Lobachevsky Nikolai Ivanovich: interesting data and facts. Lobachevsky Nikolay Ivanovich Nikolay Ivanovich Lobachevsky briefly

Nikolai Ivanovich Lobachevsky (1793-1856)

The great Russian geometer, creator of non-Euclidean geometry Nikolai Ivanovich Lobachevsky was born on November 2, 1793 in the Nizhny Novgorod province, into a poor family of a petty official. After a childhood filled with need and deprivation, after graduating from the gymnasium, which he managed to enter only thanks to the exceptional energy of his mother Praskovya Alexandrovna, we see him as a fourteen-year-old boy already a student at the newly opened Kazan University, within the walls of which all his further life and work take place. . N.I. Lobachevsky was lucky enough to study mathematics at the gymnasium with an extraordinary person and, apparently, a brilliant teacher - Grigory Ivanovich Kartashevsky. It was under his influence that the mathematical abilities of the future great geometer developed. As a student, he studied with the famous Bartels, a professor first at Kazan and then at Yuryev University, seriously mastering the mathematics of his time from primary sources, mainly from the works of Gauss and Laplace. However, despite the early manifested mathematical talents, N. I. Lobachevsky did not immediately decide to devote himself to mathematics; There is information that he initially prepared himself to practice medicine. In any case, by the age of 18 he had already chosen mathematics.

The student years of N. I. Lobachevsky were filled not only with an ardent passion for science and persistent scientific studies; they are full of youthful pranks and pranks, in which his cheerful character manifested itself very early. It is known that he was in a punishment cell for launching a rocket in Kazan at 11 pm, and that he was accused of many other mischiefs. But, besides this, more serious offenses are also noted: “free-thinking and dreamy self-conceit, perseverance” and even “outrageous actions..., which, to a large extent, showed signs of godlessness.”

For all this, N.I. Lobachevsky almost paid with expulsion from the university, and only the strong petitions of Kazan mathematics professors gave him the opportunity to graduate. His further career is developing rapidly: 21 years old N.I. Lobachevsky is an adjunct, and 23 years old he is an extraordinary professor; During these same years, in connection with the lectures on geometry that he gave in 1816-1817, he first approached the question, the solution of which was the glory of his life - the question of the axiom of parallels.

N.I. Lobachevsky’s youth was ending. The period of full disclosure of his rich and diverse personality began. Scientific creativity began, exceptional in its mathematical power. His amazingly multifaceted work, full of unyielding energy and passion, began and quickly developed as a professor, soon in all respects the first professor at Kazan University. His enthusiastic participation in all areas of activity, organization and construction of Kazan University began, which then turned into almost twenty years of complete and sole leadership of the entire university life. Just the enumeration of the various university positions he held successively, and often in parallel, gives an idea of the scope of his university work. At the end of 1819 he was elected dean; At the same time, he was given the responsibility of putting the university library in order, which was in an incredibly chaotic state. During these same years, his professorial activity received new content: after Professor Simonov left for a trip around the world, he had to read physics, meteorology and astronomy for two whole academic years. By the way, N.I. Lobachevsky never lost interest in physics and did not refuse not only from teaching it at the university, but also from giving popular lectures on physics, accompanied by carefully and interestingly prepared experiments. In 1822 N.I. Lobachevsky became an ordinary professor; at the same time, he becomes a member of the construction committee for the renovation of old and construction of new university buildings. In 1825 he was already the chairman of this committee. In fact, he is the main builder of the entire set of new buildings at Kazan University and, fascinated by these new responsibilities, carefully studies architecture from both the engineering, technical and artistic sides. Many of the most architecturally successful buildings of Kazan University are the implementation of the construction plans of N. I. Lobachevsky; These are: anatomical theatre, library, observatory.

Finally, in 1827 N.I. Lobachevsky became rector of the university and held this post for 19 years. He understands his responsibilities as a rector very broadly: from ideological leadership of teaching and the entire life of the university to personal involvement in all everyday university needs. Having become rector, he continued to carry out the duties of the university librarian for several years and laid them down only after he had raised the library to the proper height. As an example of the energy and activity shown by N. I. Lobachevsky for the benefit of the university, it should be said about his role during two tragic events that befell Kazan life during his rectorship. The first of these events was the cholera epidemic of 1830, which raged in the Volga region and claimed many thousands of lives. When cholera reached Kazan, N. I. Lobachevsky immediately took heroic measures against the university: the university was virtually isolated from the rest of the city and turned, as it were, into a fortress. Accommodation and meals for students were organized on the university territory itself - all this with the active participation of the rector. The success was brilliant - the epidemic passed by the university. The energetic, selfless work of N. I. Lobachevsky in the fight against cholera made such a great impression on the entire society of that time that even official authorities considered it necessary to note it; N. I. Lobachevsky was expressed the “highest favor” for his diligence in protecting the university and other educational institutions from cholera.

