Rembrandt autobiography and description of some paintings. rembrandt paintings

In 1792 in a city called Nizhny Novgorod a boy was born, who was subsequently destined to introduce a fashion for everything Russian into the Russian Empire and spread this fashion to European lands. Usually, interest in something so colossal was established after another war, or a popular-political revolt in the form of a revolution, an example of which could be the appearance of small cafes in France - bistros and sundresses in the wardrobes of European fashionistas. Lobachevsky, on the other hand, created a fashion for mathematics, proving to the entire scientific world that parallel lines can intersect.

risky move

Who else, if not a modest Russian mathematician, could take on a job beyond the strength of European bright minds: to overcome the theory parallel lines. In Europe it was considered this work- a disastrous thing that could deprive a person of sleep, personal time and other delights of life.

Russian rokhlya

Of course, such a painstaking task could be undertaken by a kind of botanist - an armchair scientist who did not communicate with anyone, an intellectual closed in himself. Such a person, in the opinion of European luminaries, should not be adapted to life and was certainly presented in the form of a dead man.

But such a template did not at all fit the description of such a person as Nikolai Lobachevsky. The Russian scientist at the time of his unique discovery was already the rector of Kazan University. Lobachevsky was repeatedly seen in youth in all sorts of incidents: as a student, he rode a cow in the city garden, was a ringleader in his group, even repeatedly participated in massacres, after these incidents he always spent time in a punishment cell, where he was sent to think over his actions.

1. Nikolai Lobachevsky was not liked in the gymnasium where he studied.
2. Lobachevsky co school bench he was distinguished by his free-thinking and perseverance. That did not stop him from studying perfectly.
3. Bad behavior once almost radically changed the life of a young mathematician, they wanted to expel him from an educational institution and send him to the army. The imperial government issued a decree according to which all students with bad behavior were to be sent to the army.
4. Lobachevsky was a talented student, he can even be called a young genius. This man received a master's degree at the age of 19, an associate degree in pure mathematics at 22, and at 24 he was already a professor.
5. The scientist had a passion for plants, which he loved to care for. He was held in high esteem cedars. However, he was convinced that they would not bear fruit during his lifetime. And so it happened: the cones were removed from the cedar a few months after the death of a talented mathematician.
6. Lobachevsky was interested not only in the exact sciences, he was fond of agriculture for which he was repeatedly awarded various awards and certificates.
7. Lobachevsky's talent is still not subject to a single drop of doubt, and his works are not forgotten. However, during his lifetime, the genius believed that his discoveries would be forgotten by descendants: this was his main phobia. His anguish and fears were fueled by intense criticism directed at him.
8. Great Russian mathematician had the gift of persuasion. He, already being the rector, repeatedly instructed his students on the true path. Lobachevsky never raised his voice when speaking, preferring calm conversation to shouting. Students remembered him as a wonderful person.
9. Lobachevsky gave his all to his students, but at the same time he did not allow familiarity.
10. The European king of mathematicians Karl Gauss, having heard about the scientific work of Lobachevsky, began to diligently study the Russian language in order to read the works of the genius from Russian Empire.
11. Nikolai Lobachevsky achieved tremendous success in the field of exact sciences, he especially succeeded, of course, in geometry, creating the so-called "non-Euclidean geometry."
12. The Russian mathematician is the author of a new method for solving equations, having created for this a number of theorems on trigonometric series and having studied the continuous function.
13. Lobachevsky is the author of a number of works on algebra and mathematical analysis, geometry, probability theory, astronomy and physics.
14. The great mathematician married quite late, at the age of 44. His chosen one was the Orenburg-Kazan landowner Varvara Moiseeva.

Unrecognized genius

Nikolai Ivanovich was very upset by criticism in his address during his lifetime. In the Russian Empire scientists great success did not have, since military operations were in the first place in the 19th century. In Europe, the leader was his mathematical genius - Carl Gauss. Lobachevsky believed that his works during his lifetime would turn out to be useless material for society.

The scientist was wrong in his predictions. He was recognized by his descendants as greatest genius in the field of mathematical research. Unfortunately, before his victorious triumph great mathematician did not live, 12 years after the death of Lobachevsky, his name thundered not only throughout the Russian Empire, but throughout enlightened Europe.

Even while Lobachevsky was studying at the gymnasium, the talented young man was predicted to play the role of the greatest robber for all his mischievous deeds. He once dared to nail a behavior diary to a teacher's desk using a hammer and a five-inch nail.

This prophecy came true in the future, Nikolai Ivanovich became a robber in the mathematical field, changing the usual stereotypes of scientists.

The English philosopher and mathematician William Clifford once called Lobachevsky " Copernican geometry”, which is a true statement, because the great Russian genius, like the famous Pole, became the creator of a unique research work.

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

Marius Sophus Lee

To live means to feel, to enjoy life, to feel by all means something new, which would remind us that we live ... Let us cherish life until it loses its dignity. Let examples in history, the true concept of honor, love for the fatherland, awakenings in young years, will give in advance ... a noble direction to passions.

N.I. Lobachevsky

Nikolai Ivanovich Lobachevsky (November 20, 1792 - February 12, 1856) - a great Russian mathematician, creator of non-Euclidean geometry, figure in university education and public education.

Lobachevsky was born in the Makaryevsky district of the Nizhny Novgorod province. His father occupied the place of a county architect and belonged to the number of petty officials who received a meager content. The poverty that surrounded Nikolai in the first days of his life turned into poverty when his father died in 1797 and his mother, at the age of twenty-five, was left alone with the children without any means. In 1802, she brought her three sons to Kazan and assigned them to the Kazan Gymnasium, where they quickly noticed the phenomenal abilities of her middle son.

Lobachevsky, together with his two brothers, graduated from the Kazan gymnasium only thanks to the selfless sacrifice of his mother.

When in 1804 the senior class of the Kazan gymnasium was transformed into a university, Lobachevsky was included in the number of students in the natural science department. At that time, in most cases, the teachers of Kazan University consisted of scientists invited from different countries Europe. Lectures on astronomy were read by Professor Litroff. Nikolai listened to lectures on mathematics by Professor Bartels, a pupil of such a prominent scientist as Carl Friedrich Gauss.

The young man studied brilliantly. However, his behavior was noted as unsatisfactory: the teachers did not like "dreamy self-conceit, excessive perseverance, freethinking." While still a first-year student, young Lobachevsky attracted the attention of Professor Bartels, who undertook to personally supervise the training of an unusually capable student. This was very necessary for Lobachevsky, since with his free-thinking and numerous pranks he often aroused the displeasure of the university authorities. Bartels' opinion that

... Lobachevsky, as a student, is distinguished by such abilities and has such achievements that in any of the German universities he would be recognized as an outstanding student ...

presented to the University Senate, prevented the expulsion of the future scientist from the university.

Already in 1811, Lobachevsky received a master's degree, and he was left at the university to prepare for a professorship. In 1814, Lobachevsky received the title of associate professor of pure mathematics, and in 1816 he was awarded a professorship.

At this time, Nicholas was mainly engaged in science; but in 1818 he was elected a member of the school committee, which, according to the charter, was supposed to manage all matters relating to the gymnasiums and schools of the district, then subordinate not directly to the trustee, but to the university. Since 1819, Lobachevsky taught astronomy, replacing a teacher who went on a round-the-world voyage. Lobachevsky's administrative activity began in 1820, when he was elected dean.

In 1819, an auditor, Mikhail Magnitsky, arrived in Kazan, who gave an extremely negative conclusion about the state of affairs at the university: economic disorder, squabbles, lack of piety, in which Magnitsky saw "a single foundation for public education." Magnitsky was praised only by the Faculty of Physics and Mathematics. In the report, he proposed to close the university altogether, but Emperor Alexander I imposed a resolution: "Why destroy it, it's better to fix it." As a result, Magnitsky was appointed trustee of the educational district and instructed to make a "correction". He fired 9 professors, cleared the university library of seditious books, introduced strict censorship of lectures and a barracks regime, and organized the department of theology. Bartels and other foreigners left, and the 28-year-old Lobachevsky, who had already shown outstanding organizational skills, was appointed dean of the Faculty of Physics and Mathematics instead of Bartels.

