# Great Russian Geometr. Nikolai Ivanovich Lobachevsky

*Copernicus and Lobachevsky have an interesting common feature - they are both Slavs by origin. Each of them produced a revolution in scientific views, and both of these revolutions are of tremendous importance - these are revolutions in our understanding of the Cosmos. ”*

English mathematician William Clifford

The date and place of birth of Nikolai Ivanovich is still controversial among biographers. According to some information, he was born in the city of Nizhny Novgorod, according to others - in Makaryev (Nizhny Novgorod province), according to the third - in the village of Vyazovoi, located not far from Kazan. The same uncertainty is observed with the time of birth. The generally accepted version is based on a record found in the Nizhny Novgorod archive, stating that Nikolay was born to a certain 20 1792 provincial registrar Ivan Maximov in November. The name in the old document is not specified, but there is every reason to believe that we are talking about the future of great mathematics. Ivan Maksimovich Lobachevsky was a minor official, and also performed the work of the county architect, which testifies to the good education he received. About Lobachevsky's mother - Praskovya Alexandrovna - even less is known.

Nikolai was the second of three brothers. At the age of forty, Ivan Maksimovich fell seriously ill and died, leaving the family in a difficult financial situation. The Lobachevskys lived in the house of Captain Stepan Shebarshin, who served as a surveyor. This man was distinguished by purposefulness and iron will. All the children of Praskovya Alexandrovna were brought up properly. After the death of the captain in 1797, Praskovya Alexandrovna, together with her children, moved to Kazan, the city in which Lobachevsky had spent almost his whole life. At that time, the population of Kazan did not exceed thirty thousand people, and the city itself was the center of the cultural life of the eastern lands of the Russian Empire.

Kazan gymnasium began to work in the mid-eighteenth century. In the first recruitment, Gabriel Derzhavin studied it, recalling later that the lack of good teachers and the curriculum made the pupils "although unskilful in the sciences, but giving some unleashing in circulation." In other words, the local gymnasium was preparing for secular life. By the time of training in this institution Lobachevsky situation has improved slightly. From now on, education, according to the statute, was aimed at preparing for military service. In 1802, Praskovya Alexandrovna submitted a petition requesting her three sons: eleven-year-old Alexander, nine-year-old Nikolai and seven-year-old Alexey, to be accepted to the government treasury. Separately, she reported that due to her poverty she could not fulfill the donations made at that time in favor of the school. It is curious that the entrance exams to the gymnasium were not at all simple, but, judging by the letters, the mother hardly knew the letter and could not prepare the children on her own. For all that, all three were admitted to this school.

Orders in the gymnasium reigned almost barracks. Future well-known writer Sergey Aksakov, who studied in the same years, wrote: “Rising long before the light on the bell, cold in the rooms, quarrels and fights at the washstands, walking with a breakfast for lunch, for prayer, for dinner ...”. Pupils could not have any personal belongings or money, and letters to relatives were handed over to teachers in an unsealed form. Similar orders brought Aksakov to a nervous disease, but the Lobachevsky brothers turned out to be stronger. They all studied very well. The main educator certified Nicholas, as "a very well-behaved and diligent ... with particular diligence engaged in the Latin language and mathematics." At the same time, the future scientist was distinguished by a lively and lively character. One of the teachers repeatedly told him as a joke: “Lobachevsky, a real robber will grow out of you!”.

Kazan University opened its doors at the beginning of the reign of Emperor Alexander I. According to the statute, the school had wide autonomy - all officials were elected by the Academic Council, the university had its own police and even its own court and, most importantly, could publish scientific works uncensored. A well-known astronomer and mathematician Stepan Rumovsky was invited to organize the university, appointing him the trustee of the Kazan school district. At that time, he was over seventy, and frankly he lacked the strength to work. However, the trustee still managed to do something. He focused on the Faculty of Physics and Mathematics, inviting prominent European scientists to the work of pure mathematics professor Martin Bartels, who taught Gauss himself, and the future head of the Vienna Observatory, astronomer Joseph Littrov.