Another disaster that struck Kazan was a fire, terrible in its devastating consequences, in 1842. During this terrible fire, which destroyed a huge part of the city, N. I. Lobachevsky again showed miracles of energy and stewardship in saving university property from the fire. In particular, he managed to preserve the library and astronomical instruments.

However, the central point of application of the energy and talents of N. I. Lobachevsky as the rector of the university was his direct concern for the education of youth in the broadest sense of the word. All other aspects of his activity as rector constituted only a framework for the implementation of this main task. The problems of education attracted him in all their scope and, like everything that interested him, they interested him in the most ardent way. Since 1818, N.I. Lobachevsky was a member of the school committee in charge of secondary and lower educational institutions, and since then he did not lose sight of, along with the issues of university teaching, the demands of school life. Constantly supervising entrance exams to the university, N. I. Lobachevsky knew perfectly well what knowledge a schoolchild of that time came to a higher educational institution with. Interested in the entire line of human development - from childhood to late adolescence - he demanded a lot from education, and the ideal of the human personality that was pictured before him was very high. N. I. Lobachevsky’s speech “On the Most Important Subjects of Education” is a remarkable monument not only to pedagogical thought, but, if I may put it this way, to that “educational emotion”, that pedagogical pathos, without which pedagogical activity itself turns into a deadening craft. N.I. Lobachevsky himself fully possessed the diversity and breadth of life interests that were part of his ideal of a harmoniously developed human personality. Naturally, he demanded a lot from the young man who came to the university to study. He first of all demands from him that he be a citizen, “who with high knowledge constitutes the honor and glory of his fatherland,” that is, he sets before him a high and responsible patriotic ideal, based, in particular, on high qualifications within the chosen profession. But he further emphasizes that “mental education alone does not complete education,” and makes great demands on an intelligent person as a full-fledged representative of intellectual, ethical and aesthetic culture. N.I. Lobachevsky was not only an education theorist, but in fact an educator, a teacher of youth. He was not only a professor who delivered his lectures brilliantly and carefully, but also a man who knew the direct path to a youthful heart and knew how, in all cases when it was required, to find those very necessary words that could act on a student who had gone astray and return him to work, discipline him. The authority of N. I. Lobachevsky among students was extremely high. Students loved Nikolai Ivanovich, despite his severity as a professor and, in particular, as an examiner, despite his ardor and sometimes harshness.

N. I. Lobachevsky is probably the most important person to emerge from the almost two hundred years of glorious history of Russian universities. If he had not written a single line of independent scientific research, we would nevertheless have to remember him with gratitude as our most remarkable university figure, as a person who gave the high ranks of professor and rector of the university such completeness of content, which they were not conferred by any other person who held these titles before him, during his time, or after his death. But N.I. Lobachevsky, in addition, was also a brilliant scientist, and if he had not been such, if he had not, along with all his other gifts, also had a first-class creative gift and creative experience, he would have been both in the field of university teaching and university leadership, and his very educational activities could not have been who he really was.

The main scientific merit of N. I. Lobachevsky lies in the fact that he was the first to fully understand the logical unprovability of the Euclidean axiom of parallels and drew all the main mathematical conclusions from this unprovability. The axiom of parallels, as is known, states: in a given plane to a given line, through a given point that does not lie on this line, one can draw only one parallel line. Unlike the other axioms of elementary geometry, the axiom of parallels does not have the property of immediate obviousness, if only because it is a statement about the entire infinite straight line as a whole, whereas in our experience we are faced only with larger or smaller “pieces” (segments ) straight. Therefore, throughout the history of geometry - from antiquity to the first quarter of the last century - there were attempts to prove the axiom of parallels, that is, to derive it from the other axioms of geometry. N.I. Lobachevsky also began with such attempts, accepting the assumption opposite to this axiom that at least two parallel ones can be drawn to a given line through a given point. N.I. Lobachevsky sought to lead this assumption to a contradiction. However, as he developed an increasingly long chain of consequences from the assumption he made and the totality of the rest of Euclid’s axioms, it became increasingly clear to him that no contradiction not only did not result, but could not result. Instead of a contradiction, N.I. Lobachevsky received, although unique, a logically completely harmonious and impeccable system of propositions, a system possessing the same logical perfection as ordinary Euclidean geometry. This system of propositions constitutes the so-called non-Euclidean geometry or Lobachevsky geometry.

Having received the conviction of the consistency of the geometric system he had constructed, N.I. Lobachevsky did not give a strict proof of this consistency, and could not give it, since such a proof went beyond the methods of mathematics of the early 19th century. The proof of the consistency of Lobachevsky's geometry was given only at the end of the last century by Cayley, Poincaré and Klein.

