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Biography of Nikolai Lobachevsky (1792-1856)
Short biography:
Education: Kazan University
Place of Birth: Nizhny Novgorod
Place of death: Kazan
- Russian mathematician: biography with photo, place and date of birth, discoveries in mathematics and geometry, contribution to science, non-Euclidean geometry.
One of the most outstanding mathematicians in the world, William Clifford, once called Nikolai Lobachevsky"Copernican Geometry". The Englishman knew what he was talking about - Lobachevsky created a whole new branch of this science - non-Euclidean geometry.
Nikolai Lobachevsky was born in the family of an official in 1792. When Nicholas was 8 years old, his father died. The mother of the future mathematician and three children remained practically in poverty. Fortunately, according to the then laws, all three brothers had the right to study at the expense of the treasury, and their mother sent them to the Kazan gymnasium. Nicholas finished it in 1806. An unheard of success for him and for all mathematics was that in 1805 a university was opened in Kazan, and many teachers of the gymnasium not only began to work in it, but also offered their students to take a course of study. From the second time, Lobachevsky passed the exams and became a student.
At the university, despite some complaints about his behavior, Lobachevsky was in good standing. After completing his course of study, he was left at the university and in 1814 became an adjunct (assistant professor) of mathematics. Two years later, with the personal assistance of the rector M. Saltykov, he was elected an extraordinary professor. In 1819, after the reorganization of the university, Lobachevsky became dean. After 7 years, colleagues elected him rector of the university. He successfully solved both administrative and economic problems of the educational institution, not forgetting about teaching and scientific work.
And the scientific work of Nikolai Ivanovich began in 1811 with the work "Theory of the elliptical motion of celestial bodies." Lobachevsky also wrote a paper on the theory of solving algebraic equations. But the main work of his scientific career was the creation of non-Euclidean geometry. In 1826 he read the first report on her. For that time, it bordered on a crime. Both colleagues and superiors sharply criticized the thoughts of the mathematician. Fortunately, since the time of Copernicus, morals have softened somewhat, and the support of the university superintendent M. Musin-Pushkin helped, so Lobachevsky could continue to work and was even awarded an order, and in 1938 he was raised to the nobility.
Lobachevsky's works on non-Euclidean geometry were also published abroad. Karl Gauss praised the work of Lobachevsky in his letters, but did not speak out loud, considering the thoughts of his colleague from Russia too bold. Gauss only recommended that Nikolai Ivanovich be elected a foreign member of the Göttingen Scientific Society.
Nevertheless, Lobachevsky's theories did not receive recognition during his lifetime. It was only towards the end of the 19th century that they began to be used when considering the relationship of space and time. But Lobachevsky received his share of recognition. His work at Kazan University made it possible to create a modern educational institution at that time, which had an excellent scientific base. In addition, Lobachevsky's decisive actions during the cholera epidemic in 1830 and the huge fire in 1842 not only saved the university, but also helped save the lives of the townspeople.
Lobachevsky, blinded by that time, dictated his last work called “Pangeometry” in 1855, and in February of the following year, the great mathematician died exactly 30 years after the first report on non-Euclidean geometry.
Nikolai Ivanovich Lobachevsky (November 20 (December 1) ( 17921201 ) , Nizhny Novgorod - February 12 (24), Kazan), the great Russian mathematician, creator of Lobachevsky geometry, figure in university education and public education. The famous English mathematician William Clifford called Lobachevsky the "Copernicus of geometry".
Biography
N. I. Lobachevsky was born in the Ardatovsky district of the Nizhny Novgorod province. His parents were Ivan Maksimovich Lobachevsky (an official in the geodetic department) and Praskovya Alexandrovna Lobachevsky. In 1800, after the death of his father, his mother and his family moved to Kazan. There Lobachevsky graduated from the gymnasium (-), and then (-) and the newly founded Kazan Imperial University, to which he devoted 40 years of his life.
While studying at the university, Lobachevsky was greatly influenced by Martin Fedorovich Bartels, a friend and teacher of the great German mathematician Carl Friedrich Gauss. He took patronage over a poor but gifted student. In his senior year, Lobachevsky's characterization included "dreamy conceit, stubbornness, defiance", as well as "outrageous acts" and even "signs of godlessness". The threat of expulsion loomed over him, but the intercession of Bartels and other teachers helped avert the danger.