The range of his duties was extensive - lecturing on mathematics, astronomy and physics, completing and putting in order the library, museum, physical office, creation of an observatory, etc. In the list of official duties there is even “observation of the reliability” of all students in Kazan. Relations with Magnitsky were initially good. In 1821, the trustee presented Lobachevsky for the award of the Order of St. Vladimir IV degree, which was approved and awarded in 1824. However, their relationship gradually escalates - the trustee receives many denunciations, where Lobachevsky is again accused of arrogance and lack of due piety, and Lobachevsky himself in a number of cases showed disobedience, speaking out against the administrative arbitrariness of Magnitsky. During these years, Lobachevsky prepared a textbook on geometry, condemned by a reviewer (academician Fuss) for using the metric system of measures and excessive departure from the Euclidean canon (it was never published during the author's lifetime). Another textbook written by him, on algebra, was published only 10 years later (1834). One of Lobachevsky's contemporaries says about this period:

It was especially difficult moral attitude Lobachevsky's duty as a member of the council. Lobachevsky himself never fawned over his superiors, did not try to put himself in front of his eyes, did not like this in others either. At a time when the majority of the council members, to please the trustee, was ready for anything, Lobachevsky was silently present at the meetings, silently and signed the minutes of these meetings.

Immediately after the accession of Nicholas I, in 1826, Magnitsky was removed from the post of trustee for abuses discovered during the audit and brought to trial by the senate. Count M.N. became the new trustee. Musin-Pushkin. For many years he served as a commander in the Cossack troops, participated in Patriotic War 1812. According to contemporaries, he was distinguished by rigidity, but at the same time strict justice and honesty, and was far from immoderate religiosity.

On May 3, 1827, the 33-year-old Lobachevsky was elected rector of the university by secret ballot (11 votes against 3). Soon Musin-Pushkin left for St. Petersburg for a long time and did not interfere in Lobachevsky's activities, completely trusting him and occasionally exchanging friendly letters.

The new rector, with his characteristic energy, immediately plunged into economic affairs - the reorganization of the staff, the construction of educational buildings, mechanical workshops, laboratories and an observatory, the maintenance of a library and a mineralogical collection, etc. He did a lot with his own hands. During his time at the university, he taught courses in geometry, trigonometry, algebra, analysis, probability theory, mechanics, physics, astronomy and even hydraulics, often replacing absent teachers. Simultaneously with teaching, Lobachevsky read popular science lectures for the population.

Despite the exhausting practical activity that did not leave a single minute of rest, Lobachevsky never stopped his scientific studies, and during his rectorship he published his best works in the Scientific Notes of Kazan University.

Probably even in student years Professor Bartels informed the gifted student Lobachevsky, with whom he maintained an active personal relationship until his departure, the idea of ​​his friend Gauss about the possibility of such a geometry where Euclid's postulate does not hold.

Thinking about the postulates of Euclidean geometry, Lobachevsky came to the conclusion that at least one of them can be revised. Obviously, the cornerstone of Lobachevsky's geometry is the negation of Euclid's postulate, without which geometry seemed unable to live for about two thousand years. Lobachevsky came to the conclusion about the possibility of creating a new, consistent geometry. Since its existence was impossible to imagine in the real world, the scientist called it "imaginary geometry."

On February 7, 1826, Lobachevsky submitted for publication in the “Notes of the Physics and Mathematics Department” the essay “A Concise Presentation of the Principles of Geometry with a Rigorous Proof of the Parallel Theorem” (on French).

On February 11, 1826, an event of the greatest importance took place at Kazan University, giving reason to consider this date the birthday of non-Euclidean geometry. On this day, at a meeting of the Department of Physics and mathematical sciences Lobachevsky presented this work. Information about this was preserved in the minutes of the meeting. But the publication did not materialize. The manuscript and reviews have not been preserved, but the work itself was included by Lobachevsky in his work “On the Principles of Geometry” (1829-1830), published in the journal “Kazan Vestnik”. This work was the first serious publication in world literature on non-Euclidean geometry, or Lobachevsky geometry.

Lobachevsky considers Euclid's axiom of parallelism to be an arbitrary constraint. From his point of view, this requirement is too strict, limiting the possibilities of the theory describing the properties of space. As an alternative, he proposes another axiom: in the plane through a point that does not lie on a given line, there passes more than one line that does not intersect the given one. The new geometry developed by Lobachevsky does not include the Euclidean geometry, but the Euclidean geometry can be obtained from it by passing to the limit (as the space curvature tends to zero). In the Lobachevsky geometry itself, the curvature is negative. Already in the first publication, Lobachevsky developed in detail the trigonometry of non-Euclidean space, differential geometry (including the calculation of lengths, areas and volumes) and related analytical issues.

In 1832, Lobachevsky married Varvara Alekseevna Moiseeva, who was almost 20 years younger than him. Lobachevsky's family life fully corresponded to his general mood and his activities. Pursuing the search for truth in science, he put the truth above all else in life. In the girl he decided to call his wife, he mainly valued honesty, truthfulness and sincerity. They say that before the wedding, the bride and groom gave each other honestly be sincere and restrained it. By nature, Lobachevsky's wife was a sharp contrast to her husband: Varvara Alekseevna was unusually lively and quick-tempered.

Lobachevsky had four sons and two daughters. The eldest son, Alexei, his father's favorite, very much resembled him in face, height and physique; younger son suffered from some kind of brain disease, he could hardly speak and died in the seventh year.

Not finding understanding at home, Lobachevsky tried to find like-minded people abroad. In 1837, Lobachevsky's article "Imaginary Geometry" in French appeared in the authoritative Berlin journal Crelle, and in 1840 Lobachevsky published on German a small book "Geometric Investigations in the Theory of Parallels", which contains a clear and systematic presentation of his main ideas. Two copies were given to Carl Friedrich Gauss, "the king of mathematicians" of that time. As it turned out much later, Gauss himself secretly developed non-Euclidean geometry, but he did not dare to publish anything on this topic. After reviewing the results of Lobachevsky, he enthusiastically spoke about them, but only in his diaries and in letters to close friends. For example, in a letter to the astronomer Schumacher (1846), Gauss assessed Lobachevsky's work as follows:

You know that for 54 years (since 1792) I have shared the same views (with some development of them, which I do not want to mention here); thus, I did not find anything actually new for myself in Lobachevsky's work. But in the development of the subject, the author did not follow the path that I myself followed; it is masterfully done by Lobachevsky, in a truly geometric spirit. I consider myself obligated to draw your attention to this work, which will surely give you quite exceptional pleasure.

Gauss indirectly expressed his sympathy for the ideas of the Russian scientist: he recommended that Lobachevsky be elected a foreign corresponding member of the Royal Scientific Society of Göttingen as "one of the most excellent mathematicians of the Russian state." Gauss also began to study Russian in order to familiarize himself with the details of the discoveries of the Kazan geometer. The election of Lobachevsky took place in 1842 and became the only lifetime recognition of Lobachevsky's scientific merits. However, it did not strengthen Lobachevsky's position.

Obviously, Lobachevsky's research was beyond the understanding of his contemporaries. Some ignored him, others greeted his work with rude ridicule and even scolding. While our other highly talented mathematician Ostrogradsky enjoyed well-deserved fame, no one knew Lobachevsky; Ostrogradsky himself treated him either mockingly or hostilely.

As historians of science found out, the Hungarian mathematician Janos Bolyai, independently of Lobachevsky and a little later (1832), published his version of non-Euclidean geometry. But his work did not attract the attention of his contemporaries, and the fate of Yanosh himself turned out to be even more tragic than the fate of Lobachevsky.

In April 1845, Musin-Pushkin received a new appointment - he became a trustee of the St. Petersburg educational district. The post of trustee of the Kazan educational district passes to Lobachevsky. He took office on April 18, 1845. On November 20, 1845, Lobachevsky was elected rector for the new four years for the sixth time, and unanimously.

The next, 1846, was a difficult year for Lobachevsky.

On May 7, the five-year term of his service as an emeritus professor ended. The Council of Kazan University again entered with a request to leave Lobachevsky as a professor for another five years. Despite this, due to some dark intrigue, the ministry was refused.

On August 16, 1846, the Ministry "at the direction of the Governing Senate" removed Lobachevsky not only from the professorial department, but also from the post of rector. He was appointed assistant trustee of the Kazan educational district with a significant reduction in salary.

Lobachevsky soon went bankrupt, the house in Kazan and his wife's estate were sold.

In 1852, the eldest son Alexei, Lobachevsky's favorite, died of tuberculosis. His own health was undermined, his eyesight was weakening. But despite this, Lobachevsky, to the best of his ability, tries to participate in the life of the university. He chairs the commission for the celebration of the 50th anniversary of the university. However, the commission did not work for a long time and ceased to exist, as the emperor considered that the celebration of the anniversary was unnecessary.

Lobachevsky's activities in last decade his life in its intensity was only a shadow of the past. Deprived of his chair, Lobachevsky lectured on his geometry to a select scientific audience, and those who heard them remember the thoughtfulness with which he developed his principles.