Without giving a formal proof of the logical equality of his geometric system with the usual system of Euclid, N. I. Lobachevsky essentially fully understood the indubitability of the very fact of this equality, expressing with complete certainty that given the logical impeccability of both geometric systems, the question of which of them is realized in physical world, can only be resolved by experience. N.I. Lobachevsky was the first to look at mathematics as an experimental science, and not as an abstract logical scheme. He was the first to conduct experiments to measure the sum of the angles of a triangle; the first who managed to abandon the thousand-year-old prejudice of the apriority of geometric truths. It is known that he liked to often repeat the words: “Stop working in vain, trying to extract all the wisdom from one mind, ask nature, it keeps all the secrets and will certainly answer your questions satisfactorily.” Modern science makes only one amendment to the point of view of N.I. Lobachevsky. The question of what geometry is realized in the physical world does not have the immediate naive meaning that was given to it in the time of Lobachevsky. After all, the most basic concepts of geometry - the concepts of a point and a line, having been born, like all our knowledge, from experience, are, nevertheless, not directly given to us in experience, but arose only through abstraction from experience, as our idealizations of experimental data, idealization, which alone makes it possible to apply the mathematical method to the study of reality. To explain this, we only point out that the geometric straight line, by virtue of its infinity alone, is not - in the form in which it is studied in geometry - the subject of our experience, but only an idealization of very long and thin rods or light rays that we directly perceive . Therefore, a final experimental verification of the parallel axiom of Euclid or Lobachevsky is impossible, just as an absolutely accurate determination of the sum of the angles of a triangle is impossible: all measurements of any physical angles given to us are always only approximate. We can only assert that Euclid’s geometry is an idealization of actual spatial relationships, which completely satisfies us as long as we are dealing with “pieces of space that are not very large and not very small,” that is, as long as we do not end up in either one or the other side too far beyond the limits of our usual, practical scale, while we, on the one hand, say, remain within the solar system, and on the other, do not plunge too deeply into the depths of the atomic nucleus.

The situation changes when we move to cosmic scales. The modern general theory of relativity considers the geometric structure of space as something dependent on the masses acting in this space and comes to the need to involve geometric systems that are “non-Euclidean” in a much more complex sense of the word than the one associated with Lobachevsky’s geometry.

The significance of the very fact of the creation of non-Euclidean geometry for all modern mathematics and natural science is colossal, and the English mathematician Clifford, who called N. I. Lobachevsky the “Copernicus of geometry,” did not fall into exaggeration. N.I. Lobachevsky destroyed the dogma of the “fixed, only true Euclidean geometry” in the same way as Copernicus destroyed the dogma of the stationary, constituting the unshakable center of the Universe - the Earth. N.I. Lobachevsky convincingly showed that our geometry is one of several logically equal geometries, equally impeccable, equally valuable logically, equally true as mathematical theories. The question of which of these theories is true in the physical sense of the word, that is, most adapted to the study of this or that range of physical phenomena, is precisely a question of physics, not mathematics, and, moreover, a question whose solution is not given once and for all by Euclidean theory. geometry, but depends on the range of physical phenomena we have chosen. The only, albeit significant, privilege of Euclidean geometry remains that it continues to be a mathematical idealization of our everyday spatial experience and therefore, of course, retains its basic position both in a significant part of mechanics and physics, and, moreover, in all technology. But this circumstance, of course, cannot diminish the philosophical and mathematical significance of N. I. Lobachevsky’s discovery.

These are, in brief, the main lines of the versatile cultural activities of Nikolai Ivanovich Lobachevsky. It remains to say a few more words about the last years of his life. If the 20s and 30s of the XIX century. were the period of the highest flowering of both the creative and scientific-pedagogical and organizational activities of N. I. Lobachevsky, then from the mid-forties and, moreover, quite suddenly for N. I. Lobachevsky, a period of inaction and senile burnout began. The main event that brought with it this tragic turning point in the life of N.I. Lobachevsky was his dismissal on August 14, 1846 from the post of rector. This dismissal occurred without the desire of N.I. Lobachevsky and contrary to the petition of the university council. Almost simultaneously, his dismissal from the post of professor of mathematics occurred, so that from the spring of 1847 N. I. Lobachevsky found himself removed from virtually all his duties at the university. This suspension had all the features of a gross official disqualification, bordering on direct insult.

It is quite understandable that N.I. Lobachevsky, for whom his work at the university was a large and irreplaceable part of his life, perceived his resignation as a heavy, irreparable blow. This blow was especially severe, of course, because it broke out at that time in the life of N.I. Lobachevsky, when his creative scientific work was basically completed and, therefore, university activities became the main content of his life. If we add to this the exceptionally active character of N. I. Lobachevsky and his habit, created over decades, of being a leader in organizational affairs, and not an ordinary participant, a habit to which he truly had the right, then the extent of the catastrophe that befell him will become quite clear. Personal sorrows filled the cup: the beloved son of N.I. Lobachevsky, an adult young man, died, according to contemporaries, very similar to his father in both appearance and character. N.I. Lobachevsky was never able to cope with this blow. Old age began - premature, but all the more depressing, with increasing signs of paradoxically early decrepitness. His health was rapidly declining. He began to lose his sight and by the end of his life he was completely blind. The last work, “Pangeometry,” was already dictated by him. Broken by life, a sick, blind old man, he died on February 24, 1856.

