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 activity.
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 has 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, also he 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(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 impact on the development 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 - extraordinary and in 1822 - full 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, then asks the essay to be accepted for compilation scientific notes 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 “ Concise presentation", nor other contemporaries of Lobachevsky, including 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? Which geometry describes the geometry 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 meaning 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 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, which did not leave a minute 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 a corresponding member of the Royal Society of Göttingen, but never left his homeland.
Nikolai Lobachevsky married late, at 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.
Lobachevsky's family life was quite consistent with his general mood and his activities. Searching for truth in science, he put truth above all else in life. In the girl he decided to call his wife, he mainly valued honesty, truthfulness and sincerity. They say that before the wedding, the bride and groom gave each other their word of honor to be sincere and kept it. In character, Lobachevsky's wife was a sharp contrast to her husband: Varvara Alekseevna was unusually lively and hot-tempered.
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 great pleasure was studying 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 German his theory of parallels, 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 by the German mathematician, a student of Gauss, Riemann. Studying the properties of spaces in general view 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 was repeatedly confirmed by astronomical observations, as a result of which it became clear that Lobachevsky 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.
Lobachevsky NikolaiIvanovich- great Russian mathematician" Completed by: student... Kaburkina Margarita Nikolaevna Cheboksary 2009 1. BiographyLobachevskyNicholasIvanovichLobachevskyNikolaiIvanovich }