These fatal years were followed by years of decline for Lobachevsky; he is rapidly going blind. Of course, nothing is able to give happiness in the years of the destruction of forces, but Better conditions can soften this period of life. Not seeing people around him imbued with his ideas, Lobachevsky thought that these ideas would perish with him.

The last work of the scientist, "Pangeometry", was written down under dictation by the students of a blind scientist in 1855.

Nikolai Ivanovich Lobachevsky died on February 12, 1856, on the very day on which 30 years earlier he first published his version of non-Euclidean geometry. He was buried at the Arskoye cemetery in Kazan.

Lobachevsky died unrecognized, only 10-12 years before the triumph of his ideas. Soon the situation in science changed radically. The studies of Beltrami (1868), Klein (1871), Poincaré (1883) and others played an important role in the recognition of Lobachevsky's works. The appearance of the Klein model proved that Lobachevsky's geometry is as consistent as the Euclidean one. The realization that Euclidean geometry has a full-fledged alternative made a huge impression on scientific world and gave impetus to other innovative ideas in mathematics and physics. In particular, Lobachevsky's geometry had a decisive influence on the emergence of Riemannian geometry, Felix Klein's Erlangen Program, and the general theory of axiomatic systems. It also turned out that the relationship between space and time, discovered by Lorentz, Poincaré, Einstein and Minkowski and described in the framework of the special theory of relativity, is directly related to Lobachevsky's geometry. For example, Lobachevsky geometry formulas are used in the calculations of modern synchrophasotrons.

When, in the second half of the 1860s, the works of Lobachevsky were already universally appreciated and translated into all major European languages, Kazan University requested 600 rubles. for the edition Complete collection essays on geometry" Lobachevsky. This project was carried out only 16 years later (1883). Great difficulties were encountered even in the selection of material, since many of Lobachevsky's works were neither in the library nor in bookstores, and some early works have not been found so far.

Nikolai Ivanovich Lobachevsky obtained a number of valuable results in other branches of mathematics as well. So, in algebra, he developed, independently of Dendelin, a method for the approximate solution of equations, in mathematical analysis he obtained a number of subtle theorems on trigonometric series, refined the concept of a continuous function, gave a sign of convergence of series, etc. different years he published several informative articles on algebra, probability theory, mechanics, physics, astronomy and educational problems.

In 1892, the 100th anniversary of Lobachevsky was widely celebrated in Russia and in other countries. Was established international award named after N.I. Lobachevsky (1895), awarded by the Russian Academy of Sciences for outstanding work in the field of geometry. Over the years, it has been awarded to Marius Sophus Lee, David Hilbert, Herman Weil, Elie Cartan, Alexei Vasilievich Pogorelov, Lev Semyonovich Pontryagin, Pavel Sergeevich Alexandrov, Andrei Nikolaevich Kolmogorov, Vladimir Igorevich Arnold, Grigory Alexandrovich Margulis.

In 1896, 40 years after the death of N.I. Lobachevsky, a monument to the great mathematician, created by the Russian sculptor Maria Dillon, was erected in front of the building of Kazan University.

Named after Lobachevsky:

• Prize named after N.I. Lobachevsky of the Russian Academy of Sciences, then the Academy of Sciences of the USSR and again the Russian Academy of Sciences (awarded since 1897, as a rule, once every three years, to domestic and foreign mathematicians for outstanding results in the field of geometry)
• Medal named after N.I. Lobachevsky "For outstanding work in the field of geometry" (awarded since 1991 by the Academic Council of Kazan State University once every five years to Russian and foreign mathematicians)

• minor planet
• crater on reverse side Moon
• Scientific Library of Kazan University
• streets in Moscow, Kyiv, Kazan, Lipetsk and other cities
• school number 52 in Lvov, Ukraine
• Lyceum at Kazan State University
• Nizhny Novgorod State University.

In 1992, the Bank of Russia issued a 1 ruble commemorative coin dedicated to the 200th anniversary of the birth of N.I. Lobachevsky.

The following mathematical objects bear the name of Lobachevsky:

• Lobachevsky geometry
• Lobachevsky method
• sign of Lobachevsky.

Based on the materials of the books by D. Samin "100 great scientists" (M.: Veche, 2000), "The line of great mathematicians" (Warsaw, ed. Nasha Ksengarnya, 1970), B.A. Kordemsky "Great Lives in Mathematics" (Moscow, "Prorsveshchenie", 1995) and Wikipedia.

Nikolai Ivanovich Lobachevsky(November 20 (December 1), 1792, Nizhny Novgorod - February 12 (24), 1856, Kazan) - Russian mathematician, one of the founders of non-Euclidean geometry, a figure in university education and public education. The famous English mathematician William Clifford called Lobachevsky the "Copernicus of geometry".

Lobachevsky taught at the Imperial Kazan University for 40 years, including 19 years as a rector; his activity and skillful leadership made the university one of the leading Russian educational institutions. According to N.P. Zagoskin, Lobachevsky was the “great builder” of Kazan University.

Parents, date and place of birth

Until the end of the 1940s, information about the date and place of birth of N. I. Lobachevsky was contradictory. In 1948, A. A. Andronov published an article about his research on this subject, in which he indicated that the exact date of birth of the mathematician should be considered November 20, 1792 (according to the old style), and the place was the city of Nizhny Novgorod (in 1948 - Gorky ). Later, N. I. Privalova established the location of the house of P. A. Lobachevskaya. The researches of A. A. Andronov and N. I. Privalova became universally recognized, they contributed to the fact that Gorky University was named after N. I. Lobachevsky (1956).

Nikolai is the middle of the three sons of Praskovya Alexandrovna Lobachevsky (? -1847), whose husband was Ivan Maksimovich Lobachevsky (1760-1800), an official in the geodetic department. There is a version of the origin of N. I. Lobachevsky, expressed by the professor of mathematics at the University of Nizhny Novgorod Dmitry Andreevich Gudkov (1918-1992), based on archives and literary sources; according to her, Nikolai Ivanovich Lobachevsky and his two brothers - Alexander and Alexei - were the illegitimate sons of Praskovya Alexandrovna Lobachevsky and Makaryevsky land surveyor and captain Sergei Stepanovich Shebarshin

Information about the life of the scientist's father, I. M. Lobachevsky, is extremely scarce. His father, M. V. Lobachevsky, was a Pole who lived in Little Russia. Around 1757, Prince Mikhail Ivanovich Dolgorukov (1731-1794), to whom M.V. Lobachevsky was in the service, allowed him to marry his serf Agrafena, and in 1775 the prince gave Agrafena freedom. At birth, Ivan Maksimovich was baptized according to the Catholic rite, but later converted to Orthodoxy. Around 1797, I. M. Lobachevsky was sent to serve in the survey office of Nizhny Novgorod. Soon after the move, he became seriously ill and died at the age of only 40, leaving three children and his wife Praskovya Alexandrovna in a difficult financial situation.

The first years of life (1792-1807)

In 1802, Praskovya Alexandrovna sent all three sons to the Kazan Gymnasium, the only one in those years in the entire eastern part of the Russian Empire, for “state raznochinskoe maintenance”. Nikolai Lobachevsky graduated from the gymnasium at the end of 1806, showing good knowledge, especially in mathematics and languages ​​​​- Latin, German, French. The great merit of the teacher of the gymnasium, G. I. Kartashevsky, manifested even then his interest in mathematics.

Shortly after Nikolai entered the gymnasium, opportunities for obtaining further education. On November 5, 1804, Emperor Alexander I signs the “Affirmative Letter” and the “Charter of the Imperial Kazan University”. On February 14, 1805, the university was opened. A number of teachers of the gymnasium, in parallel with the performance of their former duties, go to teach at the university. I. F. Yakovkin becomes a professor of history, geography and statistics of the Russian Empire and the director of the university, G. I. Kartashevsky - an adjunct of higher mathematics, I. I. Erich - an adjunct of antiquities, Latin and Greek languages, L. S. Levitsky - an adjunct of speculative and practical philosophy, I. I. Zapolsky - adjunct of applied mathematics and experimental physics. The University Council addressed the parents of children growing up in the Kazan Gymnasium with a proposal to send them after the end of the course of the gymnasium to continue their studies at the university. P. A. Lobachevskaya agreed. Nikolai's elder brother, Alexander, was enrolled at the university immediately, on February 18, 1805. Nikolai was tested in July 1806, but unsuccessfully, but on December 22 of the same year he passed a second test and on February 14, 1807 was enrolled in the university. In the same 1807, Nikolai's younger brother, Alexei, became a student at Kazan University.