By order of Rumovsky, the University Council appealed to the parents of the gymnasium students with the proposal to “give” them to continue their studies after completing the course of the gymnasium. The main condition was that after graduating from the university, its graduates undertook to engage in teaching for six years on the instructions of the Ministry. Praskovya Alexandrovna agreed to this proposal with joy. At the time of entering the university, Nikolai Ivanovich was not yet fifteen (February 1807). The same Aksakov recalled: “We learned both day and night. The teachers worked with us in the classrooms, as well as on all holidays and in every free time ... Soon everyone lost weight, changed faces, and the authorities were forced to take measures to cool such zeal ... " It is curious that in the first years of the university there was not even a division into faculties - the students simply signed up for various professors.

Mathematical abilities of Nikolai Ivanovich showed up early. Professor Bartels wrote to Rumovsky: “In any German university Lobachevsky would be considered an excellent student. I will tell the following about his art. I have my lectures in such a way that my students are both students and teachers. Before the end of the course, I proposed Lobachevsky to study the difficult and lengthy problem of rotation, which I decided on Lagrange. This decision was written by me, but Lobachevsky did not use the records and filed his own. I presented his decision to Academician Vishnevsky, who was delighted with him. ” Rumovsky, in turn, showed this letter to the Minister of Education, and a talented student was awarded a laudable review.

Littrov and Bartels additionally engaged with the best students of the university - Lobachevsky and subsequently known astronomer Ivan Simonov. Together they dealt with questions that were beyond the reach of other students, for example, Bartels explained the Gaussian theory of numbers to them. However, the mathematical career of Nikolai Ivanovich almost ended at the very beginning. In 1807, Alexander, the elder brother of Nicholas, drowned while swimming in the Kazanka river. Young Lobachevsky experienced a huge nervous shock. He began to pursue various obsessive thoughts, for some time he was treated at the hospital, and then decided to link his life with medicine. Nikolay Ivanovich spent his days in the anatomical theater and diligently taught Latin. Soon he was called in the city as “a young doctor”. However, the natural tendencies and persuasions of professors took their toll - Lobachevsky returned to mathematics.

In his student years, many problems for Nikolai Ivanovich brought him a cheerful and violent temper. Having received relative freedom after the hard regime that prevailed in the gymnasium, the young youth began to breathe, as they say, with full breasts. However, the authorities did not understand this. In addition, Lobachevsky contrived to quarrel with a certain Kondyrev, who oversaw students and led the conduit (behavior log), in which the future great mathematician, by the way, appears thirty-three times. In retaliation, Nicholas composed biting epigrams on the “overseer”. It should be noted that the misdeeds of the young Lobachevsky were for the most part quite innocent. One day he returned from a revel of students astride a cow, driving in front of the rector himself. Another time, at the gymnasium yard, he launched a rocket and was put in prison for that. After a while, the charges were "overwhelmed." Already in 1811, Kondyrev reported that “Lobachevsky gives bad examples for his companions, stubborn, unrepentant in his character, often disobeyed and very much dreamy about himself.” Soon the students begin to see signs of godlessness, by the way, the most serious accusation of those times. Nikolai Ivanovich was close to saying goodbye to science and becoming a soldier, but the professor of physics Bronner and Bartels stood up to his defense. With great difficulty, two scientists managed to save him, but due to similar incidents, Lobachevsky was not willing to confer the title of student candidate for a long time. The Council’s minutes noted that “According to his excellent successes and talents in the mathematical sciences, Nikolai Lobachevsky could be awarded the title of candidate if his bad behavior didn’t interfere with this.” However, after some time, the professors of physics and mathematics were able to convince their colleagues to assign a higher master's degree to a naughty student. True, before this the student was forced to repent and give the word to behave from now on.

Becoming a master, Nikolai Ivanovich began to conduct lectures on geometry and arithmetic for officials who brought up their knowledge before exams for the rank of a higher class. These classes occupied the young scientist only a few hours a week, and the rest of the time he preferred to devote to science. In 1811, Lobachevsky's argument about the elliptic motion of celestial bodies appeared. Bartels wrote in admiration: "In many places of this reasoning, compiled by him without any help, except for the works of Laplace, he found such signs of an excellent mathematical talent, which will make a glorious name for himself." In 1813, the work of Nikolai Ivanovich "On the resolution of the equation xn - 1 = 0" was published. For his success at 1814 - much earlier than the allotted time - he was awarded the title of adjunct, starting teaching at the university. And two years later, again bypassing the existing rules and despite the resistance of the part of the professorate, Nikolai Ivanovich was approved as an extraordinary professor. Fortunately, most members of the Academic Council at that time realized that they were dealing with a person of outstanding ability.

