Scientist Lobachevsky. Nikolai Ivanovich Lobachevsky: brief biography, achievements, discoveries

Nikolai Ivanovich Lobachevsky is a famous Russian scientist and mathematician. Born in November 20 (December 1), 1792.

His father, Ivan Lobachevsky, was a minor official. Mother - Praskovya Alexandrovna. Nikolai's father died early and, at the age of nine, he, along with his mother and brothers, moved to.

In a new city, he and his two brothers go to study at the local gymnasium. At the Kazan gymnasium, he shows great interest in mathematics. His teacher was Kartashevsky, wonderful teacher, graduate of Moscow State University.

In 1807 Nikolai Lobachevsky became a student. At a higher educational institution, teachers discovered his remarkable ability to study physical and mathematical sciences.

In 1811 he graduated from the university and received a master's degree. His scientific activity did not end there; the University hired the talented graduate.

Lobachevsky was an ideological man and approached his work with great enthusiasm. At his Kazan University, he taught several sciences: physics, mathematics and astronomy.

For more fruitful activities and development of the University, Lobachevsky purchased special equipment for physical experiments.

Through his efforts, books were purchased to update the University Library. Later, Nikolai Ivanovich was elected several times as dean of the Faculty of Physics and Mathematics. The scientist also headed the observatory and library.

In 1827, Lobachevsky was elected rector. With his characteristic enthusiasm, he accepted the appointment. Between 1832 and 1840, it was built a large number of various buildings intended for scientific activities.

New library, astronomical observatory, chemistry room, laboratories. The university was developing. The level of knowledge of students has grown significantly, updated in better side Teaching Staff. The position of rector did not separate Lobachevsky from his scientific activities. Nikolai Ivanovich continued to lecture at the University. The students highly valued their teacher.

Over the years of his scientific activity, Nikolai Lobachevsky made a number of interesting discoveries in the field of mathematics. He developed a method for approximate solution of equations and derived a number of theorems about trigonometric series, he also gave the most complete concept continuous function, made a huge contribution to the development of non-Euclidean geometry.

Unfortunately, Nikolai Lobachevsky belonged to that number of geniuses who were not recognized in life. His discoveries were treated with great skepticism. However, over time, the works of the Russian scientist were recognized by the domestic and world scientific community.

His works were recognized thanks to the research of such foreign scientists as Beltrami, Klein, Poincaré. For the centenary of the Great, a monument to Lobachevsky was erected in Kazan.

Nikolai Ivanovich died on February 12 (02/24), 1856.

Nikolai Ivanovich Lobachevsky(November 20 (December 1) 1792, Nizhny Novgorod - February 12 (24), 1856, Kazan) - Russian mathematician, one of the creators 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 rector; his activity and skillful leadership brought the university to the forefront of 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 matter, in which he indicated that the exact date of birth of the mathematician should be considered November 20, 1792 (old style), and the place - the city of Nizhny Novgorod (in 1948 - Gorky ). Later, N.I. Privalova established the location of P.A. Lobachevskaya’s house. The research of A. A. Andronov and N. I. Privalova became generally 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 Lobachevskaya (?-1847), whose husband was an official in the geodetic department Ivan Maksimovich Lobachevsky (1760-1800). There is a version of the origin of N. I. Lobachevsky, expressed by Dmitry Andreevich Gudkov (1918-1992), a professor of mathematics at Nizhny Novgorod University, based on archives and literary sources; according to it, Nikolai Ivanovich Lobachevsky and his two brothers - Alexander and Alexey - were illegitimate sons Praskovya Aleksandrovna Lobachevskaya 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), for whom M.V. Lobachevsky was in the service, allowed him to marry his serf Agrafena, and in 1775 the prince gave Agrafena his 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 Russian Empire, for “state-owned raznochinsky content.” Nikolai Lobachevsky graduated from the gymnasium at the end of 1806, showing good knowledge, especially in mathematics and languages ​​- Latin, German, French. In his interest in mathematics, which had already manifested itself then, great credit gymnasium teacher G.I. Kartashevsky.