Young years (1807-1814)

In the first years, only two courses of the year were related to the physical and mathematical sciences. In two half-years adjunct I. I. Zapolsky taught a course in physics. In the first half of the year, associate G. I. Kartashevsky repeated general arithmetic with students, read a course in algebra, and proceeded to present differential calculus. However, on December 5, 1806, due to a conflict with the director of the university, I.F. Yakovkin, he and a number of other teachers were fired. Students were entrusted with teaching mathematics. Students also taught other disciplines.

The situation changed only in 1808 with the arrival of prominent German scientists at the university, who were selected and invited by the then trustee of the Kazan educational district S. Ya. Rumovsky. In February 1808, a professor of pure mathematics, Martin Bartels, a friend and teacher of the great German mathematician Carl Friedrich Gauss, arrived, an excellent teacher. On March 2, he opened a course of lectures on pure mathematics. In September of the same year, the mathematician Kaspar Renner arrived in Kazan, and in 1810, Bronner, professor of theoretical and experimental physics, and Litrov, professor of astronomy.

The influence of new talented teachers affected Nikolai's interests. If in 1808 he most attention devoted to chemistry and pharmacology (which at that time was called medical science), then under the influence of Bartels he became interested in the physical and mathematical sciences. However, there was also a place for student pranks. If in 1807, in the reports of chamber students, Lobachevsky's behavior was recognized as good, then in 1808 for pyrotechnic experiments (on August 13, he and his comrades launch a rocket) he was punished by a punishment cell. Pranks, however, did not prevent Nikolai from becoming a chamber student on May 31, 1809, having received a positive attestation from Yakovkin, where not only good behavior was noted, but also success in the sciences. And indeed, Lobachevsky enjoyed confidence at the university - it was Nikolai in the autumn of 1809 who was instructed to check the inventory of the chemistry room left after the death of Adjunct Everst. However, trouble soon began. In January 1810, despite the prohibitions, he goes to new year holidays visit and participate in a masquerade. For this, he was deprived of the title of the ruling position of a chamber student and payments for books and teaching aids. In the last year of study (1811), a report on Lobachevsky's behavior notes: stubbornness, "dreamy conceit, stubbornness, disobedience", as well as "outrageous acts" and even "signs of godlessness". The threat of expulsion and return to the soldiers loomed over him, but the intercession of Bartels and Bronner helped to avert the danger.

In 1811, after graduating from the university, Lobachevsky received a master's degree in physics and mathematics with honors and was left at the university; before that, he was forced to repent for his “bad behavior” and make a promise to behave in an exemplary manner in the future. Lobachevsky's scientific work continues. At the end of August 1811, Litrov, together with Lobachevsky and Simonov, observed a comet. And from October of the same year, Bartels began to study Lobachevsky classical works Gauss and Laplace. The study of these works became an incentive for independent research. At the end of 1811, Lobachevsky presented the argument "Theory of elliptical motion celestial bodies". In 1813, another work was presented - “On the permission algebraic equation x m − 1 = 0 ". In addition to scientific studies, Nikolai is also engaged in pedagogical activities - he works with students and gives special lectures on arithmetic and geometry for officials who have not received a university education, but who want to get positions in the 8th grade. On March 26, 1814, the 21-year-old Lobachevsky, at the request of Bronner and Bartels, was approved as an adjunct in pure mathematics.

Beginning of teaching activity (1814-1820)

Start teaching activities Lobachevsky coincided with fundamental changes in university life. The organization of the university, through the efforts of the trustee M. A. Saltykov, was finally brought into line with the charter of 1804. On February 24, 1814, I. O. Brown was approved as rector, four departments were allocated at the university (moral and political department, department of physical and mathematical sciences, verbal department, medical department), deans of departments were appointed. Bartels was appointed dean of the department of physical and mathematical sciences. The first course that the young adjunct was assigned to teach was the number theory course according to Gauss and Legendre. He will continue to read the same course in the next 1815/1816 academic year.

On July 7, 1816, Lobachevsky, on the initiative of Saltykov, was approved as an extraordinary professor. These elections were not smooth. In the university council, to which Saltykov filed a motion against Lobachevsky, disagreements arose over the compliance of such an election with the university charter. The offended Saltykov fusses directly to the minister and achieves desired result. After being elected an extraordinary professor, Lobachevsky is trusted to teach more responsible courses. In the 1816/1817 academic year, he read a course in arithmetic, algebra and trigonometry in his notebook, in 1817/1818 - a course in plane and spherical geometry in his notebook, in 1818/1819 - a course in differential and integral calculus according to Monge and Lagrange. We have to take a more active part in the rest of university life. So Lobachevsky is a member of a special committee elected on October 13, 1816 in the case “on disobedience of students against superiors and rudeness,” and on May 23, 1818, he is approved as a member of the School Committee in charge of the schools of the entire educational district.

However, both in the field of education in Russia and in the life of a provincial university, changes are coming. In 1816, Prince A.N. Golitsyn occupied the post of Minister of Public Education, and already in January 1817, Saltykov wrote in one of his letters: “It is more than likely that, with the exception of Moscow, all provincial universities will be closed. The question of closing Kharkiv and Kazan University is already on the agenda. Klinger, not wanting to attend his university's funeral, resigns. I'm going to do the same..." In 1817, the affairs of public education were combined with the affairs of religions - the Ministry of Spiritual Affairs and Public Education was formed.

Dean (1820-1827)

In 1819, an auditor, Mikhail Magnitsky, arrived in Kazan, who gave an extremely negative conclusion about the state of affairs at the university: economic disorder, squabbles, lack of piety, in which Magnitsky saw "a single foundation for public education." Magnitsky was praised only by the Faculty of Physics and Mathematics. In the report, he proposed to close the university altogether, but Emperor Alexander I imposed a resolution: "Why destroy it, it's better to fix it." As a result, Magnitsky was appointed trustee of the educational district and instructed to make a "correction". He fired 9 professors, expelled Yakovkin in disgrace and without a pension as having failed, cleared the university library of "seditious" books, introduced strict censorship of lectures and a barracks regime, and organized the department of theology. Bartels and other foreigners left, and the 28-year-old Lobachevsky, who had already shown outstanding organizational skills, was appointed dean of the Faculty of Physics and Mathematics instead of Bartels.

The range of his duties was extensive - lecturing on mathematics, astronomy and physics, completing and putting in order the library, museum, physics office, creating an observatory, etc. The list of official duties even includes “monitoring the reliability” of all Kazan students. Relations with Magnitsky were initially good; in 1821, the trustee presented Lobachevsky for the award of the Order of St. Vladimir IV degree, which was approved and awarded in 1824. However, their relationship gradually escalates - the trustee receives many denunciations, where Lobachevsky is again accused of arrogance and lack of due piety, and Lobachevsky himself in a number of cases showed disobedience, speaking out against the administrative arbitrariness of Magnitsky. I. I. Lazhechnikov, who served under Magnitsky as the director of Kazan schools and an inspector of the university (from 1823 to 1826), recalled the educational environment with disgust:

The university was breaking everything that had previously existed in it. Chiefs, professors, students, everything was subject to strict clerical discipline. Science has taken a backseat. The persecution of philosophy reached ridiculous fanaticism... the teaching of many academic subjects, based on theological principles, seemed to prepare students for a spiritual rank.

During these years, Lobachevsky prepared a textbook on geometry, condemned by a reviewer (academician Fuss) for using the metric system of measures and excessive departure from the Euclidean canon (it was never published during the author's lifetime). Another textbook written by him, on algebra, was published only 10 years later (1834).

M. N. Musin-Pushkin in 1830

Immediately after the accession of Nicholas I, in 1826, Magnitsky was removed from the post of trustee for abuses discovered during the audit and brought to trial by the senate. The new trustee was Count M. N. Musin-Pushkin, who in his youth (1810) passed the exams (for the rank) at Kazan University, after which he served as a commander in the Cossack troops for many years, and participated in the Patriotic War of 1812. According to contemporaries, he was distinguished by rigidity, but at the same time strict justice and honesty, and was far from immoderate religiosity. On May 3, 1827, 35-year-old Lobachevsky was elected rector of the university by secret ballot (11 votes against 3). Soon Musin-Pushkin left for St. Petersburg for a long time and did not interfere in Lobachevsky's activities, completely trusting him and occasionally exchanging friendly letters.