The last years of the reign of Alexander I were marked by numerous reactions that dealt a heavy blow to the current system of higher education. Kazan University was on the verge of closure, and education was now supposed to be built on the basis of humility and faith. A new auditor arrived in Kazan - Mikhail Leontyevich Magnitsky, with whom the darkest pages of the university are connected stories. Magnitsky reported to St. Petersburg: "The act of abolishing the Kazan University more naturally now seems that, without any doubt, the government will soon pay attention to the general system of educational education, which, having thrown off the modest veil of philosophy, is already in the middle of Europe with a dagger in it" . Fortunately, his plan was never executed - at the last moment the emperor decided not to close the universities, taking up their "correction". However, it was Magnitsky who was appointed trustee of the Kazan school district.

A new trustee marked his work with the dismissal of nine professors. Very soon, the university left all the teachers Lobachevsky. The content of the lectures was kept under the strictest control, and many textbooks were banned. The students were so carefully supervised that even the regime of the Kazan Gymnasium from now on seemed like a model of liberty. The daily routine, characterized by total control and constant prayers, was more suitable for a monastery with a strict charter. A lecture on geometry, for example, could begin with these words: "With God's help, these two triangles are equal." The guilty students were called "sinners", and on holidays with the purpose of developing the "spirit of humility" in the university courtyard they set up tables for beggars served by students. And, of course, medals and awards were distributed not for academic success, but for piety.

Lobachevsky, as a mathematician, was in a more advantageous position in comparison with professors of the social and natural sciences. However, Nikolai Ivanovich had a hard time. He was forced to attend the meetings of the Academic Council and, together with its other members, silently, without a murmur, sign insane decisions initiated by a zealous trustee. It is curious that Magnitsky himself trusted the young professor and even presented him to Saint Vladimir of the fourth degree. Even numerous denunciations of Lobachevsky, in which they pointed to a “proud mind in love with themselves” and “lack of piety,” did not have a course. The words of the trustee are known: “Lobachevsky with me never said a bad word about anyone. For this, I respect him. ” At the end of the reign of Alexander I, the Magnitsky era came to an end. Among other things, it was found that Mikhail Leontievich very freely disposed of state funds allocated for the university, and soon a new trustee appeared in Kazan District.

In those years, a contemporary described Lobachevsky in the following way: “Thin, tall, somewhat stooping. Almost always head down with a cap of thick dark blond hair sticking out in all directions with whirlwinds ... Dark gray gloomy pensive eyes, eyebrows shifted, straightening out in rare moments of joyful mood. At 1820 (Nikolai Ivanovich was not even thirty), he became the dean of the Faculty of Physics and Mathematics, and two years later he became an ordinary professor. There were not enough teachers during the “renovation”, and Lobachevsky had to take on the responsibilities of Bartels who had left - the teaching of a physics course and the management of a physical room. And in 1819, when Simonov, a professor of astronomy, went on a world expedition led by Lazarev and Bellingshausen, Nikolai Ivanovich took up geodesy and astronomy courses, as well as supervising an observatory. In the same years, Lobachevsky, on his own initiative, began to put in order the university library, which is in a very poor condition. It was not cataloged, book volumes, arranged in disarray, were simply taken away. The scientist was engaged in this business for many years. Radey about enlightenment, Lobachevsky opened the doors of the library for all comers on certain days. And with 1822, the mathematician became a member and then chairman of the building committee. At this time a new main building of the university was being built, an anatomical theater, an observatory. This activity took a lot of nerves and time, accompanied by constant conflicts with lazy workers and roguish contractors.