Upon graduation, Lobachevsky received a master's degree in physics and mathematics with honors () and was left at the university. In 1814 he became an adjunct, after 2 years - an extraordinary, and in 1822 - an ordinary professor. The students highly appreciated Lobachevsky's lectures.
The range of his duties was extensive - lecturing on mathematics, astronomy and physics, completing and putting in order the library and museum, etc. The list of official duties even includes "monitoring the reliability" of all Kazan students.
The 200th anniversary of Lobachevsky was celebrated in 1992. The Bank of Russia issued a commemorative coin in the Outstanding Personalities of Russia series.
A crater on the Moon is named after Lobachevsky. Streets in Moscow and Kazan, the scientific library of Kazan University are also named after him. On March 20, 1956, the Presidium of the Supreme Soviet of the USSR issued a decree on awarding the Gorky (Nizhny Novgorod) University named after N.I. Lobachevsky.
Geometry of Lobachevsky
Main article: Lobachevsky geometryStudent notes of Lobachevsky's lectures (from 1817) have been preserved, where he made an attempt to prove the fifth postulate of Euclid, but in the manuscript of the textbook "Geometry" () he already abandoned this attempt. AT " Reviews of teaching pure mathematics” for 1822/23 and 1824/25 Lobachevsky pointed out the “still invincible” difficulty of the problem of parallelism and the need to take in geometry as initial concepts directly acquired from nature.
How can one think that Mr. Lobachevsky, an ordinary professor of mathematics, would write a book for any serious purpose that would bring a little honor even to the last school teacher? If not learning, then at least common sense should be in every teacher, and in the new geometry this latter is often lacking.
Title page of Lobachevsky's book
But Lobachevsky does not give up. B - he publishes articles on “imaginary geometry” in Uchenye Zapiski, and then the most complete of his works comes out. New beginnings of geometry with a complete theory of parallels».
Not finding understanding at home, he tries to find like-minded people abroad. In 1840, Lobachevsky published in German "Geometric Research on the Theory of Parallels", which contains a clear presentation of his main ideas. One copy is given to Gauss, the "king of mathematicians" of that time.
As it turned out much later, Gauss himself secretly developed non-Euclidean geometry, but he did not dare to publish anything on this topic. After reviewing the results of Lobachevsky, he indirectly expressed his sympathy for the ideas of the Russian scientist: he recommended that Lobachevsky be elected a foreign corresponding member of the Göttingen Royal Society. Gauss entrusted rave reviews about Lobachevsky only to his diaries and closest friends.
In popular culture
Proceedings
- N. I. Lobachevsky. Complete works in five volumes.
- N. I. Lobachevsky. Geometric Studies in the Theory of Parallel Lines, Translation, Commentaries, Introductory Papers and Notes by Prof. V. F. Kagan. M.-L.: Publishing House of the Academy of Sciences of the USSR, 1945, 176 s, djvu.
- N. I. Lobachevsky. Geometric research on the theory of parallel lines. 1941, pdf.
- N. I. Lobachevsky. About the beginnings of geometry. (1 part). imaginary geometry. (1 part). New beginnings of geometry with a complete theory of parallels (Introduction).
- On the foundations of geometry. A collection of classical works on Lobachevsky's geometry and the development of its ideas. Moscow: Gostekhizdat, 1956.
Notes
Literature
- Bell E.T. creators of mathematics. M .: Education, 1979, 256 p., Chapter 15.
- Vasiliev A.V. Nikolai Ivanovich Lobachevsky. - M.: Science. 1992. - 229 s (Scientific and biographical series).
- Glazer G.I. History of mathematics in the school. - M.: Education, 1964. - S. 345-350.
- Museum of History and Local Lore of N. I. Lobachevsky in Kozlovka, Chuvashia.
- Kagan V.F. Lobachevsky. M.-L.: Publishing House of the Academy of Sciences of the USSR, 1948, 507 pp. + 17 inserts.