Soon after Nikolai entered the gymnasium, opportunities for further education expanded. On November 5, 1804, Emperor Alexander I signed the “Affirmative Letter” and the “Charter of the Imperial Kazan University”. On February 14, 1805, the university was opened. A number of gymnasium teachers, in parallel with fulfilling their previous duties, move to teach at the university. I. F. Yakovkin becomes professor of history, geography and statistics of the Russian Empire and director of the university, G. I. Kartashevsky - adjunct higher mathematics, I. I. Erich - adjunct of antiquities, Latin and Greek languages, L. S. Levitsky - adjunct of speculative and practical philosophy, I. I. Zapolsky - adjunct of applied mathematics and experimental physics. The University Council appealed to the parents of children raised in the Kazan gymnasium with a proposal to send them after completing the gymnasium course to continue their studies at the university. P. A. Lobachevskaya agreed. Nicholas's elder brother, Alexander, was enrolled in the university immediately, on February 18, 1805. Nicholas was tested in July 1806, but unsuccessfully, but on December 22 of the same year he passed retest and on February 14, 1807, was enrolled in the university. In the same 1807, Nikolai’s younger brother, Alexey, also became a student at Kazan University.

Early life (1807-1814)

In the first years, only two courses per year were related to physical and mathematical sciences. In two semesters, adjunct I.I. Zapolsky taught a course in physics. In the first half of the year, adjunct G.I. Kartashevsky repeated general arithmetic with students, read an algebra course and moved on to exposition 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 assigned to teach mathematics. Students taught classes in other disciplines as well.

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, professor of pure mathematics Martin Bartels, friend and teacher of the great German mathematician Carl Friedrich Gauss, an excellent teacher, arrived. On March 2, he opened a course of lectures on pure mathematics. In September of the same year, mathematician Caspar Renner came to Kazan, and in 1810, professor of theoretical and experimental physics Bronner and professor of astronomy Litrov.

The influence of new talented teachers affected Nikolai's interests. If in 1808 he paid most attention to chemistry and pharmacology (which at that time was called medical science), then under the influence of Bartels he became interested in physical and mathematical sciences. However, there was still room 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 launched a rocket with his comrades) he was punished in a punishment cell. Pranks, however, did not prevent Nikolai from becoming a chamber student on May 31, 1809, having received a positive certification from Yakovkin, which noted not only good behavior, but also success in science. Indeed, Lobachevsky enjoyed trust at the university - it was Nikolai who, in the fall of 1809, was tasked with checking the inventory of the chemistry room left after the death of adjunct Everst. However, trouble soon began. In January 1810, despite the prohibitions, he went to new year holidays to visit and participate in a masquerade. For this he was deprived of rank ruling position of chamber student and payments for books and teaching aids. In the last year of his studies (1811), a report on Lobachevsky’s behavior noted: stubbornness, “dreamy self-conceit, perseverance, disobedience,” as well as “outrageous actions” and even “signs of godlessness.” The threat of expulsion and conscription loomed over him, but the intercession of Bartels and Bronner helped avert the danger.

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

Beginning of teaching activity (1814-1820)

Start teaching activities Lobachevsky coincided with radical changes in university life. The organization of the university, through the efforts of trustee M. A. Saltykov, was finally brought into compliance with the charter of 1804. On February 24, 1814, I. O. Brown was confirmed as rector, four departments were established at the university (the moral and political department, the department of physical and mathematical sciences, the verbal department, and the medical department), and the deans of the 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 a course in number theory on Gauss and Legendre. He will continue to teach the same course in the next 1815/1816 academic year.

On July 7, 1816, Lobachevsky, on the initiative of Saltykov, was approved extra full professor. This election was not smooth sailing. In the university council, to which Saltykov submitted a proposal to Lobachevsky, disagreements arose over the compliance of such an election with the university charter. The offended Saltykov works directly with the minister and achieves the desired result. After being elected as an extraordinary professor, Lobachevsky is entrusted with teaching more responsible courses. In the 1816/1817 academic year he taught a course in arithmetic, algebra and trigonometry from his notebook, in 1817/1818 - a course in plane and spherical geometry from 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 was included in a special committee elected on October 13, 1816 in the case of “disobedience of students against the authorities and rudeness committed,” and on May 23, 1818 he was confirmed as a member of the School Committee, in charge of schools throughout the educational district.