As a scientist, N.I. Lobachevsky is, in the full sense of the word, a revolutionary in science. Having for the first time broken through the idea of Euclidean geometry as the only conceivable system of geometric knowledge, the only conceivable set of proposals about spatial forms, N. I. Lobachevsky did not find not only recognition, but even a simple understanding of his ideas. It took half a century for these ideas to enter mathematical science, become its integral part and become the turning point that largely determined the entire style of mathematical thinking of the subsequent era and from which, in fact, Russian mathematics began. Therefore, during his lifetime, N.I. Lobachevsky found himself in the difficult position of an “unrecognized scientist.” But this lack of recognition did not break his spirit. He found a way out in the varied, vigorous activity that is briefly outlined above. The strength of Lobachevsky’s personality triumphed not only over all the difficulties of the dark time in which he lived, it also triumphed over what may be the most difficult thing for a scientist to survive: over ideological isolation, over a complete misunderstanding of what was dearest and most necessary to him - his scientific discoveries and ideas. However, one should not blame his contemporaries, among whom were prominent scientists, for not understanding Lobachevsky. His ideas were far ahead of his time. Of the foreign mathematicians, only the famous Gauss understood these ideas. But while Gauss owned them, he never had the courage to publicly declare it. However, he understood and appreciated Lobachevsky. He took the initiative in the only scientific honor that fell to Lobachevsky: at the suggestion of Gauss, Lobachevsky was elected in 1842 as a corresponding member of the Gottingen Royal Society of Sciences.

If N. I. Lobachevsky undoubtedly won the right to immortality in the history of science with his geometric works, then we should not forget that in other areas of mathematics he published a number of brilliant works on mathematical analysis, algebra and probability theory, as well as on mechanics, physics and astronomy.

The name of N. I. Lobachevsky entered the treasury of world science. But the brilliant scientist always felt like a fighter for Russian national culture, an everyday builder of it, living by its interests, caring for its needs.

The main works of N. I. Lobachevsky: Complete works on geometry, Kazan, 1833, vol. I (contains: On the principles of geometry, 1829; Imaginary geometry, 1835; Application of imaginary geometry to certain integrals, 1836; New principles of geometry with the complete theory of parallels, 1835-1838); 1886, vol. II (contains works in foreign languages, including: Geometrische Untersuchungen zur Theorie der Parallellinien, 1840, in which N. I. Lobachevsky outlined his ideas about non-Euclidean geometry); Geometric research on the theory of parallel lines (Russian translation by A. V. Letnikov of the famous memoir of N. I. Lobachevsky Geometrische Untersuchungen...), "Mathematical collection", M., 1868, III; Pangeometry, "Scientific Notes of Kazan University", 1855; Complete works, M. - L., Gostekhizdat, 1946.

About N. I. Lobachevsky:Yanishevsky E., Historical note about the life and work of N. I. Lobachevsky, Kazan, 1868; Vasiliev A.V., Nikolai Ivanovich Lobachevsky, St. Petersburg, 1914; Sintsov D. M., Nikolai Ivanovich Lobachevsky, Kharkov, 1941; Nikolai Ivanovich Lobachevsky (to the 150th anniversary of his birth; articles by P. S. Aleksandrov and A. N. Kolmogorov), M. - L., 1943; Nikolai Ivanovich Lobachevsky (articles by B. L. Laptev, P. A. Shirokov, N. G. Chebotarev), ed. Academy of Sciences of the USSR, M. - L., 1943; Kagan V.F., The great scientist N.I. Lobachevsky and his place in world science, M. - L., 1943; by him, N.I. Lobachevsky, ed. Academy of Sciences of the USSR, M. -L., 1944.

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

Risky step

Who else but a modest Russian mathematician could take on a task that was beyond the capabilities of bright European minds: to overcome the theory of parallel lines. In Europe, this work was considered a disastrous job that could deprive a person of sleep, personal time and other delights of life.

Russian bastard

Of course, such a painstaking task could have been undertaken by such a botanist - an armchair scientist who did not communicate with anyone, an intellectual who kept to himself. Such a person, according to European luminaries, should not be adapted to life and was certainly presented as a weakling.

But such a template did not at all fit the description of such a person as Nikolai Lobachevsky. At the time of his unique discovery, the Russian scientist was already the rector of Kazan University. Lobachevsky was repeatedly noticed in his youth in all sorts of incidents: as a student, he rode a cow in the city garden, was the leader 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 about his actions. .