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Lobachevsky, Nikolai Ivanovich Nikolai Ivanovich Lobachevsky Date of birth: November 20 (December 1) 1792 Place of birth: Nizhny Novgorod Date of death: February 12 (February 24 ... Wikipedia
Bust N.I. Lobachevsky, alley of scientists of Moscow State University on Sparrow Hills
Nikolay Ivanovich Lobachevsky(, Nizhny Novgorod - February 24, Kazan) - Russian scientist, mathematician, organizer of science. He was engaged in mathematical analysis, algebra, applied mathematics, mechanics and invention. Known as the creator of non-Euclidean geometry
“The vain effort since the time of Euclid, in the course of two thousand years, made me suspect that the very concepts do not yet contain the truth that they wanted to prove and which, like other physical laws, can only be verified by experiments, such as, for example, astronomical observations. » N.I. Lobachevsky,
Biography
Concerning the date of birth N.I. Lobachevsky there are disagreements:
- October 22 of the year ()
- or gg. ()
- December 1 of the year ()
- November 20 (December 1) of the year ()
- year (on the bust of the alley of scientists of Moscow State University, on the Sparrow-Lenin Hills, about a year)
The place of his birth is not entirely clear either - in the city of Makaryev, Makaryevsky district or in Nizhny Novgorod. Agreement on these matters was not reached until the centenary of his death. N.I. Lobachevsky per year, thanks to the efforts of the Nizhny Novgorod archivist Ivan Ivanovich Vishnevsky and academician Alexander Alexandrovich Andronov, who in the late 1940s wrote to the President of the USSR Academy of Sciences S.I. Vavilov:
“uncertainties regarding the place of birth of N.I. Lobachevsky, in the date of his birth, in the occupations and social status of his parents: a) do not allow compiling a benign biography of N.I. Lobachevsky (of course, in that part of it that concerns his origin and his childhood and youth), they do not allow to mark the place of his birth (in the city of Gorky or in the city of Makaryev, Gorky region) by setting up a monument or a memorial plaque.As a result of the study A.A. Andronov archival and church documents, it was decided that "The greatest Russian mathematician Nikolai Ivanovich Lobachevsky was born in Nizhny Novgorod (now the city of Gorky) on November 20 (old style)". The place where his mother's house was located was also determined, Praskovia Alexandrovna Lobachevskaya ( –).
About childhood Nikolai Lobachevsky very little is known, as he apparently concealed the details of his origins. It is assumed that his father Ivan Maksimovich Lobachevsky(-) was the son of a Russified Pole Maxim Vasilyevich, chorister and clerk of the prince M.I. Dolgoruky who married the serf of this prince Agrafena Andreevna and received his freedom in the year. Ivan Maksimovich served in the land surveying office of various provinces for a year, receiving salaries there 60 rubles a year, and rose to the rank of provincial registrar in a year ( 14 -th, the lowest possible, corresponding to the military rank of ensign), soon received a place in Nizhny Novgorod. Around this time he married Praskovya Alexandrovna(there is an assumption that her maiden name is Vysheslavtseva and her father Alexander Ignatievich Vysheslavtsev in the year, for some reason, he shot himself, wounding his wife at the same time, and his daughter was sent from Moscow to relatives in the province). per year Ivan Masimovich retired due to illness. For about a year, his wife lived separately from him, and her children - Alexander(b.b.), Nicholas(b.b.) and Alexei(b.b.) were considered "pupils" of the surveyor captain (titular adviser) Sergei Stepanovich Shebarshin, who died of a long illness in the year, and according to the laws of the Russian Empire, "education" could mean their illegitimacy. However, this version is based on indirect evidence from church confession books and the guesswork of Soviet historians.
From these studies it follows that the brothers Lobachevsky grew up in a wealthy and cultured family - they had their own house, land and yard servants (serfs), S.S. Shebarshin graduated from Moscow University and received about 300 rubles a year, his mother was an educated noblewoman. In Nizhny Novgorod, the brothers graduated from the free 4th grade Main Public School, which later became an all-class provincial gymnasium.
After the Second World War, the award was transferred to the Academy of Sciences of the USSR and it began to be given out "for outstanding work in the field of geometry", after which it was received N.V. Efimov (), HELL. Alexandrov (), A.V. Pogorelov (), L.S. Pontryagin (), H. Hopf (), P.S. Alexandrov (), B.N. Delaunay (), S.P. Novikov (), A.N. Kolmogorov (), F. Hirzebruch (), IN AND. Arnold () , G.A. Margulis (), SOUTH. Reshetnyak ( 0), Zhen Shen-Shen ().
To the centenary of the birth Lobachevsky a bust-monument was erected in Kazan, executed Maria Lvovna Dillon. In the year the medal “In Memory of N.I. Lobachevsky", which was first given to reviewers of works submitted for the award N.I. Lobachevsky- got it first Felix Klein. In the year the awarding of the medal was resumed N.I. Lobachevsky"For outstanding work in the field of geometry" - awarded by the Academic Council of Kazan State University once every five years to Russian or foreign scientists. She received - A.P. Norden (), B.P. Komrakov and M. Gromov ().