However, changes are coming both in the sphere of education in Russia and in the life of a provincial university. In 1816, the post of Minister of Public Education was occupied by Prince A.N. Golitsyn, 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 issue of closing Kharkov and Kazan universities is already on the agenda. Klinger, not wanting to attend his university's funeral, resigns. I propose to do the same...” In 1817, matters of public education were combined with matters of religion - the Ministry of Spiritual Affairs and Public Education was formed.

Dean (1820-1827)

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, expelled Yakovkin in disgrace and without a pension as someone who had 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 28-year-old Lobachevsky, who had already managed to show 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 students in Kazan. Relations with Magnitsky were initially good; in 1821, the trustee nominated Lobachevsky to be awarded the Order of St. Vladimir IV degree, which was approved and awarded in 1824. However, their relationship gradually worsens - 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. I. I. Lazhechnikov, who served under Magnitsky as director of Kazan schools and university inspector (from 1823 to 1826), recalled the educational environment with disgust:

The university saw a break in everything that had previously existed there. Chiefs, professors, students, everything was subject to strict clerical discipline. Sciences have moved into the background. The persecution of philosophy reached the point of ridiculous fanaticism... the teaching of many educational subjects, based on theological principles, seemed to prepare students for the clergy.

During these years, Lobachevsky prepared a textbook on geometry, which was condemned by the reviewer (Academician Fuss) for using metric system measures and an 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).

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 rank) at Kazan University, after which he served for many years as a commander in Cossack troops, participated in Patriotic War 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, 35-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.

Rector (1827-1845)

The new rector, with his characteristic energy, immediately plunged into economic affairs - reorganizing the staff, building educational buildings, mechanical workshops, laboratories and an observatory, maintaining a library and mineralogical collection, participating 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. First draft new theory- Lobachevsky made a report “A concise presentation of the principles of geometry” 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 record, seven children survived.

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

In 1832-1834. Lobachevsky's published work on non-Euclidean geometry was subjected to sharp, ignorant criticism in St. Petersburg (see below for more details). His official authority was shaken, for the third term (1833) Lobachevsky was elected rector by only 9 votes to 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. St. Petersburg professors always assessed Lobachevsky's scientific works negatively; he was never able to defend his dissertation.

Despite the complications, Musin-Pushkin firmly supported Lobachevsky, and gradually the situation somewhat returned to normal. In 1836, Tsar Nicholas I visited the university, was pleased and awarded Lobachevsky prestigious order Anna II degree, which gave the right to hereditary nobility. On April 29, 1838, “for merits in service and science,” N. I. Lobachevsky was granted nobility and given a coat of arms, the description of which says: The shield is crossed. In the first, scarlet part, there is a golden one with six rays, a star composed of two trigons and a golden bee. In the second, azure part, there is a silver overturned arrow, above the same overturned horseshoe. The shield is topped with a noble helmet and crown. Crest: three silver ostrich feathers. The mantle on the right is scarlet with gold, on the left is azure with silver. Rector of the Imperial Kazan University Nikolai Lobachevsky entered the service in 1814; On December 31, 1818, he was promoted to Court Councilor and, holding the rank of State Councilor, received a diploma for hereditary nobility on April 29, 1838. The coat of arms of Lobachevsky is included in the General Arms of Arms 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 welcomed 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, while traveling to the Orenburg province (to collect materials about the Pugachev rebellion), Alexander Sergeevich Pushkin visited Kazan, but assumptions about his meeting with Lobachevsky were not confirmed. In the summer of 1837, the heir to Tsarevich Alexander Nikolaevich 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. This period included a cholera epidemic (1830) and a severe fire (1842), which destroyed half of Kazan. Thanks to the energy and skillful actions of the rector, casualties and losses in both cases were minimal. Through the efforts of Lobachevsky, Kazan University is becoming first-class, authoritative and well-equipped educational institution, one of the best in Russia.