Nikolai Lobachevsky was not liked at the gymnasium where he studied.
From his school days, Lobachevsky was distinguished by freethinking and perseverance. That did not stop him from studying excellently.
Bad behavior once almost radically changed the life of a young mathematician; they wanted to expel him from the educational institution and send him to military service. The imperial government issued a decree according to which all students with bad behavior were to be sent to the army.
Lobachevsky was a talented student; he could 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 the age of 22, and at 24 he already became a professor.
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 he would not receive fruit from them during his lifetime. And so it happened: the cones were removed from the cedar a few months after the death of the talented mathematician.
Lobachevsky was interested not only in the exact sciences, he was also interested in agriculture, for which he was repeatedly awarded various awards and certificates.
Lobachevsky's talent is still not subject to the slightest doubt, and his works have not been forgotten. However, during his lifetime, the genius believed that his discoveries would be forgotten by his descendants: this was his main phobia. His anguish and fears were fueled by the intense criticism directed at him.
Great Russian mathematician had the gift of persuasion. Already at the post of rector, he repeatedly instructed his students on the right path. Lobachevsky never raised his voice when speaking, preferring a calm conversation to shouting. Students remembered him as a wonderful person.
Lobachevsky gave all of himself to his students, but at the same time he did not allow familiarity.
The European king of mathematicians, Carl Gauss, having heard about Lobachevsky’s scientific works, began to diligently study the Russian language in order to read the works of the genius from the Russian Empire in the original.
Nikolai Lobachevsky achieved enormous success in the field of exact sciences, and he especially succeeded, of course, in geometry, creating the so-called “non-Euclidean geometry.”
The Russian mathematician is the author of a new method for solving equations, having created a number of theorems on trigonometric series and studied continuous functions.
Lobachevsky is the author of a number of works on algebra and mathematical analysis, geometry, probability theory, astronomy and physics.
The great mathematician married quite late, at 44 years old. His chosen one was the Orenburg-Kazan landowner Varvara Moiseeva.

Unrecognized genius

During his lifetime, Nikolai Ivanovich had a very hard time with criticism addressed to him. In the Russian Empire, scientists did not have much success, since military operations came first in the 19th century. Europe was led by its own 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 posterity as the greatest genius in the field of mathematical research. Unfortunately, the great mathematician did not live to see his victorious triumph; 12 years after Lobachevsky’s death, 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 assigned the role of the greatest robber for all his mischievous deeds. One day he dared to nail the behavior log to the 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 established 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 outstanding Russian mathematician, creator of non-Euclidean geometry Nikolai Ivanovich Lobachevsky was born on December 1 (November 20, old style) 1792 in Nizhny Novgorod.

His father, a minor official Ivan Maksimovich Lobachevsky, died when the boy was 7 years old, after which his mother and her three sons were forced to move to Kazan. Here Lobachevsky attended the gymnasium as a volunteer. After graduating from high school, in 1807 he entered Kazan University.

In 1811, having completed his studies, Lobachevsky received a master's degree in physics and mathematics with honors and was retained at the educational institution. At the end of 1811, Lobachevsky presented his argument “Theory of elliptical motion of celestial bodies.” On March 26, 1814, Lobachevsky, at the request of Bronner and Bartels, was appointed adjunct of pure mathematics.

On July 7, 1816, Lobachevsky was confirmed as an extraordinary professor. Lobachevsky's teaching activity until 1819 was devoted exclusively to mathematics. He taught courses in arithmetic, algebra and trigonometry, plane and spherical geometry, and in 1818 began a course in differential and integral calculus according to Monge and Lagrange.

In 1846, after 30 years of service, the ministry, according to the charter, had to make a decision on leaving Lobachevsky as a professor or electing new teachers. Despite the opinion of the university council, according to which there was no reason to remove Lobachevsky from teaching, the ministry, on the instructions of the Governing Senate, removed Lobachevsky not only from the professorial chair, but also from the post of rector. He was appointed assistant trustee of the Kazan educational district with a significant reduction in salary.

Soon Lobachevsky went bankrupt, his 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 health was undermined, his eyesight was weakening. The last work of the almost blind scientist, Pangeometry, was dictated by his faithful students in 1855. Lobachevsky died on February 24, 1856, the same day on which thirty years earlier he first published his version of non-Euclidean geometry.

Lobachevsky's geometry received full recognition and widespread use 12 years after his death. In 1868, the Italian mathematician Beltrami in his work “An Experience in the Interpretation of Non-Euclidean Geometry” showed that in Euclidean space on pseudospherical surfaces there is the geometry of a piece of the Lobachevsky plane if geodesic lines are taken as straight lines. The interpretation of Lobachevsky's geometry on the surfaces of Euclidean space decisively contributed to the general acceptance of Lobachevsky's ideas.

Lobachevsky obtained a number of valuable results in other branches of mathematics: for example, in algebra he developed, independently of Germinal Dendelen, a method for approximate solution of equations, in mathematical analysis he obtained a number of subtle theorems on trigonometric series, and clarified the concept of a continuous function.