Rector (1827-1845)

The new rector, with his characteristic energy, immediately plunged into economic affairs - the reorganization of the staff, the construction of educational buildings, mechanical workshops, laboratories and observatories, the maintenance of the library and the mineralogical collection, participates in the publication of the Kazan Bulletin, etc. He did a lot with his own hands . During his time at the university, he taught courses in geometry, trigonometry, algebra, analysis, probability theory, mechanics, physics, astronomy and even hydraulics, often replacing absent teachers. Simultaneously with teaching, Lobachevsky read popular science lectures for the population. And at the same time, he tirelessly developed and polished the main work of his life - non-Euclidean geometry. The first draft of the new theory - the report "A Concise Presentation of the Principles of Geometry" Lobachevsky made on February 11 (23), 1826, the date of this speech is considered the birthday of non-Euclidean geometry.

In 1832, Lobachevsky married Varvara Alekseevna Moiseeva, who was almost 20 years younger than him. The exact number of children born is unknown. According to the track record, seven children survived.

It is known that one of his daughters - Sofia Nikolaevna (married Kazina) - was married to a hereditary nobleman Nil Dmitrievich Kazin, in whom she gave birth to two children; she died on July 15, 1871 and was buried next to her father (together with her son, the grandson of Lobachy - N. N. Kazin, who died on October 20, 1872).

In 1832-1834. Lobachevsky's published work on non-Euclidean geometry is subjected to sharp, ignorant criticism in St. Petersburg (for more details, see below). His official authority was shaken, for the third term (1833) Lobachevsky was elected rector by only 9 votes against 7. In 1834, on the initiative of Lobachevsky, instead of the Kazan Bulletin, the publication of Scientific Notes of the Kazan University began, where, challenging his opponents, he published his new discoveries. Petersburg professors evaluated scientific works Lobachevsky invariably negatively, he never managed to defend his dissertation.

Despite the complications, Musin-Pushkin firmly supported Lobachevsky, and gradually the situation somewhat normalized. In 1836, Tsar Nicholas I visited the university, was pleased and awarded Lobachevsky with the prestigious Order of Anna II degree, which gave the right to hereditary nobility. On April 29, 1838, "for merits in the service and in science," N. I. Lobachevsky was granted the nobility and given a coat of arms, the description of which says: Shield crossed. In the first, scarlet part, there is a golden star with six rays, made up of two triangles, and a golden bee. In the second, azure part, there is a silver overturned arrow, above the same overturned horseshoe. The shield is surmounted by a nobleman's helmet and crown. Crest: three silver ostrich feathers. The namet on the right is scarlet, with gold, on the left - azure, with silver. The rector of the Imperial Kazan University, Nikolai Lobachevsky, entered the service in 1814; On December 31, 1818, he was promoted to Court Councilors and, being in the rank of State Councilor, on April 29, 1838, he received a diploma for hereditary noble dignity. The coat of arms of Lobachevsky is included in the General armorial of the noble families of the All-Russian Empire (part 11, p. 127).

Portrait of Lobachevsky
works by L. D. Kryukov (between 1833 and 1836)

In addition to the tsar, Kazan University met other eminent guests during these years: the German naturalist Alexander von Humboldt (1829), the Russian polar explorer Admiral Ferdinand Wrangel (also 1829). On September 5, 1833, on his way to the Orenburg province (to collect materials about the Pugachev rebellion), Alexander Sergeevich Pushkin visited Kazan, but the assumptions about his meeting with Lobachevsky were not confirmed. In the summer of 1837, the heir, Tsarevich Alexander Nikolayevich, visited future emperor Alexander II, together with the poet V. A. Zhukovsky, traveled around Russia.

The end of the 1830s was sad for Lobachevsky. Bartels and Kartashevsky died, and on February 27, 1840, his mother Praskovya Alexandrovna died in his house.

Lobachevsky was the rector of Kazan University from 1827 to 1846. During this period, there was an epidemic of cholera (1830) and a severe fire (1842), which destroyed half of Kazan. Thanks to the energy and skillful actions of the rector, the casualties and losses in both cases were minimal. Through the efforts of Lobachevsky, Kazan University becomes a first-class, authoritative and well-equipped educational institution, one of the best in Russia.

Last years (1845-1856)

Commemorative plaque on the Rector's House,
in which N. I. Lobachevsky lived from 1827 to 1846

In April 1845, Musin-Pushkin received a new appointment - he became a trustee of the St. Petersburg educational district. The post of trustee of the Kazan educational district passes to Lobachevsky. He took office on April 18, 1845. On November 20, 1845, Lobachevsky was elected rector for the new four years for the sixth time, and unanimously.

The next, 1846, was a difficult year for Lobachevsky. February 8 he dies two year old daughter Hope. In the same year, after 30 years of service, the ministry, according to the charter, had to decide whether to leave Lobachevsky and Simonov as professors or choose new teachers. On June 11, the university council informed the minister that it "finds no reason" to remove Lobachevsky and Simonov from teaching. Lobachevsky himself, in a restrained letter, supported Simonov, and with regard to himself left the decision to the discretion of the minister, in the case of a negative resolution, he asked to appoint A. F. Popov to his department (“pure mathematics”).

In the last year of life (daguerreotype 1855)

Despite the opinion of the council, on August 16, 1846, the Ministry "at the direction of the Governing Senate" removed Lobachevsky not only from the professorial department, but also from the post of rector. He was appointed assistant trustee of the Kazan educational district with a significant reduction in salary. The department, according to his request, was transferred to A.F. Popov, the future academician. I. M. Simonov became the rector of the university.

Lobachevsky soon went bankrupt, the house in Kazan and his wife's estate were sold for debts. In 1852, the eldest son Alexei, Lobachevsky's favorite, died of tuberculosis. His own health was undermined, his eyesight was weakening. But despite this, Lobachevsky, to the best of his ability, tries to participate in the life of the university. He chairs the commission for the celebration of the 50th anniversary of the university. However, the commission soon ceased to exist, as the emperor considered that the celebration of the anniversary was unnecessary.

The last work of the scientist, "Pangeometry", was written down under dictation by the students of a blind scientist in 1855. He died on February 12 (24), 1856, on the very day on which 30 years earlier he first published his version of non-Euclidean geometry. He was buried at the Arskoye cemetery in Kazan.

When, in the second half of the 1860s, Lobachevsky's writings were already universally appreciated and translated into all major European languages, Kazan University requested 600 rubles. for the publication of Lobachevsky's Complete Works on Geometry. This project was carried out only 16 years later (1883). Great difficulties were encountered even in the selection of material, since many of Lobachevsky's works were not found either in the library or in bookstores, and some early works have not been found to this day.

Geometry of Lobachevsky

Student notes of Lobachevsky's lectures (from 1817) have been preserved, where he made an attempt to prove the fifth postulate of Euclid, but in the manuscript of the textbook "Geometry" (1823) he already abandoned this attempt. IN " Reviews of the Teaching of Pure Mathematics”for 1822/23 and 1824/25, Lobachevsky pointed out the “still invincible” difficulty of the problem of parallelism and the need to take in geometry as initial concepts directly acquired from nature.

On February 7 (19), 1826, Lobachevsky presented for publication in " Notes of the Physics and Mathematics Department" composition: " Concise presentation of the beginnings of geometry with a rigorous proof of the theorem on parallel" (in French). But the publication did not materialize. The manuscript and reviews have not been preserved, but the essay itself was included by Lobachevsky in his work " On the principles of geometry"(1829-1830), published in the magazine" Kazan Bulletin ". This work was the first serious publication in world literature on non-Euclidean geometry, or Lobachevsky geometry.

Lobachevsky considers Euclid's axiom of parallelism to be an arbitrary constraint. From his point of view, this requirement is too strict, limiting the possibilities of the theory describing the properties of space. As an alternative, he proposes another axiom: in a plane through a point not on a given line there passes more than one line that does not intersect the given line. The new geometry developed by Lobachevsky does not include the Euclidean geometry, but the Euclidean geometry can be obtained from it by passing to the limit (as the space curvature tends to zero). In the Lobachevsky geometry itself, the curvature is negative. Already in the first publication, Lobachevsky developed in detail the trigonometry of non-Euclidean space, differential geometry (including the calculation of lengths, areas and volumes) and related analytical issues.

However scientific ideas Lobachevsky were not understood by contemporaries. His work "On the Principles of Geometry", presented in 1832 by the university council to the Academy of Sciences, received a negative assessment from M.V. Ostrogradsky. In an ironically caustic review of the book, Ostrogradsky frankly admitted that he did not understand anything in it, except for two integrals, one of which, in his opinion, was calculated incorrectly (in fact, Ostrogradsky himself was mistaken). Among other colleagues, almost no one supported Lobachevsky either, misunderstanding and ignorant ridicule grew.