"There is only one line parallel to the given one, passing through the given point."Russian historians of mathematics Boris Abramovich Rosenfeld and Rustam Sultanov in a year found attempts to prove the fifth postulate from an Arab mathematician Nasir-Eddin of Merag (Abu Jafar Mohammed ibn Hasan al-Tuzi, allegedly 1201-1274).
The first reliable known, but erroneous attempt to substantiate the Euclidean postulate of parallels belongs to the Italian Jesuit scientist Giovanni Girolamo Saccheri (Saccheri, -) in the work “Euclides ab omni naevo vindicatus” (“On the viciousness of Euclid’s statements”, Milan,) - it was discovered at the end of the 19th century, when the works N.I. Lobachevsky were understood and confirmed.
German mathematician Georg Simon Klugel (Klugel, -) in the "Review of the most important attempts to prove the theorem on parallel lines" (Göttingen, ) considered about 30 various erroneous "proofs" of the fifth postulate.
German mathematician, philosopher, physicist and astronomer Johann Heinrich Lambert (Lambert, -), unsuccessfully trying to prove the V postulate, as if he came to the conclusion that such a proof is impossible and received some initial theorems following from the negation of the Vth postulate.
French mathematician, member of the Paris Academy of Sciences Adrien Marie Legendre (Legendre, -) from year to year in twelve editions of his exemplary textbook "Principles of Geometry" over and over again gave new "proofs" of the V postulate, correcting the errors of the previous version. A translation of his book was published in Russia in 2008, became popular and was well known N.I. Lobachevsky who mentions it in his works.
German lawyer Ferdinand Karl Schweikart (Schweikart, -), who occupied the Department of Law of Kharkov University in - years, wrote a letter in the year K.F. Gauss where he proved the existence of "astral" geometry, in which the sum of the interior angles of a triangle is less than two straight lines. His idea was tacitly supported by Gauss, which became clear after the publication of the correspondence between Gauss and the astronomer Heinrich Christian Schumacher in - years. Book mentioned Schweikart"The Theory of Parallels with a Proposal for their Expulsion from Geometry", allegedly published in the year.
German lawyer and mathematician Franz Adolf Taurinus (Taurinus, -), nephew F. Schweikart, in the works "Theorie der Parallellinien" (Cologne, ) and "Geometriae prima elementa" (Cologne, ) came to the possibility of the existence of non-Euclidean geometry. He entered into correspondence with Gauss, but their relationship did not work out and Taurinus burned his pamphlets. His work also became known only at the end of the 19th century, when it was discovered by a mathematician Friedrich Engel (Engel, –).
Hungarian mathematician and engineer Janos Bolyai (Boyai, boyai, Boljai, -) in the year came to the main provisions of non-Euclidean geometry, which he published in an appendix to his father's book, Farkasha (Wolfgang) Bogliai year (sometimes indicate the year). K.F. Gauss being a friend Farkas Bolyai, informally expressed his approval of his son's work. Already after death Gaussian in his drafts, they found old entries related to the problem of substantiating the postulate of parallels.