Last years (1845-1856)

Memorial 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 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 February 8, his two-year-old daughter Nadezhda dies. In the same year, after 30 years of service, the ministry, according to the charter, had to make a decision on leaving Lobachevsky and Simonov as professors or choosing new teachers. On June 11, the university council informed the minister that it “found no reason” to remove Lobachevsky and Simonov from teaching. Lobachevsky himself supported Simonov in a restrained letter, and with regard to himself, he left the decision at the discretion of the minister, and in the event 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 chair, 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.

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 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 soon ceased to exist, as the emperor considered that celebrating the anniversary was unnecessary.

The scientist's last work, Pangeometry, was taken from dictation by the students of a blind scientist in 1855. He died on February 12 (24), 1856, on 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.

When, in the second half of the 1860s, Lobachevsky’s works 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 completed only 16 years later (1883). Great difficulties were encountered even when selecting 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 yet.

Lobachevsky geometry

Student notes of Lobachevsky’s lectures (from 1817) have been preserved, where he attempted to prove Euclid’s fifth postulate, but in the manuscript of the textbook “Geometry” (1823) he already abandoned this attempt. IN " Reviews of teaching pure mathematics"for the years 1822/23 and 1824/25, Lobachevsky pointed out the “still invincible” difficulty of the problem of parallelism and the need to accept in geometry as original concepts, directly acquired from nature.

On February 7 (19), 1826, Lobachevsky submitted for publication in “ Notes of the Physics and Mathematics Department" composition: " A concise presentation of the principles of geometry with a rigorous proof of the parallel theorem" (on French). 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 offers 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.

However scientific ideas Lobachevsky was not understood by his 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, misunderstanding and ignorant ridicule grew.

The crowning achievement of the persecution was a mocking anonymous libel (signed with a 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 for some serious purpose a book that would bring a little honor to the last parish teacher? If not scholarship, then at least common sense every teacher should have, and in new geometry this latter is often lacking.<…>New Geometry<…>written in such a way that no one who read it understood almost anything.

Lobachevsky's attempt to publish a response to the libel in the same magazine was ignored by the editors. Despite the complications, Lobachevsky, confident that he was right, 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 complete theory parallel».

Not finding understanding in his homeland, Lobachevsky tried to find like-minded people abroad. In 1837, Lobachevsky’s article “ Imaginary geometry" in French ( Geometrie imaginaire) appeared in the authoritative Berlin magazine Krelle, and in 1840 Lobachevsky published on 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, believing that the scientific community was not yet ready to accept such radical ideas. 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 G. H. 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 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 Gottingen scientific society 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 scientific merits Lobachevsky. However, it did not strengthen Lobachevsky’s position; he had to work at his native university for another four years. His new article(solving some problems of analysis) again receives a sharply negative review from Ostrogradsky (1842).

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.

Lobachevsky died unrecognized, only 10-12 years before the triumph of his ideas. Soon the situation in science changed radically. A major role in the recognition of Lobachevsky’s works was played by the studies of E. Beltrami (1868), F. Klein (1871), A. Poincaré (1883) and others. The models they constructed - (Projective model, Conformally Euclidean model and pseudosphere model) - proved that Lobachevsky’s geometry is also consistent if Euclidean’s is consistent. The realization that Euclidean geometry has a full-fledged alternative made a huge impression on scientific world and gave impetus to others 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 he developed, independently of J. Dandelin, 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 and etc. B different years he published several substantive articles on algebra, probability theory, mechanics, physics, astronomy and educational problems.

Students

• Bolzani, Joseph Antonovich
• Zinin, Nikolai Nikolaevich, who became an academician-chemist.
• Popov, Alexander Fedorovich.
• Yanishevsky, Erast Petrovich.