Wide recognition of Lobachevsky's geometry came to his 100th anniversary - in 1895, the International Lobachevsky Prize was established - an award awarded by the Russian Academy of Sciences for outstanding work in the field of geometry; in 1896, a monument to the outstanding mathematician was erected in Kazan.

After the Second World War, by a resolution of the Council of Ministers of the USSR dated January 29, 1947, “On prizes named after the great Russian scientist N. I. Lobachevsky,” it was decided to establish two prizes, an international one and an incentive one for Soviet scientists. On June 8, 1993, the Presidium of the Russian Academy of Sciences approved the Regulations on gold medals and prizes named after outstanding scientists awarded by the Russian Academy of Sciences. In accordance with it, the Lobachevsky Prize was awarded once every three years “For outstanding results in the field of geometry.”

On June 10, 2004, the opening of the Lobachevsky House Museum took place in the city of Kozlovka (Chuvashia).

The material was prepared based on information from open sources

Lobachevsky's enduring glory is that he solved a problem for us that had remained unsolved for two thousand years.

Marius Sophus Lee

To live means to feel, to enjoy life, to certainly feel something new that would remind us that we are living... 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, give in advance... a noble direction to passions.

N.I. Lobachevsky

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

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

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 were scientists invited from different European countries. Lectures on astronomy were given by Professor Litroff. Nikolai listened to lectures on mathematics from Professor Bartels, a student 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 his “dreamy self-conceit, excessive persistence, 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 freethinking and numerous pranks he often caused the displeasure of the university authorities. Bartels's 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 future scientist from being expelled 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 the title of professor.

At this time, Nikolai 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, which were then subordinate not directly to the trustee, but to the university. Since 1819, Lobachevsky taught astronomy, replacing the teacher who went around the world. Lobachevsky's administrative activities began in 1820, when he was elected dean.

In 1819, an auditor, Mikhail Magnitsky, came to 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 “the single basis of public education.” Only the Faculty of Physics and Mathematics received Magnitsky’s praise. In his report, he proposed closing the university altogether, but Emperor Alexander I imposed a resolution: “Why destroy, it’s better to fix it.” As a result, Magnitsky was appointed trustee of the school district and tasked with making 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 28-year-old Lobachevsky, who had already demonstrated extraordinary organizational skills, was appointed dean of the Faculty of Physics and Mathematics instead of Bartels.

The range of his responsibilities was extensive - lecturing on mathematics, astronomy and physics, equipping 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 good at first. In 1821, the trustee nominated Lobachevsky to be awarded the Order of St. Vladimir IV degree, which was approved and awarded in 1824. However, gradually their relationship becomes strained - the trustee receives many denunciations, where Lobachevsky is again accused of arrogance and lack of proper piety, and Lobachevsky himself in a number of cases showed disobedience, speaking out against Magnitsky’s administrative arbitrariness. During these years, Lobachevsky prepared a textbook on geometry, which was condemned by the 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 he wrote, on algebra, was published only 10 years later (1834). One of Lobachevsky’s contemporaries says about this period:

Lobachevsky’s duty as a member of the council was especially difficult morally. Lobachevsky himself never curried favor with his superiors, did not try to show off, and did not like this in others either. At a time when the majority of the council members were ready to do anything to please the trustee, Lobachevsky was silently present at the meetings, silently signing 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. 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 toughness, but at the same time by strict justice and honesty, and was far from immoderate religiosity.

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

The new rector, with his characteristic energy, immediately plunged into economic affairs - reorganizing the staff, building educational buildings, mechanical workshops, laboratories and observatories, maintaining a library and mineralogical collection, etc. I did a lot of things with my 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 grueling practical activity, which did not leave a moment 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, back in his student years, Professor Bartels told his gifted student Lobachevsky, with whom he maintained an active personal relationship until his departure, the idea of his friend Gauss about the possibility of a geometry where Euclid’s postulate does not apply.

Reflecting on the postulates of Euclidean geometry, Lobachevsky came to the conclusion that at least one of them could be revised. It is obvious that the cornerstone of Lobachevsky's geometry is the negation of Euclid's postulate, without which geometry for about two thousand years seemed unable to live. Lobachevsky came to the conclusion that it was possible to create 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 Exposition of the Principles of Geometry with a Rigorous Proof of the Parallel Theorem” (in French).

On February 11, 1826, an event of the greatest importance occurred at Kazan University, which gives reason to consider this date as the birthday of non-Euclidean geometry. On this day, at a meeting of the Department of Physical and Mathematical Sciences, Lobachevsky presented this essay. Information about this was preserved in the minutes of the meeting. But the publication did not materialize. The manuscript and reviews have not survived, but the essay itself was included by Lobachevsky in his work “On the Principles of Geometry” (1829-1830), published in the magazine “Kazansky Vestnik”. This work became the first serious publication in world literature on non-Euclidean geometry, or Lobachevsky geometry.