The culmination of the bullying was a mocking anonymous libel (signed under the pseudonym S.S.), which appeared in F. Bulgarin's magazine "Son of the Fatherland" in 1834:

Why write, and even print, such ridiculous fantasies?<…>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 learning, then at least common sense should be in every teacher, and in the new geometry this latter is often lacking.<…>New Geometry<…>It is written in such a way that no one who reads it understands almost anything.

Lobachevsky's attempt to publish an answer to the libel in the same journal was ignored by the editors. Despite the complications, Lobachevsky, confident in his innocence, continued to work. In 1835-1838 he published articles on "imaginary geometry" in "Scientific Notes", and then the most complete of his works " New beginnings of geometry with a complete theory of parallels».

Not finding understanding at home, Lobachevsky tried to find like-minded people abroad. In 1837 Lobachevsky's article " Imaginary geometry" in French ( Geometry imaginaire) appeared in the authoritative Berlin magazine Crelle, and in 1840 Lobachevsky published a small book in German called " Geometric studies on the theory of parallel”, which contains a clear and systematic presentation of his main ideas. Two copies were given to Carl Friedrich Gauss, "the king of mathematicians" of that time. As it turned out much later, Gauss himself secretly developed non-Euclidean geometry, but he did not dare to publish anything on this topic, believing that the scientific community was not yet ready to accept such radical ideas. After reviewing the results of Lobachevsky, he enthusiastically spoke about them, but only in his diaries and in letters to close friends. For example, in a letter to the astronomer G. H. Schumacher (1846), Gauss assessed the work of Lobachevsky as follows:

You know that for 54 years (since 1792) I have shared the same views (with some development of them, which I do not want to mention here); thus, I did not find anything actually new for myself in Lobachevsky's work. But in the development of the subject, the author did not follow the path that I myself followed; it is masterfully done by Lobachevsky, in a truly geometric spirit. I consider myself obligated to draw your attention to this work, which will surely give you quite exceptional pleasure.

Gauss indirectly expressed his sympathy for the ideas of the Russian scientist: he recommended that Lobachevsky be elected a foreign corresponding member of the Royal Scientific Society of Göttingen as "one of the most excellent mathematicians of the Russian state." Gauss also began to study Russian in order to familiarize himself with the details of the discoveries of the Kazan geometer. The election of Lobachevsky took place in 1842 and became the only lifetime recognition of Lobachevsky's scientific merits. However, it did not strengthen Lobachevsky's position; he had four more years to work at his native university. His new article (the solution of some problems of analysis) again received a sharply negative review from Ostrogradsky (1842).

As historians of science found out, the Hungarian mathematician Janos Bolyai independently of Lobachevsky and a little later (1832) published his version of non-Euclidean geometry. But his work did not attract the attention of contemporaries.

Lobachevsky died unrecognized, only 10-12 years before the triumph of his ideas. Soon the situation in science changed radically. The studies of E. Beltrami (1868), F. Klein (1871), A. Poincaré (1883) and others played an important role in the recognition of the works of Lobachevsky. that Lobachevsky's geometry is also consistent if Euclidean is consistent. The realization that there was a viable alternative to Euclidean geometry made a huge impression on the scientific world and gave impetus to other innovative ideas in mathematics and physics. In particular, Lobachevsky's geometry had a decisive influence on the emergence of Riemannian geometry, Felix Klein's Erlangen Program, and the general theory of axiomatic systems.

Other scientific achievements

Lobachevsky obtained a number of valuable results in other branches of mathematics: for example, in algebra, independently of J. Dandelin, he developed a method for the approximate solution of equations, in mathematical analysis he obtained a number of subtle theorems on trigonometric series, refined the concept of a continuous function, gave a sign of convergence of series and etc. Over the years, he published several informative articles on algebra, probability theory, mechanics, physics, astronomy and education.

Students

• Bolzani, Joseph Antonovich
• Zinin, Nikolai Nikolaevich, who became an academic chemist.
• Popov, Alexander F.
• Yanishevsky, Erast Petrovich.

Awards and titles

Monument to N. I. Lobachevsky in Kazan, sculptor Maria Dillon

During his life, N. I. Lobachevsky received a number of awards for his tireless and fruitful service:

• 1818 - as a professor received the rank of court adviser.
• 1824 - Order of St. Vladimir IV degree, rank of collegiate adviser.
• 1831 - personal gratitude of the king for the successful fight against the cholera epidemic and a ring with a diamond. Lobachevsky was forced to sell the royal gift during the years of need.
• 1833 - Order of St. Stanislaus III degree, rank of State Councilor.
• 1836 - Order of St. Anna II degree, title of hereditary nobleman (approved in 1838).
• 1838 - rank of real state councilor.
• 1841 - title of honored professor after 25 years of service.
• 1842 - on the recommendation of Gauss, he was elected a corresponding member of the Göttingen Royal Scientific Society.
• 1842 - Order of St. Vladimir III degree, to the 50th anniversary.
• 1844 - Order of St. Stanislaus, 1st class.
• 1852 - Order of St. Anne, 1st class, for the 60th anniversary.
• 1855 - on the occasion of the centenary of Moscow University, he was elected an honorary member, with a silver medal.

Memory

Grand opening of the monument to N. I. Lobachevsky in Kazan, September 1, 1896

Annual celebration of the birthday of N. I. Lobachevsky by the participants of the Volga Region Mathematical Olympiad for Students

In 1892, the 100th anniversary of Lobachevsky was widely celebrated in Russia and in other countries. An international prize named after N. I. Lobachevsky was established (1895), a monument to the scientist was opened in Kazan (sculptor M. L. Dillon, architect N. N. Ignatiev) (1896).

The 200th anniversary of Lobachevsky was celebrated in 1992. The Bank of Russia issued a commemorative coin in the series " Prominent figures Russia".

In 1994, in the city of Kozlovka (Chuvashia), which once housed the estate of N. I. Lobachevsky (then it was the village of Slobodka, Cheboksary district), the opening of the Lobachevsky house-museum took place.

Named after Lobachevsky:

• Nizhny Novgorod State University named after N.I. Lobachevsky, Nizhny Novgorod. March 20, 1956 issued a decree of the Presidium Supreme Council USSR on the assignment of the name of N. I. Lobachevsky to the Gorky (Nizhny Novgorod) University (Kazan University since 1925 was named after V. I. Ulyanov-Lenin, Lenin studied there from September to December 1887).
• Small planet (1858) Lobachevsky.
• A crater on the far side of the Moon (9.76°N, 113.07°E).
• Scientific Library of Kazan University.
• Lobachevsky streets in various settlements states of the former USSR.



In the 1950s, the American composer, singer and mathematician Tom Lehrer wrote a song jokingly saying that Nikolai Ivanovich was prone to plagiarism, and also encouraged other scientists to do the same. However, later Lehrer admitted that he was not going to accuse the Russian mathematician of anything, and mentioned the name of Lobachevsky simply because he liked its sound.

In 1965, the Tatar scholar and writer Dzhavad Tarjemanov published the documentary novel Youth of Lobachevsky (The Birth of a Genius) (Kazan: Tatar Book Publishing House), dedicated to the years of study at the university and difficult relationships with Yakovkin and Magnitsky. The novel was republished in 1968, and in 1987 it was released under the title “Youth of Lobachevsky. The start of a genius.

In his poem about the fate of Russia "The End belle epoch"(1969) Joseph Brodsky mentions the world of Lobachevsky as a metaphor:

To live in the era of achievements, having an exalted disposition,
unfortunately difficult. Beauty dress up,
you see what you were looking for, and not new marvelous divas.
And it’s not that Lobachevsky is firmly observed here,
but the expanded world must narrow somewhere, and here -
here is the end of perspective.

The song of the same name was written on the same verses in the solo album of the soloist of the Splin group Alexander Vasiliev.

Yevgeny Yevtushenko dedicated a chapter to Lobachevsky in the poem "Kazan University"; the events of the scientist's life are mentioned in other chapters of this poem.

Nikolai Ivanovich Lobachevsky (1792 - 1856) - an outstanding mathematician, teacher. The researcher is the founder of non-Euclidean geometry.

Childhood

The future scientist was born in the city of Nizhny Novgorod. His father was a raznochinets Ivan Maksimovich Lobachevsky, who held minor administrative positions. The head of the family died when Kolya was only 7 years old. His mother, in order to feed three children, moved to Kazan. Here begins the gymnasium period in the boy's life. He attended classes as a free listener. In 1807 he successfully passed the entrance exams to the University of Kazan.