Awards and titles

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

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

• 1818 - as a professor, he received the rank of court councilor.
• 1824 - Order of St. Vladimir, IV degree, rank of collegiate adviser.
• 1831 - personal gratitude from the Tsar for the successful fight against the cholera epidemic and a diamond ring. Royal gift Lobachevsky was forced to sell in times of need.
• 1833 - Order of St. Stanislaus, III degree, rank of state councilor.
• 1836 - Order of St. Anne, II degree, title of hereditary nobleman (approved in 1838).
• 1838 - rank of actual state councilor.
• 1841 - title of emeritus professor after 25 years of service.
• 1842 - on the recommendation of Gauss, elected corresponding member of the Royal Scientific Society of Göttingen.
• 1842 - Order of St. Vladimir, III degree, for the 50th anniversary.
• 1844 - Order of St. Stanislaus, 1st degree.
• 1852 - Order of St. Anne, 1st degree, for the 60th anniversary.
• 1855 - on the occasion of the centenary of Moscow University, he was elected its honorary member, with the presentation of 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 participants of the Volga Mathematical Olympiad of students

In 1892, Lobachevsky’s 100th anniversary was widely celebrated in Russia and other countries. The international prize named after N. I. Lobachevsky was established (1895), and a monument to the scientist was unveiled 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 commemorative coin in the series “Outstanding Personalities of Russia”.

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

The following were named in honor of Lobachevsky:

• Nizhny Novgorod State University named after N.I. Lobachevsky, Nizhny Novgorod. On March 20, 1956, a decree of the Presidium was issued Supreme Council USSR on naming Gorky (Nizhny Novgorod) University after N.I. Lobachevsky (Kazan University since 1925 was named after V.I. Ulyanov-Lenin, Lenin studied there from September to December 1887).
• Small Planet (1858) Lobachevsky.
• Crater on back side Moon (9.76°N, 113.07°E).
• Scientific library of Kazan University.
• Streets of Lobachevsky in various populated areas states of the former USSR.



In the 1950s, American composer, singer and mathematician Tom Lehrer wrote a song that jokingly said that Nikolai Ivanovich was prone to plagiarism, and also called on other scientists to do the same. However, Lehrer later admitted that he did not intend to accuse the Russian mathematician of anything, and mentioned Lobachevsky’s last name simply because he liked the sound of it.

In 1965, the Tatar scientist and writer Javad Tarjemanov published documentary novel“The Youth of Lobachevsky (The Birth of a Genius)” (Kazan: Tatarskoe book publishing house), dedicated to his years of study at the university and difficult relationships with Yakovkin and Magnitsky. The novel was republished in 1968, and in 1987 it was published under the title “Lobachevsky’s Youth. The start of a genius."

In his poem about the fate of Russia “The End of the Belle Epoque” (1969), Joseph Brodsky mentions Lobachevsky’s world as a metaphor:

To live in an era of achievements, having an exalted character,
unfortunately, it's difficult. I lifted up the beauty's dress,
you see what you were looking for, and not new marvelous divas.
And it’s not that Lobachevsky is strictly watched here,
but the widened world must narrow somewhere, and here -
this is the end of perspective.

The song of the same name was written on the same verses in the solo album of the lead singer of the group “Splin” Alexander Vasiliev.

Evgeny Yevtushenko dedicated a chapter to Lobachevsky in the poem “Kazan University”; Events in the scientist’s life are mentioned in other chapters of this poem.

Nikolai Ivanovich Lobachevsky(1792-1856) - creator of non-Euclidean geometry (Lobachevsky geometry). Rector of Kazan University (1827-46). Lobachevsky's discovery (1826, published 1829-30), which did not receive recognition from his contemporaries, revolutionized the understanding of the nature of space, which was based on the doctrine of Euclid, and had a huge influence on the development of mathematical thinking. Works on algebra, mathematical analysis, probability theory, mechanics, physics and astronomy.

Nikolai Lobachevsky was born November 2(December 11) 1792 Nizhny Novgorod. Died on February 12 (24), 1856, in Kazan.