Lobachevsky considers Euclid's parallelism axiom to be an arbitrary restriction. 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: on a plane, through a point not lying 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 Euclidean geometry, however, Euclidean geometry can be obtained from it by passing to the limit (as the curvature of space tends to zero). In Lobachevsky geometry itself, the curvature is negative. Already in his 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 was quite consistent with his general mood and his activities. Searching for truth in science, he put 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 their word of honor to be sincere and kept it. In character, Lobachevsky's wife was a sharp contrast to her husband: Varvara Alekseevna was unusually lively and hot-tempered.

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

Not finding understanding in his homeland, Lobachevsky tried to find like-minded people abroad. In 1837, Lobachevsky's article “Imaginary Geometry” in French appeared in the authoritative Berlin journal Krelle, and in 1840 Lobachevsky published in German a small book “Geometric Studies on the Theory of Parallel”, which contains a clear and systematic presentation of his main ideas. Carl Friedrich Gauss, the “king of mathematicians” of that time, received two copies. As it turned out much later, Gauss himself secretly developed non-Euclidean geometry, but never decided to publish anything on this topic. Having familiarized himself with Lobachevsky's results, he spoke enthusiastically 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, 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 was made masterfully by Lobachevsky, in a true geometric spirit. I consider myself obliged to draw your attention to this work, which will probably give you absolutely exceptional pleasure.

Gauss expressed his sympathy for the ideas of the Russian scientist indirectly: he recommended electing Lobachevsky as 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 become familiar with the details of the discoveries of the Kazan geometer. Lobachevsky's election 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 works with rude ridicule and even abuse. 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 have found out, the Hungarian mathematician Janos Bolyai, independently of Lobachevsky and a little later (1832), published his version of non-Euclidean geometry. But his works did not attract the attention of his contemporaries, and the fate of Janos 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 position 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 sixth time for a new four-year term, and unanimously.

The next year, 1846, was difficult for Lobachevsky.

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

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

Soon Lobachevsky 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 tries to participate in the life of the university to the best of his ability. He chairs the commission for celebrating the 50th anniversary of the university. However, the commission did not work for long and ceased to exist, since the emperor considered that celebrating the anniversary was unnecessary.

Lobachevsky's activities in the last decade of his life were only a shadow of the past in their intensity. Deprived of his chair, Lobachevsky gave lectures on his geometry to a select scientific public, and those who heard them remember how thoughtfully he developed his principles.

After these fatal years came years of decline for Lobachevsky; he is rapidly going blind. Of course, nothing can give happiness during the years of destruction of strength, but better conditions can soften this period of life. Not seeing people around him imbued with his ideas, Lobachevsky thought that these ideas would die with him.

The scientist's last work, Pangeometry, was taken from dictation by the students of a blind scientist in 1855.

Nikolai Ivanovich Lobachevsky died on February 12, 1856, the same day on which 30 years earlier he first published his version of non-Euclidean geometry. He was buried at the Arskoe 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 a major role in the recognition of Lobachevsky’s works. The appearance of Klein’s model proved that Lobachevsky’s geometry is as consistent as Euclidean. The realization that Euclidean geometry had a viable alternative 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. It also turned out that the relationship between space and time, discovered by Lorentz, Poincaré, Einstein and Minkowski and described within the framework of the special theory of relativity, is directly related to Lobachevsky’s geometry. For example, in the calculations of modern synchrophasotrons, Lobachevsky geometry formulas are used.

When, in the second half of the 1860s, Lobachevsky’s works were already widely appreciated and translated into all major European languages, Kazan University asked for 600 rubles. for the publication of Lobachevsky’s “Complete Works on Geometry”. This project was completed 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 yet been found.

Nikolai Ivanovich Lobachevsky obtained a number of valuable results in other areas of mathematics. Thus, in algebra, he developed, independently of Dendelen, a method for approximate solution of equations, in mathematical analysis he obtained a number of subtle theorems about trigonometric series, clarified the concept of a continuous function, gave a test for the convergence of series, etc. Over the years, he published several informative articles on algebra, probability theory, mechanics, physics, astronomy and educational problems.

In 1892, Lobachevsky’s 100th anniversary was widely celebrated in Russia and other countries. An international prize named after N.I. was established. Lobachevsky (1895), awarded by the Russian Academy of Sciences for outstanding work in the field of geometry. Over the years, it was awarded to Marius Sophus Lie, David Gilbert, Hermann Weil, Elie Cartan, Alexey Vasilyevich Pogorelov, Lev Semenovich 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 Russian sculptor Maria Dillon, was erected in front of the building of Kazan University.

The following were named in honor of Lobachevsky:

Prize named after N.I. Lobachevsky Russian Academy of Sciences, then the USSR Academy of Sciences and again the Russian Academy of Sciences (awarded since 1897, usually 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 the far side of the Moon
Scientific library of Kazan University
streets in Moscow, Kyiv, Kazan, Lipetsk and other cities
school No. 52 in Lviv, Ukraine
Lyceum at Kazan State University
Nizhny Novgorod State University.