Medal to them. N.I. Lobachevsky
N.I. Lobachevsky wrote the manuscript of a gymnasium textbook on geometry in the year, sending it for review to the trustee of the Kazan educational district M.L. Magnitsky. He gave the manuscript to a former student and assistant Leonhard Euler academician and secretary of the St. Petersburg Academy Nikolai Ivanovich Fuss(-), who, being himself the author of textbooks on geometry, gave a sharp negative review of it, recommending that it be corrected. Lobachevsky he refused to correct and did not even bother to take his work back. This manuscript was found in the archive of the office of the trustee of the Kazan educational district N.P. Zagoskin and was published in Kazan in (or) year. fuss wrote in particular:
“... if the writer thinks that it can serve as an educational book, then he thereby proves that he does not have an exact understanding of the needs of an educational book, i.e. about the completeness of geometric truths, about the entire system of the initial course of science components, about the mathematical method, about the need for precise and clear definitions of all concepts, about the logical order and methodical arrangement of objects, about the proper gradualness of geometric truths, about the unmissable and, if possible, purely geometric rigor of their evidence and so on. There is no trace of all these necessary qualities in the geometry I have considered..N.I. Fussa also resented the innovations N.I. Lobachevsky- application of the metric system of measures and centigrade division of the right angle:
“It is known that this division was invented during the French Revolution, when the frenzy of the nation, to destroy the former, spread even to the calendar and the division of the circle, but this novelty has long been abandoned in France itself”.It is sometimes reported that in the same year N.I. Lobachevsky wrote a manuscript on non-Euclidean geometry, sending it to the same Magnitsky, also rejected fussom. As if, it was also discovered at the very end of the 19th century, in the archives of Kazan University. Apparently, here we are talking about the manuscript of the mentioned gymnasium textbook, which outlines the plan of his future work:
“A rigorous proof of this truth,” Lobachevsky says of Euclid's postulate, has not yet been found; which have been given can only be called explanations, but do not deserve to be honored in the full sense of the mathematical proofs..Manuscript on Non-Euclidean Geometry "Abbreviated Exposition of the Principles of Geometry" ("Exposition succincte des principes de la Géométrie") N.I. Lobachevsky wrote in the year, presenting it on February 12 at the Physics and Mathematics Department of Kazan University. The manuscript was not published, meeting the tacit disapproval of colleagues, turned out to be lost, but was partially included in the memoir "On the Principles of Geometry", published in the "Kazan Bulletin" for - years. Nikolay Ivanovich sent a memoir to the Academy of Sciences, where he got a review from an outstanding mathematician of his time M.V. Ostrogradsky ( –). Ostrogradsky wrote arrogant, contemptuous, and in one mathematical place erroneous (as later proved V.F. kagan) a report read at the Academy on November 7th. academics, following Ostrogradsky who did not understand the essence of the problems and methods, were given a job Lobachevsky negative feedback, entering it into the protocol:
"... the work is done with such little effort that most of it is incomprehensible." ()Confession Lobachevsky began to come only posthumously, when the German astronomer Carl Friedrich Wilhelm Peters in - years published a correspondence Carl Friedrich Gauss with German scientists. French mathematician and theoretical astronomer Guillaume Jules Guell (G.J. Howel, -) translated into French "Geometric Studies" Lobachevsky and in the same year he published them, together with excerpts from Gauss's letters, in the Proceedings of the Society of Physical and Natural Sciences of Bordeaux.
Corresponding Member of the Russian Academy of Sciences Konstantin Alekseevich Andreev(-) wrote about G.Zh. Uele:
“... a worker of science, whose energy was not excited by any selfish interests, even such as the desire for fame by personal scientific merits, which is the weakness of almost all scientists. Doing everything possible to ensure that the merits of other scientists were appreciated, he did not leave himself time to declare himself as a more or less respectable scientific owner, which, no doubt, he could have achieved with another less disinterested direction of his activity. »(“Life and scientific activity of V.G. Imshenetsky”, - M .: University Printing House, , pp. 17–18)First cautious approval of works N.I. Lobachevsky took place in Russia in the year when the article A.V. Letnikova“On the theory of parallel lines by N.I. Lobachevsky". In addition to presenting the ideas of the Kazan geometer, the article contains positive reviews K.F. Gaussian about him from correspondence with G.H. Schumacher.
However, academic V.Ya. Bunyakovsky(-) in memoir "Considerations sur quelques singularités qui se presentent dans les constructions de la Géométrie non-euclidienne" ("Consideration of some oddities that take place in the constructions of non-Euclidean geometry", Reports of the St. Petersburg Academy of Sciences. 7 series. -
Date of birth: December 1, 1792
Date of death: February 24, 1856
Place of birth: Nizhny Novgorod, Russia
N.I. Lobachevsky famous Russian mathematician. Also Lobachevsky Nikolay Ivanovich known for his work on non-Euclidean geometry.
In 1792, the future famous mathematician Lobachevsky was born in Nizhny Novgorod. His father was a surveyor and served in the department. Nikolai's mother did not work anywhere and raised three children. In 1802, Lobachevsky was sent to the gymnasium. The boy mastered many subjects well. Here he studied for four years.
After graduating, Nikolai tried to enter the university, but could not, as he failed the entrance exams. But on the second attempt, Lobachevsky managed to pass the exams and become a student.
At first, Nikolai studied medicine, but then he decided to take up the exact sciences. He was even put in a punishment cell, as he was fond of pyrotechnic experiments.
