the first time in Russian pedagogical thought, he distinguished between "education" and "education", and also showed the connection between them, Professor of the Main Pedagogical Institute A.G. Obodovsky in 1835 in the book "Guide to Pedagogy or the Science of Education". Two years later, his second work "A Guide to Didactics, or the Science of Teaching" 1 (1837) was published. Both textbooks were written by him using the book of the German teacher A.N. and own teaching experience. Thus, gradually the concept of "education" ceases to be identical to the concept of "education". With the development of pedagogical theory and practice, it acquired an independent meaning. The above-mentioned feature of the consideration of the concept of "education" was also reflected in the pedagogical views of N.I. Lobachevsky, which we will dwell on later.

Before analyzing the pedagogical views of N.I. Lobachevsky on education, we will consider the problem of education in modern pedagogy.

For example, K.D. Ushinsky interpreted "education" as a broad concept that includes upbringing, education and training.

Yu.K. Babansky studied this concept more narrowly: “Education in a special pedagogical sense is the process and result of a purposeful influence on the development of a person, his relationships, traits, qualities, attitudes, beliefs, ways of behavior in society. Some authors (for example, H.I. Liimets, L.N. Novikova, A.V. Mudrik) argued that “education is a purposeful management of the process of personality development” .

As V.I. Andreev notes, “if we consider education as a strict pedagogical control of the pupil’s behavior, then we are inevitably forced to characterize education as nothing more than an impact on the personality.” This approach is found in the works of P.P. Blonsky and A.P. Pinkevich.

We believe that it is more correct to consider education as a two-way process of "interaction" between the educator and the pupil.

An interesting interpretation is F.M.

V.I. Andreev, after analyzing different formulations and approaches, gave, as it seems to us, the most complete and accurate definition: “upbringing is one of the types of human activity that is mainly carried out in situations of pedagogical interaction between the educator and the pupil in the management of the game, labor and other activities and communication of the pupil with the aim of developing his personality or individual personal qualities, including the development of his abilities for self-education.

We agree with V.I. Andreev that “pedagogical theories of education most often arise and are determined by what ideal model of the personality of the pupil they are oriented to. Moreover, this ideal is most often determined by the socio-economic needs of the society in which the pedagogical process itself is carried out.

At the same time, the author singled out 5 approaches in education: personal, activity (a three-dimensional model for analyzing the activity of the pupil, organized by the teacher for the purpose of education), cultural, value, humanistic.

Education as a social phenomenon is characterized by the following main features that express its essence:

1. Education arose from the practical need to adapt, to familiarize the younger generations with the conditions of social life and production, to replace the aging and dying generations. As a result, children, becoming adults, provide for their own lives and the lives of older generations that have lost the ability to work.

2. Education is an eternal, necessary and general category. It appears together with the emergence of human society and exists as long as society itself lives. It is necessary because it is one of the most important means of ensuring the existence and continuity of society, the preparation of its productive forces and the development of mankind. The category of education is general. It reflects the regular interdependencies and interconnections of this phenomenon with other social phenomena. Education includes the training and education of a person as part of a multifaceted process.

3. Education at each stage of socio-historical development, in its purpose, content and forms, is of a concrete historical nature. It is determined by the nature and organization of the life of society and therefore reflects the social contradictions of its time. In a class society, the fundamental tendencies in the education of children of different classes, strata, and groups are sometimes opposite.

4. The upbringing of the younger generations is carried out through their mastering the basic elements of social experience, in the process and as a result of their involvement by the older generation in social relations, in the system of communication and in socially necessary activities. Social relations and relationships, influences and interactions between adults and children are always educational and educative, regardless of the degree of their awareness by both adults and children. In the most general form, these relationships are aimed at ensuring the life, health and nutrition of children, determining their place in society and the state of their spirit. As adults become aware of their educational relationships with children and set themselves certain goals for the formation of certain qualities in children, their relationship becomes more and more pedagogical, consciously purposeful.