It seemed that the responsibilities lying on the shoulders of Lobachevsky, enough for a few people. However, the mathematician found time for scientific studies by composing two textbooks and reflecting on the discovery that immortalized his name. The works written by him on geometry and algebra had a difficult fate. The point was the novelty of presentation and originality, which conservative reviewers could not appreciate. In his textbook on mathematics, Nikolai Ivanovich reviewed a number of new methods, including those discovered by himself. For some time the manuscript lay motionless, and Lobachevsky was able to publish it only after thorough processing. However, the most severe reviews received a textbook of geometry written by him. Academician Nikolai Fuss responded about it this way: “If the writer thinks that it can serve as a learning book, then he argues that he does not have an exact concept of the book’s educational needs, that is, the completeness of geometric truths that make up the entire system of the initial scientific course. . " The reviewers were particularly displeased by the author’s use of the metric system generally accepted today: “It’s well known that this division was invented during the French Revolution ... The rage of the nation to destroy everything that used to be there even before the division of the circle and calendar ... This novelty has not been accepted anywhere, and has long been left in France itself for reasons of obvious inconvenience. ” The old school professors remained committed to the traditional teaching of geometry, based on the Euclidean system. Nikolai Ivanovich, in his work, followed the new views expressed by Dalamber and included in the category of “unreliable”. Lobachevsky did not want to rework his textbook, his manuscript of “Geometry” was considered lost for many years and was found only at the end of the nineteenth century.

Echlid's "Principles" are probably the most famous and significant book in the history of science. Suffice it to say that geometry has been taught for more than two thousand years. In general, and current training follows the provisions of Euclid, and the geometry that we use in everyday life is called Euclidean. The book of this scholar of antiquity is based on an axiomatic principle. At the beginning of it, a number of postulates and axioms are given that are considered indisputable, and from them, with the help of rigorous reasoning, new propositions are derived, called theorems. Among all the Euclidean axioms, the fifth postulate attracted the special attention of scientists. If all the others are intuitively understood and formulated quite clearly, then the definition of the fifth postulate (sounding in a simplified form: “Through a point that does not lie on a given plane, you can draw one and only one line parallel to this one”) was puzzling. Mathematicians have assumed that the statement is actually a theorem, that is, it can be proved by taking other axioms as a basis. Over the centuries, many great mathematicians - Ptolemy and Omar Khayyam, Lambert and Lagrange - tried to prove this statement. However, no one achieved success, and in 1816 Gauss was disappointed to write: “In the field of mathematics, there are few problems that we would work on so much as over the gap in the beginning of geometry. And yet, if we frankly admit, for two thousand years we have not gone further than Euclid. ”

11 February 1826 forever remains in the history of mathematics. On this very day, at a regular meeting of the Physics and Mathematics Department at Kazan University, Lobachevsky read a report in which he identified the main tenets of the new geometry. According to his conclusions, it was possible to construct a geometry that negates the fifth postulate of Euclid. The simplest properties of it consisted in the fact that through one point it was possible to draw a set of straight lines that do not intersect the given one, and the angles of the triangle in total could be less than 180 degrees. Of course, this is in contradiction with our “everyday” ideas, but such a world, indeed, turned out to be realizable, in accordance with the laws of physics and logic. Colleagues, however, in the discovery of Nikolai Ivanovich, who made a revolution in the concept of the nature of space, did not understand and, in order to save his comrade's pride, they decided not to give any feedback.

But Lobachevsky, being sure that he was right, did not give up. In 1829 and in 1830, in Kazan Kazan, he published a memoir (as the scientific article was then called) titled On the Principles of Geometry, which became the first printed version of the new theory. This was followed by "Imaginary Geometry", then "New Beginnings" and, as a result, "Studies in the theory of parallel". In the foreword of one of the works, the great scientist formulated his main idea in this way: “Everyone knows that the theory of parallel in geometry is still imperfect. Vain diligence from the time of Euclid made me think that the concepts themselves do not yet contain the truth that they wanted to prove ... My basic conclusion admits the presence of geometry in a broader sense than Euclid presented it to us. ” It is worth emphasizing that Lobachevsky did not refute the works of the ancient Greek mathematician, but proved the probability of the existence of geometry based on a different assumption about the nature of parallelism. In particular, Nikolai Ivanovich believed that his - non-Euclidean - geometry can work in the microworld, that is, at the molecular level.