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

The following mathematical objects are named after Lobachevsky:

Lobachevsky geometry
Lobachevsky method
Lobachevsky's sign.

Based on materials from the books by D. Samin “100 Great Scientists” (M.: Veche, 2000), “Rank of Great Mathematicians” (Warsaw, published by Nasha Ksengarnya, 1970), B.A. Kordemsky “Great Lives in Mathematics” (Moscow, “Prorsveshchenie”, 1995) and Wikipedia.

Lobachevsky Nikolai Ivanovich

L Obachevsky, Nikolai Ivanovich - a great mathematician, one of the creators of non-Euclidean geometry. Born on October 22, 1793 in the Nizhny Novgorod province. Studied at Kazan University; He attracted attention early with his success in mathematics, but was certified by the inspectorate as “a stubborn, unrepentant young man, who dreamed a lot about himself,” even showing “signs of godlessness.” Only the intercession of the professors prevented Lobachevsky from being expelled from the university and delivered it to him in 1811; after his promise to improve, a master's degree. The first (unpublished) works of Lobachevsky date back to the same year: a commentary on one of the questions of Laplace’s “Celestial Mechanics” and a memoir written under the influence of the study of Gauss’s “Disquisitiones Arithmeticae” and his observations of a large comet. In 1814, Lobachevsky received the title of adjunct and began lecturing on number theory. In subsequent years, Lobachevsky lectured on a wide variety of branches of mathematics, as well as physics and astronomy; At the same time, he put the university library in order, streamlined its publishing activities, and took care of the construction of a number of buildings for the university. After leaving, Lobachevsky, at that time an ordinary professor, was elected rector (1827) and held this position for 19 years. In 1828, he delivered a remarkable speech “On the Most Important Subjects of Education,” which reflected his passion for the educational ideas of the 18th century. In 1846 - 1855, Lobachevsky held the position of assistant trustee of the Kazan educational district. He died on February 12, 1856. Lobachevsky's great fame is based on his geometric research, which began in 1814 - 1817. The surviving record of Lobachevsky's lectures given during these years shows that initially Lobachevsky stood on the traditional point of view, offering various proofs of the parallel lines axiom; but already in 1823, in the geometry textbook he compiled (published in 1910 by the Kazan Physics and Mathematics Society), he spoke in the sense that “a rigorous proof of this truth still could not be found; what were given... do not deserve to be honored in the full sense of mathematical proofs." By 1826, he came to a definite formulation of his new geometric system, which he called “imaginary geometry” in contrast to the “usual” Euclidean one. On the essence of Lobachevsky's geometry, see Geometry (Brockhaus-Efron, XIII, 97 et seq.). Lobachevsky's brilliant discovery, made independently of the simultaneous work of other geometers, was first briefly presented by him in February 1826. at a meeting of the department of physical and mathematical sciences (see "On the principles of geometry", "Kazan Bulletin", 1829 - 1830) and then most fully developed in "New principles of geometry with a complete theory of parallels" ("Scientific Notes of Kazan University", 1835 - 1838). Completely misunderstood by his compatriots, Lobachevsky tried to acquaint Western European scientists with his system and published “Geometrie imaginaire” (“Journal Crelle”) in 1837, “Geometrische Untersuchungen zur Theorie der Parallellinien” (Bern) in 1840, and in 1855 ., with the exertion of his last strength, almost already blind - “Pangeometrie ou precis de geometrie, fondee sur une theorie generale et rigoureuse des paralleles” (in the anniversary collection of Kazan University, Kazan, 1856). However, even abroad, Lobachevsky’s ideas remained incomprehensible: the only person who appreciated them, Gauss, during his lifetime refrained from openly recognizing non-Euclidean geometry. In the 1860s, Gauss's correspondence was published, where he testifies that the development of non-Euclidean geometry was done by Lobachevsky "masterfully in a truly geometric spirit." Since then, Lobachevsky's merits have gradually gained general recognition. Lobachevsky's works are translated into foreign languages; Kazan University, at the initiative of the Frenchman Guell, is undertaking the publication of the “Complete Works on Lobachevsky’s Geometry” (Kazan, 1883 - 1886); in 1893, on the centenary of Lobachevsky’s birth, a monument to him was erected in Kazan using funds raised by international subscription, and a prize was established in his name for works on non-Euclidean geometry. During Lobachevsky's lifetime, his works on other questions of mathematics brought him fame, and here in some respects he anticipated the later development of science (the distinction between continuity and differentiability, the combined presentation of planimetry and stereometry). Vasiliev has a complete list of Lobachevsky's works ("Russian Biographical Dictionary", St. Petersburg, 1914 and separately, ib.). - See Yanishevsky “Historical note on the life and work of Lobachevsky” (ib., 1868); Litvinov "Lobachevsky" (1894, biographical sketch in the new edition of "New Principles" (detailed bibliography). Compare literature in article Geometry (XIII, 100).

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