Pedagogical activity

Kolya Lobachevsky was born into a poor family of a small employee. Almost all of Lobachevsky's life is connected with Kazan University, which he entered after graduating from high school in 1807. After graduating from the university in 1811, he became a mathematician, in 1814 - an adjunct, in 1816 - an extraordinary and in 1822 - an ordinary professor. Twice (1820-22 and 1823-25) he was dean of the Faculty of Physics and Mathematics, and from 1827 to 1846 - rector of the university.

Under Lobachevsky, Kazan University flourished. Possessing a high sense of duty, Lobachevsky took on the task of fulfilling difficult tasks and every time he fulfilled the mission entrusted to him with honor. Under his leadership, the university library was put in order in 1819.

In 1825 Nikolai Lobachevsky was elected librarian of the university and remained in this post until 1835, combining (from 1827) the duties of a librarian with the duties of a rector. When the construction of buildings began at the university, Lobachevsky became a member of the construction committee (1822), and from 1825 he headed the committee and worked in it until 1848 (with a break in 1827-33).

On the initiative of Lobachevsky, “Scientific Notes of Kazan University” began to be published (1834), an astronomical observatory and a large physics laboratory were organized.

Lobachevsky's active university activities were stopped in 1846, when the Ministry of Education rejected the request of the university's academic council to retain Lobachevsky not only at the department, but also as rector. The undeserved blow was all the more noticeable because the Ministry granted the request of the academic council, requested in the same petition, to retain astronomer I. M. Simonov, a member of the expedition of F. F. Bellingshausen and M. P. Lazarev (1819-21) at the department. the shores of Antarctica.

Non-Euclidean geometry

The greatest scientific feat of Nikolai Lobachevsky is considered to be his creation of the first non-Euclidean geometry, the history of which is usually counted from the meeting of the Department of Physical and Mathematical Sciences at Kazan University on February 11, 1826, at which Lobachevsky made a report “A concise presentation of the foundations of geometry with a rigorous proof of the parallel theorem.” The minutes of the meeting about this great event contain the following entry: “The presentation of G. Ord was heard. Professor Lobachevsky dated February 6 of this year with the attachment of his essay in French, about which he wants to know the opinion of the members of the Department and, if it is beneficial, he asks the essay to be accepted into the compilation of scientific notes of the Faculty of Physics and Mathematics.”

In 1835, Nikolai Lobachevsky briefly formulated the motivations that led him to the discovery of non-Euclidean geometry: “The futile efforts since the time of Euclid for two thousand years made me suspect that the concepts themselves do not yet contain the truth that they wanted to prove and verify, like others physical laws, can only be experiments, such as, for example, astronomical observations. Having finally been convinced of the correctness of my guess and considering the difficult question completely resolved, I wrote a discussion about this in 1826.”

Lobachevsky proceeded from the assumption that several straight lines pass through a point lying outside a given line but do not intersect with a given line. Developing the consequences arising from this assumption, which contradicts the famous V postulate (in other versions the 11th axiom) of Euclid’s Elements, Lobachevsky was not afraid to take a daring step, which his predecessors stopped at for fear of contradictions: to construct a geometry that contradicts everyday experience and " common sense" - the quintessence of everyday experience.

Neither the commission consisting of professors I. M. Simonov, A. Ya. Kupfer and adjunct N. D. Brashman, appointed to consider the “Condensed Presentation”, nor Lobachevsky’s other contemporaries, including the outstanding mathematician M. V. Ostrogradsky, could not appreciate Lobachevsky’s discovery. Recognition came only 12 years after his death, when in 1868 E. Beltrami showed that Lobachevsky’s geometry can be realized on pseudospherical surfaces in Euclidean space, if geodesics are taken as straight lines.

Janos Bolyai also came to non-Euclidean geometry, but to a lesser extent. full form and 3 years later (1832).