First successes. Teaching activity

• 1811 - a master's degree in physical and mathematical sciences, Lobachevsky completes his studies at the university. A red diploma allows him to stay to work at his alma mater. At the end of the same year, he submits his report "The Theory of the Elliptical Motion of Celestial Bodies" to the judgment of the professorial community.
• The master receives the title of teacher of mathematical disciplines in 1814 and becomes a university professor in 1816. As a teacher, N. I. Lobachevsky was focused on mathematics and related disciplines.
• 1819 - N. I. Lobachevsky was appointed dean of his native faculty. The activity of the scientist is noted at the state level and the Order of Vladimir is awarded in 1821. During this period, Lobachevsky is tutorial in geometry, which caused controversy. Academician Fuss condemned the scientist for departing from scientific traditions and Euclidean geometry. Due to fierce disputes, the work was doomed to rest on the shelf: the textbook did not see the light during the author's lifetime. Algebra did not cause such a wave of controversy, but was not published until 1834.
• 1827 - Lobachevsky reaches the highest post at Kazan University and becomes rector. In this position, he proved himself to be a practical and economic person.

Revolution in geometry

Despite the success in pedagogy, non-Euclidean mathematics remained the main business of the scientist's life.

Lobachevsky presents "Exposition of the Principles of Geometry" (1826). February 23 becomes the starting point of Lobachevsky's new geometry. In the article "On the Principles of Geometry", the scientist writes about how for many centuries the scientific community has not questioned Euclid's hypothesis "about parallel". Nikolai Ivanovich went from trying to prove this hypothesis to completely denying it. And as a result, he discovered "absolute geometry", highlighting in the teachings of Euclid everything that did not depend on the fifth postulate. As a result of long research, the scientist created a new system of geometry.

The most important discovery of our hero is the discovery that there is more than one "true" geometry.

A study called "A Concise Statement of the Fundamentals of Geometry" remained misunderstood during the life of a mathematician. The "Principles of Geometry" was condemned, few supported the old friend.

The scientist's opus magnum, New Beginnings of Geometry, 1838, was acclaimed by the research community. For services to education and science, Lobachevsky becomes a nobleman.

1846 - by personal decree of the tsarist government, Lobachevsky was removed from pedagogical activity and dismissed from the post of rector, which greatly surprised the colleagues of the researcher and the mathematician himself, who gave his best years to the university.

Last years

An unexpected demotion led to debts and the need to sell the estate. His son Alexei dies of consumption, which irreparably hurts his father. Lobachevsky weakens, begins to go blind.

1855 - a summing up is created scientific life work "Pangeometry", written by students under the dictation of a blind teacher. Nikolai Ivanovich died on February 24, 1856, which was very symbolic. After all, it was on this very day that the scientist put forward his revolutionary vision of geometry many years ago.

The legacy of the scientist received recognition many years later. Only in 1868 did the Italian Beltrami prove that Lobachevsky's views on geometry were correct in many respects. He left a mark in other mathematical fields as well. In algebra, mathematical analysis and trigonometry.

Only when N. I. Lobachevsky was 100 years old, the State established nominal prize Russian Academy Sciences for his contribution to the study of geometry. A monument to the scientist was erected in the city of Kazan. The 200th anniversary of the birth of Lobachevsky was widely celebrated in many cities in 1992. A coin was prepared in memory of the outstanding explorer. Today in the village of Slobodka there is a mathematician's estate-museum.

The contribution of N. I. Lobachevsky to the development of domestic science cannot be overestimated. He left an indelible mark on mathematics. His research in mathematics made a splash in the field of geometry.

Nikolai Ivanovich Lobachevsky was born on December 1 (November 20), 1792 in Nizhny Novgorod in a poor family of a petty official.

As a nine-year-old boy, he was brought by his mother to Kazan and through her efforts he was placed with his two brothers in a gymnasium for state support. Since that time, his life and work have been going on in Kazan.

In the gymnasium, as we know from S.T. Aksakov's "Memoirs", the talented teacher G.I. Kartashevsky, a graduate of Moscow University, taught mathematics in a fascinating way. He took the study of mathematics to a considerable height. And when the young 14-year-old Lobachevsky became a university student in February 1807 (also a government student), he soon showed a particular inclination to study the physical and mathematical sciences, showing outstanding abilities. This one, undoubtedly, was affected by the results of the pedagogical activity of G.I. Kartashevsky.

However, Lobachevsky was no longer able to listen to Kartashevsky's lectures at the university, since the latter in December 1806 was dismissed from his post by director I.F. Yakovkin, as "having shown the spirit of disobedience and disagreement." Mathematical courses at the university began to be conducted by M.F. Bartels, who arrived in Kazan in 1808.

The successes of the student N.I. Lobachevsky, who competed in his studies with I.P. Simonov, later a famous astronomer and participant in the circumnavigation, invariably aroused the approval of M.F. Bartels and other professors.

August 3, 1811 Lobachevsky is approved by the master. Its leader, Professor M.F. Bartels, was a qualified mathematician and an experienced teacher, but did not creative work. Lobachevsky studied under his guidance the classic works on mathematics and mechanics: "The Theory of Numbers" (Disquisitiones Arithmeticae) by Gauss and the first volumes of "Celestial Mechanics" by Laplace. Presenting two scientific research in mechanics and algebra ("Theory of the elliptical motion of celestial bodies" (1812) and "On the solvability of an algebraic equation x n - 1 = 0" (1813), he was promoted ahead of schedule in 1814 to adjunct professor (associate professor).

Starting next year, he taught independently, gradually expanding the range of courses he taught and already thinking about the restructuring of the principles of mathematics. A year later he received the title of Extraordinary Professor.

But soon a very difficult environment for work is created at the university. In order to combat revolutionary sentiments and "free-thinking", the government of Alexander I, pursuing an increasingly reactionary policy, is looking for ideological support in religion, in mystical-Christian teachings. Universities are the first to be scrutinized.

M. L. Magnitsky, a member of the Main Board of Schools, was appointed to examine Kazan University and arrived in March 1819, who used his appointment for careeristic purposes. In his report, he concludes that the university "causes public harm by the semi-scholarship of its students .

However, the university was not destroyed. Alexander I decided to fix it. Magnitsky was appointed trustee of the Kazan educational district, and he began an energetic "renovation of the university." He started his career by dismissing nine professors. Careful surveillance of the content of lectures and student notes was established, and a harsh barracks regime was introduced for students.

Seven years of this church-police system brought severe trials to Lobachevsky, but did not break his rebellious spirit. Only his extensive and diverse pedagogical, administrative and research activities helped him to withstand this oppression. He teaches mathematics in all courses instead of Bartels, who left for Dorpat (Tartu); replaces Professor K. Bronner, who did not return to Kazan after a vacation; reads physical courses and manages a physical cabinet; replaces the astronomer I.P. Simonov, who went on a circumnavigation; reads astronomy and geodesy, taking over the observatory. For a number of years he has been the dean of the Physics and Mathematics Department. He invests colossal work in ordering the library and in expanding its physical and mathematical part. At the same time, he is one of the most active members, and then the chairman of the construction committee involved in the construction of the main university building. Finally, despite thousands of current affairs and responsibilities, Lobachevsky does not stop intense creative activity. He writes two textbooks for gymnasiums: "Geometry" (1823) and "Algebra" (1825). "Geometry" receives a negative review from Academician N.I. Fuss, who did not appreciate the changes that Lobachevsky made to the traditional presentation, and condemned the introduction of the metric system of measures, since it was created in revolutionary France. "Algebra" was also not printed due to internal delays at the university.

Soon clashes with the trustee begin. Lobachevsky, according to Magnitsky, shows impudence, violation of instructions. Magnitsky decides to establish special supervision over his actions.

However, even in these degrading conditions, Lobachevsky's thought is tirelessly working on a strict construction of the principles of geometry. We find the first traces of this work in the student notes of his lectures on geometry for 1817. The manuscript of the textbook "Geometry" and his "Reviews on the Teaching of Pure Mathematics" for 1822 - 1823 and 1824 - 1825 testify to it. Finally, his quest ends with a brilliant discovery. Breaking the shackles of millennial traditions, Lobachevsky comes to the creation of a new geometry. On February 23 (11), 1826, he makes a report on the new "Imaginary Geometry" at the faculty. This report "A concise presentation of the principles of geometry with a rigorous proof of the parallel theorem" was submitted for review to professors I.M. Simonov, A.Ya. Kupfer and adjunct N.D. Brashman. Lobachevsky wanted to know the opinion of his collaborators about the discovery, the greatness of which he recognized, and asked that his essay be accepted for the proposed publication of the department's Uchnye Zapiski.