Surely, publishing his work, Nikolai Ivanovich knew that he would meet with some misunderstanding and, possibly, ridicule. However, the mathematician hardly expected that they all would merge into a single loud chorus. A real persecution of Lobachevsky unfolded in the academic world, academician Mikhail Ostrogradsky (by the way, the most prominent Russian mathematician of that era) left the following pejorative review of one of his works: “Apparently, the author set himself the goal of writing in such a way that it was impossible to understand. And he achieved this goal - most of his book remained as unknown to me as if I had never seen it ... ”. If the first mathematicians of the country did not understand the works, then what was to be said about the rest. The journal “Son of the Fatherland”, published by Faddey Bulgarin, published a malicious, anonymous libel: “Not a scholarship, but at least common sense is required for every teacher, and the latter is often lacking in the“ new ”geometry. The fact that it was too much, even Sergey Uvarov, the former Minister of Education, noted. True, they did not allow Lobachevsky to print the answer. They criticized the scientist and in the camp of the left, in particular, Chernyshevsky wrote from exile to his son: “You took up the geometry of Lobachevsky - such idiocy! I saw this man, we all know that he is insane ... ". It is curious that Nikolai Gavrilovich compared the theory of Lobachevsky with Fet's verse without verbs “Shelest. Easy breathing. Trills nightingale, "over which in those years also" laughed to colick in the sides. "

Of all the Russian scientists, only the professor of mechanics Peter Kotelnikov expressed confidence that Nikolai Ivanovich’s discovery would still find his admirers. By the way, not finding support in his homeland, Lobachevsky published his works in German. But even in Europe, a scientist, in fact, found a single reader, but what kind! It turned out to be Karl Gauss, who admired the work of the Russian scientist and petitioned for his election as a corresponding member of the Mathematical Society in Göttingen. At the same time, a cautious German did not dare openly support Nikolai Ivanovich. It should be said that the work of Lobachevsky are really very complex. The same Gauss noted that they "are like a tangled forest, through which it is impossible to find ways without first examining every tree." There is a legend that already in old age the “king of mathematicians” undertook to study Russian in order to read all the studies of Lobachevsky.

At the beginning of May, 1827, Nikolai Ivanovich, 34, was elected rector of Kazan University. In this post, he spent a long nineteen years, turning a provincial university, living in a rather miserable existence, into one of the best educational institutions in the country. It is curious that for the first time Lobachevsky was elected rector with a minimum margin, and the last (sixth) time - unanimously, which is the rarest case in university history. After the removal of Magnitsky, Mikhail Musin-Pushkin was appointed trustee of the school district. He was a fairly typical figure for the Nikolaev time — rude, despotic, not too educated, however, at the same time, direct and honest, sincerely desiring blessings, both to the university and to education in general. Mikhail Nikolaevich, quickly appreciating the administrative talents and personality of Lobachevsky, treated him with confidence, supporting all the undertakings of the scientist. Later, Musin-Pushkin admitted: “If it were not for Nikolai Ivanovich, I would do a lot of injustices, I would take a lot of sin to the soul”.

In September, 1830 began to panic in Kazan - a cholera epidemic was moving towards the city. Lobachevsky developed an active activity - the university was actually in a state of siege, under the guidance of professors two hospitals were organized, the strictest disinfection measures were observed. While in the city itself, the victims numbered in the thousands, only forty of them got sick at the university, and thirteen people died. When the epidemic began to decline, the emperor presented his rector with a ring. And in 1842 in Kazan, there was a fire that destroyed most of the urban buildings. Lobachevsky and Musin-Pushkin led students who embarked on the defense of university buildings. Thanks to their efforts, they managed to save the library, the main building and a lot of valuable equipment, only the magnetic station and the observatory burned down. For his actions during the fire, Lobachevsky again received personal thanks from the king. Thus, not scientific, but administrative activity of the scientific authority was appreciated. He was promoted to actual state councilor and received many orders, including Anna II and Stanislav of the first degree.

It should be noted that with the appointment of Lobachevsky as rector, the university atmosphere has changed significantly. Nikolai Ivanovich said: “Young people need more movement, air, life,” and eventually achieved that they started teaching gymnastics and various arts at university and city gymnasiums. Under Lobachevsky, new areas of study were developed at the university, for example, at the Faculty of Philosophy, an oriental level was organized to teach the culture and languages of the peoples of the East. By the way, it was to this department that the writer Leo Tolstoy acted. After a short time, Kazan University became the center of Russian oriental studies. Lobachevsky's educational activities spread beyond the walls of the university. He sought time for public reading of various educational lectures, mainly on physics. Under him, the scientific journal “Notes of the Kazan University” also began to appear, where his own articles on algebra, astronomy, probability theory, physics, mechanics, and education were also published.