Lobachevsky graduated from the university four years later with a master's degree in physics and mathematics. After graduation, he decides to stay at the faculty in order to do research.
In 1814, Lobachevsky began teaching exact sciences at the university. Somehow, an inspection was carried out at the university, and the auditor noted only the high quality of the Faculty of Physics and Mathematics. The state of other faculties was unsatisfactory. After checking all the deans were foreigners, they left the service, and Lobachevsky was appointed dean of the faculty.
When the Kazan University trustee Magnitsky was fired for abuse of authority, Lobachevsky was appointed rector of the university. The scientist was a good organizer, and over the years of his service, new educational buildings were built, the staff was reorganized, a mineralogical collection was collected, etc.
Lobachevsky taught courses in algebra, trigonometry, physics and mechanics. In the absence of teachers, the rector of Kazan University replaced them in the service.
In parallel, Nikolai Lobachevsky was engaged in the work of his whole life - he worked on the creation of non-Euclidean geometry. In 1826, the mathematician presented a paper on geometry. Today is the day of this report, February 23, is the date of the creation of non-Euclidean geometry.
After some time, troubles began to occur in the Lobachevsky family. For debts, the house of the former rector and the estate of his wife were sold.
Lobachevsky's son died of tuberculosis, and he himself began to go blind. His last work on the study of geometry was completed in 1855. Lobachevsky dictated this work to his students.
Achievements of Nikolai Lobachevsky:
The works of Lobachevsky relate primarily to geometry. His main achievement is the creation of non-Euclidean geometry. All his works were collected only a few years after the death of the mathematician, but some of them are still considered lost.
Lobachevsky discovered a new way to solve equations
Important dates of Nikolai Lobachevsky:
1811 - A work on the theory of the elliptical motion of the planets was published
1824 - Received the Order of St. Vladimir IV degree from Nicholas I
1826 - Published a work on the creation of non-Euclidean geometry
1836 - Received the Order of Anna II degree
1855 - Finished work on the mathematical opus "Pangeometry".
Interesting facts of Nikolai Lobachevsky:
At the age of 19, Lobachevsky graduated from the university with a master's degree, and at the age of 24 he received the title of professor
Lobachevsky enjoyed gardening and was especially fond of caring for cedars. He said many times that he would not have time to see the cedar fruits. They were collected a few months before the scientist's death.
Lobachevsky also participated in agricultural life. He introduced new technologies, for which he received various awards.
In 1992, a medal named after this outstanding scientist was established. It is issued every five years for achievements in modern geometry.
Nikolay Ivanovich Lobachevsky(1792-1856) - creator of non-Euclidean geometry (Lobachevsky's geometry). Rector of Kazan University (1827-46). The discovery of Lobachevsky (1826, published 1829-30), which did not receive recognition from his contemporaries, made a revolution in the idea of the nature of space, which was based on the doctrine of Euclid, and had a huge impact 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. He 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, where 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 professor, and in 1822 an ordinary professor. Twice (1820-22 and 1823-25) he was the dean of the Faculty of Physics and Mathematics, and from 1827 to 1846 he was the rector of the university.
Under Lobachevsky, Kazan University flourished. Possessing a high sense of duty, Lobachevsky undertook difficult tasks and each time 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 (since 1827) the duties of a librarian with the duties of a rector. When the construction of buildings began at the university, Lobachevsky joined the building committee (1822), and from 1825 he headed the committee and worked in it until 1848 (with a break in 1827-33).
At the initiative of Lobachevsky, the Scientific Notes of the Kazan University (1834) began to be published, an astronomical observatory and a large physics room were organized.
Lobachevsky's active university activities were stopped in 1846, when the Ministry of Education rejected the application of the academic council of the university to leave Lobachevsky not only at the department, but also at the post of rector. The undeserved blow was all the more tangible because the Ministry granted the request of the Academic Council requested in the same petition to leave the astronomer I. M. Simonov, a member of the expedition of F. F. Bellingshausen and M. P. Lazarev (1819-21) to coast 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." There is the following entry in the minutes of the meeting about this great event: “G. Ord's presentation was heard. Professor Lobachevsky dated February 6 of this year, with an appendix 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 to accept the essay in the compilation of scientific notes of the Faculty of Physics and Mathematics.
In 1835, Nikolai Lobachevsky briefly formulated the motives that led him to the discovery of non-Euclidean geometry: other physical laws, can only experiments, such as, for example, astronomical observations. Being finally convinced of the validity of my conjecture and considering the difficult question completely resolved, I wrote an argument about this in 1826.