Further development of Lobachevsky's ideas

The discovery of Nikolai Ivanovich Lobachevsky posed at least two fundamental issues for science important issues, which have not been raised since Euclid’s Elements: “What is geometry in general? What geometry describes the geometry of the real world? Before the advent of Lobachevsky’s geometry, there was only one geometry - Euclidean, and, accordingly, only it could be considered as a description of the geometry of the real world. The answers to both questions were given by the subsequent development of science: in 1872 Felix Klein defined geometry as the science of the invariants of a particular group of transformations (different geometries correspond to various groups movements, i.e. transformations that preserve the distances between any two points; Lobachevsky geometry studies group invariants Lorenz, and precision geodetic measurements have shown that on areas of the Earth’s surface that can be considered flat with sufficient accuracy, Euclidean geometry is fulfilled).

As for Lobachevsky's geometry. then it acts in the space of relativistic (i.e. close to the speed of light) speeds. Lobachevsky went down in the history of mathematics not only as a brilliant geometer, but also as an author fundamental work in the field of algebra, theory of infinite series and approximate solution of equations. (Yu. A. Danilov)

More about Nikolai Lobachevsky from another source:

In the history of science, it often happens that the true significance of a scientific discovery is revealed not only many years after this discovery was made, but, what is especially interesting, as a result of research in a completely different field of knowledge. This happened with the geometry proposed by Lobachevsky, which now bears his name.

Nikolai Ivanovich Lobachevsky was born in 1792 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 him 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 her children without any means. In 1802, she brought three sons to Kazan and sent them to the Kazan gymnasium , where they quickly noticed the phenomenal abilities of her middle son.

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. The young man studied brilliantly, but his behavior was noted as unsatisfactory; the teachers did not like “dreamy self-conceit, excessive perseverance, freethinking.”

The young man received an excellent education. Lectures on astronomy were given by Professor Litroff. He listened to lectures on mathematics from Professor Bartels, a student of such a prominent scientist as Carl Friedrich Gauss. It was Bartels who helped Lobachevsky choose scientific interests geometry.

Already in 1811, Nikolai 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 one who went to circumnavigation teacher. Lobachevsky's administrative activities began in 1820, when he was elected dean.

Unfortunately, the university was then headed by Magnitsky, who, to put it mildly, did not contribute to the development of science. Nikolai Lobachevsky decides to remain silent for the time being. Yanishevsky condemns this behavior of Lobachevsky, but says: “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.”

But Nikolai Lobachevsky’s silence reached the point that during Magnitsky’s time he did not publish his research on imaginary geometry, although, as is reliably known, he was engaged in them during this period. It seems that Lobachevsky deliberately avoided a useless struggle with Magnitsky and saved his strength for future activities, when dawn replaced the night. Musin-Pushkin appeared at such a dawn; at his appearance, all the teachers and students in Kazan came to life and began to move, emerging from a state of stupor that lasted about seven years... On May 3, 1827, the university council elected Lobachevsky as rector, although he was young - he was thirty-three at the time.

Despite the grueling practical activities, who did not leave a moment of rest, Nikolai Lobachevsky never stopped his scientific studies, and during his rectorship he published his best works in the “Scientific Notes of Kazan University”. Probably still in student years Professor Bartels informed the gifted student Lobachevsky, with whom until his departure he maintained an active personal relationship, the thought of his friend Gauss about the possibility of such a geometry where Euclid’s postulate does not hold.

Reflecting on the postulates of Euclidean geometry, Nikolai 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.

Based on the statement that, under certain conditions, lines that seem parallel to us can intersect, 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.”

Lobachevsky's first work related to this subject was presented to the Faculty of Physics and Mathematics in Kazan in 1826; it was published in 1829, and in 1832 a collection of works on non-Euclidean geometry by Hungarian scientists, father and son Boliai, appeared. Boliai's father was a friend of Gauss, and, undoubtedly, he shared his thoughts about new geometry with him. Meanwhile, the right of citizenship was received in Western Europe namely the geometry of Lobachevsky. Although both scientists were elected members of the Hannover Academy of Sciences for this discovery.

This is how Lobachevsky’s life went in academic pursuits and worries about the university. Almost all the time of his service he did not leave the Kazan province; He spent only from October 1836 to January 1837 in St. Petersburg and Dorpat. In 1840, Nikolai Lobachevsky traveled with Professor Erdman, a deputy from Kazan University, to Helsingfors to celebrate the university’s bicentennial anniversary. In 1842 he was elected corresponding member of the Göttingen Royal Society, but never left the borders of his fatherland.