Surprisingly and sadly, however, all the mathematical work of Nikolai Ivanovich did not find support. Regardless of Dundelen, Lobachevsky developed a method for the approximate solution of equations, gave a sign of series convergence, clarified the concept of a continuous function, and made many other discoveries. He sent his works to the Academy of Sciences, but Ostrogradsky who disliked him answered them with devastating reviews: “The rector of Kazan University, Mr. Lobachevsky, is already known for its rather disadvantageous geometry ... The memoir submitted to my consideration does not contribute to a change in the author’s reputation.”

In 1832, Nikolai Ivanovich, 40, was married. His wife, Varvara Alekseevna Moiseeva, was fifteen. The girl fell in love with mathematics, and his friends, teasing scientists, advised to marry. To their surprise, he did. Varvara Alekseevna was from a wealthy landowner family, and as a dowry to the newlyweds were granted three estates and a three-story house in the city. A contemporary wrote: "The rector's house has always been full of selected society, and cooks were considered the best." Unfortunately, the mistress of the young wife was useless, easy to spend money, loved the card games. Her brother had similar inclinations. When the Lobachevskys made a decision to sell their small estates and buy one big one, the brother, acting as a confidant, managed to lower part of the nursing money. Lobachevsky had to bail him out, debts appeared, arrest was imposed on the property several times. This adversely affected the health of a scientist accustomed to accuracy and accuracy. The true number of children born to the Lobachevsky couple is unknown, most of them died in infancy, and the survivors, two daughters and four sons, brought math more grief than joy. The eldest son Alexei, who looked like his father by his appearance, character and mind, died of consumption in his youth. Another son lived until his mature years, but he was born mentally disabled. The third entered military service and was accused of embezzling public money.

In 1845, Musin-Pushkin was transferred to St. Petersburg, and Nikolai Ivanovich served as a school district custodian for more than a year. And in 1846, he was unexpectedly removed from the rector’s office, having appointed a new trustee assistant. Probably, there was some kind of ministerial intrigue. Relations with the new chief, General Molostvov, did not take shape, and as a result, the fifty-three-year-old Lobachevsky was actually removed from work. His new position, though honorable, did not solve anything. The students of Lobachevsky, even after his resignation, continued to have enormous prestige. Once, students, in condemning the order established by General Molostvov and the new rector Simonov, organized a gathering. Nobody could calm them down, it was a matter of calling the police, but the appearance of Nikolai Ivanovich calmed the audience.

The last years of his life Lobachevsky lived in his estate and was engaged in agriculture. He got down to business scientifically, trying the most modern technologies. He wrote reports on the storage of potatoes in the winter, on the design of water mills, on how to feed livestock. After selling the imperial ring, Lobachevsky bought a flock of merino sheep, and after some time, for a number of improvements in the field of wool processing, he was awarded a silver medal from the Imperial Society of Agriculture. In the declining years of Nikolai Nikolaevich, his eyesight began to fail, and he became completely blind. Despite this, the mathematician did not give up his scientific studies. His main goal was the creation of "Pangeometria" - a synthesis of labor that can cover all this complex science. He dictated his work to his students. Its full version was published after the death of the brilliant mathematician.

Lobachevsky 12 passed away on February 1856, exactly thirty years after his turn-over geometry report. He was buried at the Arsk cemetery in Kazan, his record, stretching over four decades, in the position about the holidays is a concise mark: "He was not." Nikolai Ivanovich did not live to see the triumph of his works for only ten or twelve years. Very soon, the situation in science has changed radically. The appearance of the Klein model justified the fact that Lobachevsky’s geometry is as consistent as Euclidean. Understanding the fact that the geometry of the ancient scientist has a full-fledged alternative, made an enormous impression on the scientific world, giving impetus to many other ideas both in physics and in mathematics. In particular, Lobachevsky's geometry “remarkably approached” to the general theory of relativity created by Einstein, one of the main provisions of which is time-space curvature.

*Based on materials from the site http://kpfu.ru/ and the books of E.F. Litvinova “N.I. Lobachevsky.*

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