Lobachevsky proceeded from the assumption that through a point lying outside a given line there pass several lines that do not intersect with the given line. Developing the consequences arising from this assumption, which contradicts the famous postulate V (in other versions, the 11th axiom) of Euclid's "Beginnings", Lobachevsky was not afraid to take a bold step, before which his predecessors stopped for fear of contradictions: to construct a geometry that contradicts everyday experience and "common sense" - the quintessence of everyday experience.
Neither the commission composed of professors I. M. Simonov, A. Ya. Kupfer and adjunct N. D. Brashman, appointed to consider the "Compressed presentation", nor other contemporaries of Lobachevsky, including the outstanding mathematician M. V. Ostrogradsky, failed to appreciate Lobachevsky's discovery. Recognition came only 12 years after his death, when in 1868 E. Beltrami showed that Lobachesky'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 in a less complete form and 3 years later (1832).
Further development of Lobachevsky's ideas
The discovery of Nikolai Ivanovich Lobachevsky posed before science at least two fundamentally important questions that had not been raised since the time of Euclid's Elements: “What is geometry in general? What geometry describes the geometry of the real world? Prior to the advent of Lobachki'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 different groups of motions, i.e. transformations that preserve the distances between any two points; Lobachevsky's geometry studies group invariants Lorenz, and precision geodetic measurements have shown that in areas of the Earth's surface, which can be considered flat with sufficient accuracy, Euclid's geometry is fulfilled).
As for the geometry of Lobachevsky. then it acts in the space of relativistic (ie close to the speed of light) velocities. Lobachevsky entered the history of mathematics not only as a brilliant geometer, but also as the author of fundamental works in the field of algebra, the theory of infinite series, and the approximate solution of equations. (Yu. A. Danilov)
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In the history of science, it often happens that the true meaning 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 the Makaryevsky district of the Nizhny Novgorod province. His father was a county architect and belonged to the number of petty officials who received meager support. Poverty, which surrounded him in the first days of his life, turned into poverty, when in 1797 his father and mother died, at the age of twenty-five, he was left alone with the children without any means. In 1802, she brought three sons to Kazan and assigned them to the Kazan gymnasium , where the phenomenal abilities of her middle son were very quickly noticed.
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 by Professor Bartels, a pupil of such a prominent scientist as Carl Friedrich Gauss. It was Bartels who helped Lobachevsky choose geometry as his area of scientific interest.
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 a professorship. 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 related to the gymnasiums and schools of the district, then subordinated not directly to the trustee, but to the university. Since 1819, Lobachevsky taught astronomy, replacing the teacher who went on a round-the-world voyage. Lobachevsky's administrative activity 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 such behavior of Lobachevsky, but says: “The duty of Lobachevsky as a member of the council was especially difficult in moral terms. Lobachevsky himself never fawned over his superiors, did not try to put himself in front of his eyes, did not like this in others either. At a time when the majority of the members of the council, to please the trustee, were ready for anything, Lobachevsky was silently present at the meetings, silently and signed the minutes of these meetings.
But the silence of Nikolai Lobachevsky reached the point that during the time of Magnitsky he did not publish his research on imaginary geometry, although, as is known for certain, he was engaged in them during this period. It seems that Lobachevsky consciously avoided a useless struggle with Magnitsky and saved his strength for future activities, when dawn replaced the night. Such a dawn was Musin-Pushkin, when he appeared, all teachers and students in Kazan came to life and stirred, came out of a state of stupor, which 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 exhausting practical activities that did not leave a single moment of rest, Nikolai Lobachevsky never stopped his scientific studies, and during his rectorship published his best works in the Scientific Notes of Kazan University. Probably, even in his student years, Professor Bartels informed the gifted student Lobachevsky, with whom he maintained an active personal relationship until his departure, the thought of his friend Gaussian about the possibility of such a geometry where Euclid's postulate does not hold.
Thinking about the postulates of Euclidean geometry, Nikolai Lobachevsky came to the conclusion that at least one of them could be revised. Obviously, the cornerstone of Lobachevsky's geometry is the negation of Euclid's postulate, without which geometry seemed unable to live for about two thousand years.