Nikolai Lobachevsky married late, at the age of forty-four, to a wealthy Orenburg-Kazan landowner Varvara Alekseevna Moiseeva. As a dowry for his wife, he received, among other things, the small village of Polyanka in the Spassky district of the Kazan province. Subsequently, he also bought the Slobodka estate, on the very banks of the Volga, in the same province.

Family life Lobachevsky 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.

Nikolai Ivanovich Lobachevsky had four sons and two daughters. The eldest son, Alexei, his father’s favorite, very much resembled him in face, height and build; younger son suffered from some kind of brain illness, he could barely speak and died in his seventh year. Lobachevsky's family life brought him a lot of grief. He loved his children, cared deeply and seriously about them, but knew how to keep his sorrows within limits and not lose his balance. In the summer he gave free time children and taught them mathematics himself. He sought relaxation in these activities.

He enjoyed nature and had great fun doing agriculture. On his estate, Belovolzhskaya Slobodka, he planted a beautiful garden and grove that has survived to this day. While planting cedars, Lobachevsky sadly told his loved ones that he would not see their fruits. This premonition came true: the first pine nuts were removed in the year of Lobachevsky’s death, when he was no longer in the world.

In 1837, Lobachevsky's works were published in French. In 1840, he published his theory of parallels in German, which earned the recognition of the great Gauss. In Russia, Lobachevsky did not see the assessment of his scientific works. 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, and Ostrogradsky himself treated him either mockingly or with hostility.

Quite correctly, or rather, thoroughly, one geometer called Lobachevsky’s geometry stellar geometry. You can get an idea of ​​infinite distances if you remember that there are stars from which light takes thousands of years to reach the Earth. So, Lobachevsky’s geometry includes the geometry of Euclid not as a particular one, but as a special case. In this sense, the first can be called a generalization of the geometry known to us.

Now the question arises whether the invention belongs to Lobachevsky fourth dimension? Not at all. The geometry of four and many dimensions was created German mathematician, student of Gauss, Riemann. The study of the properties of spaces in a general form now constitutes non-Euclidean geometry, or Lobachevsky geometry. Lobachevsky space is a space of three dimensions, differing from ours in that Euclid’s postulate does not hold in it. The properties of this space are currently being understood with the assumption of a fourth dimension. But this step belongs to the followers of Lobachevsky. Naturally, the question arises where such space is located. The answer was given by the greatest physicist of the 20th century Albert Einstein. Based on the works of Lobachevsky and Riemann's postulates, he created the theory of relativity, which confirmed the curvature of our space.

According to this theory, any material mass bends the space around her. Einstein's theory has been confirmed many times astronomical observations, as a result of which it became clear that Lobachevsky’s geometry is one of the fundamental ideas about the Universe around us.

IN last years Lobachevsky's life was haunted by all kinds of grief. His eldest son, who bore a great resemblance to his father, died as a university student; the same unbridled impulses that distinguished his father in his early youth manifested themselves in him.

The Lobachevskys' fortunes, according to their son, were upset by the not entirely successful purchase of the estate. Lobachevsky bought the latter, counting on his wife’s capital, which was in the hands of her brother, a passionate gambler, theatergoer and poet. The brother lost his sister's money at cards along with his own. And Lobachevsky, despite all his hatred of debt, was forced to borrow; the house in Kazan was also mortgaged. Lobachevsky's surviving children brought him little comfort.

In 1845, Riemann was unanimously elected rector of the university for a new four-year term, and in 1846, on May 7, his five-year term of service as an emeritus professor ended. The Council of Kazan University again came in with a request to retain Lobachevsky as a professor for another five years. Despite this, due to some dark intrigue, the ministry refused.

On top of that, Lobachevsky also lost financially. Having lost his professorial title, he had to be content with a pension, which under the old charter was 1 thousand 142 rubles and 800 rubles in canteens. Lobachevsky continued to perform his duties as rector without receiving any remuneration.

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.

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