But there was no response. The manuscript of the report has not reached us. The material of this report was included by Lobachevsky in his first work "On the Principles of Geometry", published in 1829-1830. in "Kazanskiy vestnik".

Lobachevsky's discovery was made by him on the path of a fundamental critical revision of the very first, initial, geometric concepts adopted in geometry since the time of Euclid (3rd century BC). This requirement of unconditional rigor and clarity in the beginnings, this close attention to questions of the foundations of science and an in-depth analysis of the original concepts are characteristic of Lobachevsky's work in general. The direction of research chosen by him contributed to the fact that not only in geometry, but also in a number of other areas of mathematics, he surpasses the level of science achieved at that time: for example, he gave a refinement of the concept of a function, which was later attributed to Dirichlet; he clearly distinguishes between the continuity of a function and its differentiability; he carried out deep research on trigonometric series, ahead of his era by many decades; he developed a method for the numerical solution of equations, which later unfairly received the name of the Greffe method, while Lobachevsky and, independently of him, the Belgian mathematician Dandelin developed this method much earlier.

The report of N.I. Lobachevsky coincided in time with the fall of Magnitsky. A special audit revealed a number of abuses, and the obscurantist trustee was removed and expelled.

The new trustee of the Kazan educational district, M.N. Musin-Pushkin, was able to appreciate the ebullient active nature of N.I. Lobachevsky. The great geometer was soon elected rector in 1827, and for 19 years he worked selflessly in this post, achieving the flourishing of Kazan University.

Lobachevsky sought to put into practice his broad advanced program of university education, an idea of ​​which is given by his speech "On the Most Important Subjects of Education", delivered by him a year after his appointment as rector.

Lobachevsky achieves a significant increase in the level of scientific and educational work at all faculties. He is building a whole complex of university auxiliary buildings: a library, an astronomical and magnetic observatory, an anatomical theater, a physics room and a chemical laboratory. He tries to create a "Society of Sciences" at the university, but does not receive permission for this. He replaces the journal of mixed content "Kazanskiy Vestnik" with the strict scientific journal "Scientific Notes of Kazan University" organized by him, the first book of which is published in 1834 and opens with a preface by Lobachevsky, highlighting the goals of scientific publication. For 8 years, he continues to manage the library at the same time as the rector. He himself teaches a number of special courses for students. He writes instructions for teachers of mathematics and takes care of the organization of teaching also in schools and gymnasiums. He takes part in a trip to Penza in 1842 to observe a solar eclipse. He skillfully protects the staff and students of the university during the cholera epidemic in 1830, isolating the university territory and carrying out thorough disinfection. He organized the rescue of astronomical instruments and the removal of books from the burning library during the huge fire of Kazan in 1842, and he manages to defend almost all university buildings from the fire. Finally, he organizes the reading of popular science lectures for the population and provides free access to the library and museums of the university.

And at the same time, he finds time for continuous and extensive scientific research, mainly devoted to the development of new geometry. His ideas were so unusual, spongy and new, he was so far ahead of his era that his contemporaries could not understand him and correctly evaluate him. His first work "On the Principles of Geometry" (1829 - 1830) was presented by the University Council in 1832 to the Academy of Sciences. But even Academician M.V. Ostrogradsky did not understand its meaning and gave a negative review of it: "... Mr. Rector Lobachevsky's book is defamed by a mistake ... it is carelessly presented and ... therefore, it does not deserve the attention of the Academy" . And in 1834, in the reactionary journal of F. Bulgarin "Son of the Fatherland", a mocking anonymous review of this work appeared. “How can one think that Mr. Lobachevsky, an ordinary professor of mathematics, would write a book for some serious purpose, which would bring a little honor to the latter school teacher! If not erudition, then at least every teacher should have common sense, and in the new geometry this latter is often lacking, ”wrote an unknown reviewer, hiding behind two letters S.S.

Faced with misunderstanding and even mockery, Lobachevsky did not stop his research. After work 1829 - 1830. "On the Beginning of Geometry" Lobachevsky prints in "Scientific Notes":
in 1835 "Imaginary Geometry"
in 1836 "Application of imaginary geometry to certain integrals".

From 1835 to 1838 he publishes his most extensive work, New Beginnings of Geometry with a Complete Theory of Parallels. Finally, in 1840, "Geometric Investigations in the Theory of Parallels" was published in German, which contains an extremely clear and concise presentation of his main ideas.

This courageous struggle for scientific truth sharply distinguishes Lobachevsky from other contemporaries, who were also approaching the discovery of non-Euclidean geometry.

The remarkable Hungarian mathematician Janos Bolyai published his study "Appendix" 3 years later than Lobachevsky - an addition to his father's book. In this work, he approached the same results from a somewhat different angle than Lobachevsky. But not having met with approval and support, he stopped the fight. The outstanding German mathematician Gauss, as it turned out from his posthumously published correspondence, received some initial relations of the new geometry, but, protecting his peace, and also, perhaps, not being sure of the correctness and objective significance of these results, forbade his correspondents to make any statements. about his views. While admiring the geometric works of Lobachevsky in private correspondence with friends, he did not say a single word about them in public.

Lobachevsky does not receive a single positive response, except for the only statement of the professor of mechanics of the Kazan University P.I. sooner or later will find its connoisseurs.

Lobachevsky's many years of fruitful work could not receive a positive assessment from the government of Nicholas I. In 1846, Lobachevsky was actually suspended from work at the university. Outwardly, he received a promotion - he was appointed assistant trustee (however, he was not paid a salary for this work), but at the same time he lost his chair and rectorship.

It should be noted that less than a year before, he was approved for the sixth time by the rector of the university for the next four years. At the same time, for more than a year he managed the Kazan educational district, replacing M.N. Musin-Pushkin, who was transferred to St. Petersburg. Pointing to these duties of his, Lobachevsky, shortly before the unexpected order of the Ministry, recommended instead of himself to the Department of Mathematics the teacher of the Kazan Gymnasium, A.F. Popov, who defended his doctoral dissertation. He considered it necessary to encourage a young capable scientist and found it unfair to occupy the chair under such circumstances. But, having lost the chair and rectorship and found himself in the position of assistant trustee, Lobachevsky lost the opportunity not only to lead the university, but also to effectively participate in the life of the university in general.

Forced removal from the activity to which he devoted his life, the deterioration of his financial situation, and then family misfortune (in 1852 his eldest son died) had a devastating effect on his health; he became very decrepit and began to go blind. But even deprived of sight, Lobachevsky did not stop coming to exams, to solemn meetings, attended scientific debates and did not stop scientific work.

Misunderstanding of the significance of his new geometry, the cruel ingratitude of his contemporaries, material hardships, family misfortune and, finally, blindness did not break his courageous spirit. A year before his death, he completed his last work "Pangeometry", dictating it to his students.

On February 24 (12), 1856, the life of the great scientist, wholly devoted to Russian science and Kazan University, ended.

Literature about N.I. Lobachevsky

1. Vasiliev A.V. - M.: Science. 1992. - 229 p. (Scientific and biographical series).
2. Norden A.P. 125 years of non-Euclidean geometry.- Advances in Mathematical Sciences, 1951. - 6, no. 3 (48). - S.3 - 9.
3. Norden A.P. On the presentation of the basic theorems of Lobachevsky geometry.- In: One Hundred and Twenty Five Years of Lobachevsky's Non-Euclidean Geometry. - M.-L.: Gostekhizdat. 1952. - S.117 - 128.
4. Norden A.P. An elementary introduction to Lobachevsky geometry.- M.: Gostekhizdat, 1953. - 248 p.
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11. Laptev B.L. N.I. Lobachevsky and his geometry.- M.: Enlightenment, 1976. - 112 p.
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13. Norden A.P. The great discovery of Lobachevsky."Quantum" 1976. N2.
14. Laptev B.L. What did Lobachevsky read?- Kazan. Publishing house Kazan. un-ta, 1979. - 126 p.
15. Shirokov P.A. A brief outline of the foundations of Lobachevsky's geometry.- 2nd ed. - M.: Science. Main edition of physical and mathematical literature, 1983. - 80 p.
16. Laptev B.L. Nikolai Ivanovich Lobachevsky.- In the book: Stories about Kazan scientists. - Kazan: Tatknigoizdat, 1983. - P.5 - 19.
17. N.I. Lobachevsky. To the 200th anniversary.(Authors: Vishnevsky V.V., Pisareva S.V.). - Kazan. Publishing house Kazan. un-ta, 1992.