Based on the assertion that, under certain conditions, lines that seem parallel to us can intersect, Lobachevsky came to the conclusion that it is 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 on 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 by Hungarian scientists, father and son Boliay, appeared on non-Euclidean geometry. Bolyai the father was a friend of Gauss, and, no doubt, he shared with him his thoughts on the new geometry. Meanwhile, it was Lobachevsky's geometry that received the right to citizenship in Western Europe. Although both scientists were elected members of the Hanover Academy of Sciences for this discovery.
So Lobachevsky's life went on in scientific studies and in caring for the university. Almost all the time of his service he did not leave the Kazan province; only from October 1836 to January 1837 did he spend in St. Petersburg and Dorpat. In 1840, Nikolai Lobachevsky, together with Professor Erdman, traveled as a deputy from Kazan University to Helsingfors to celebrate the university's bicentennial anniversary. In 1842 he was elected a corresponding member of the Göttingen Royal Society, but he 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 Polyanki in the Spassky district of the Kazan province. Subsequently, he bought another estate Slobodka, on the very banks of the Volga, in the same province.
Lobachevsky's family life was in full accordance with his general mood and his activities. Pursuing the search for truth in science, he put the truth above all else in life. In the girl he decided to call his wife, he mainly valued honesty, truthfulness and sincerity. They say that before the wedding, the bride and groom gave each other their word of honor to be sincere and kept it. By nature, Lobachevsky's wife was a sharp contrast to her husband: Varvara Alekseevna was unusually lively and quick-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 physique; the youngest son suffered some kind of cerebral sickness, he could hardly speak and died in his seventh year. Lobachevsky's family life brought him much grief. He loved his children, deeply and seriously cared for them, but he knew how to restrain his sorrows within and did not get out of balance. In the summer, he gave free time to children and taught them mathematics himself. In these studies he sought rest.
He enjoyed nature and took great pleasure in farming. On his estate, Belovolzhskaya Slobodka, he planted a beautiful garden and a grove that has survived to this day. Planting cedars, Lobachevsky sadly told his loved ones that he would not wait for 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 in German his theory of parallels, which deserved the recognition of the great Gauss. In Russia, Lobachevsky did not see the evaluation of his scientific works. Obviously, Lobachevsky's research was beyond the understanding of his contemporaries. Some ignored him, others greeted his work with rude ridicule and even scolding. While our other highly talented mathematician Ostrogradsky enjoyed well-deserved fame, no one knew Lobachevsky, and Ostrogradsky himself treated him either mockingly or hostilely.
Quite correctly, or rather, thoroughly, one geometer called Lobachevsky's geometry stellar geometry. One can form an idea of infinite distances if one remembers that there are stars from which light reaches the Earth for thousands of years. So, the geometry of Lobachevsky includes the geometry of Euclid not as a particular, 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, does Lobachevsky own the invention of the fourth dimension? Not at all. The geometry of four and many dimensions was created by the German mathematician, a student of Gauss, Riemann. The study of the properties of spaces in a general form now constitutes non-Euclidean geometry, or the geometry of Lobachevsky. The Lobachevsky space is a space of three dimensions, which differs from ours in that the postulate of Euclid does not take place in it. The properties of this space are now being understood by assuming a fourth dimension. But this step already belongs to the followers of Lobachevsky. Naturally, the question arises, where is such a space. The answer to it was given by the largest physicist of the XX 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 curves the surrounding space. Einstein's theory was repeatedly confirmed by 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 the last years of his life, Lobachevsky was haunted by all kinds of grief. His eldest son, who had a great resemblance to his father, died a university student; he showed the same unbridled impulses that distinguished his father in early youth.
The state of the Lobachevskys, according to his son, was 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 player, 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. The surviving children of Lobachevsky brought him little consolation.
In 1845, Riemann was unanimously elected rector of the university for a new four-year term, and in 1846, on May 7, the five-year term of his service as an honored professor ended. The Council of Kazan University came back again with a request to keep Lobachevsky in the professorship for another five years. Despite this, due to some dark intrigue, the ministry refused.
On top of that, Lobachevsky also lost financially. When he lost his professorship, he had to be content with a pension, which, under the old charter, was 1,142 rubles and 800 canteen rubles. Lobachevsky continued to perform his duties as rector without receiving any remuneration.
Lobachevsky's activity in the last decade of his life was, in its intensity, only a shadow of the past. Deprived of his chair, Lobachevsky lectured on his geometry to a select scientific audience, and those who heard them remember the thoughtfulness with which he developed his principles.
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