World of Mathematics on Nikolai Ivanovich Lobachevsky
Nikolai Ivanovich Lobachevsky is the first mathematician to publicly publish a system of non-Euclidean geometry. Although Karl Friedrich Gauss preceded him in the late 18th century and János Bolyai had devised a similar (though less analytical) conclusions around the same time, Lobachevsky showed that Euclid's Fifth postulate(also known as the Parallel postulate) could not be proved on the basis of the other postulates, and in turn created a new way of looking at geometry and geometric problems. Most of Lobachevsky's contemporaries scoffed at his conclusions, and he only became credited with his discoveries after his death. In fact, Lobachevsky sought credibility by publishing in different languages, but only a few of his colleagues supported his findings, including Gauss. Lobachevsky also did relevant research in other areas, including infinite series theory, integral calculus, probability, and the approximation of roots of algebraic equations.
Lobachevsky was born on December 1, 1792, in Nizhny Novgorod (known as Gorky from 1932 to 1990), Russia. His father, Ivan Maksimovich Lobachevsky, was a peasant of Polish descent who worked as a clerk in a provincial land-surveying office. His mother was named Praskovia Aleksandrovna Lobachevskaya. Lobachevsky's father died when he was about six or seven, depending on the source, and his mother took him and his two brothers, Alexander and Alexei, to Kazan where he spent the rest of his life. He attended the local Gymnasium on scholarship, then entered the University of Kazan when he was 14. Lobachevsky began his higher education in medicine, but when he began to study mathematics with Johann Bartels (a friend of Gauss), Lobachevsky switched majors. He earned his Master's degree in both mathematics and physics in 1811 or 1812.
Serves University of Kazan in Many Ways
Soon after graduation, in 1814, Lobachevsky joined Kazan's faculty as a lecturer. Later that year, he was promoted to associate professor of mathematics, then became an extraordinary professor in 1816. In these early years, Lobachevsky attempted to deduce the Fifth postulate as a theorem, but he found that he could not make it work. He then started critically analyzing various versions of the postulate.
As Lobachevsky came to his earthshattering non-Euclidean conclusions, he also played a huge role in the development of his University. In 1820, he began administrative duties at Kazan. He served as dean of the mathematics and physics' faculty twice, from 1820 to 1821, then again in 1823 to 1825. In 1822, he became a member of the committee that supervised new building construction on campus and studied architecture to better understand the duties involved. He became the chair of this committee in 1825. Lobachevsky then became the University librarian from 1825 to 1835, and was elected University Rector (equivalent to president) in 1827, a post he held until 1846. His skills in administration did much to improve Kazan, taking it from a chaotic state, and in addition to restoring innovation, raised both academic standards and the faculty's equanimity. Lobachevsky also founded an academic journal Uchenye zapiski("Scientific Memoirs").
In addition to these many administrative duties, Lobachevsky held a full professorship at Kazan from 1823 to 1846 and still found time to accomplish important mathematical progresses. He wrote Geometriya in 1823, in which he outlined his initial ideas that developed into his non-Euclidean geometry. This book remained unpublished as written until 1909, another example of his contemporaries' disregard of his ideas. Still, Lobachevsky described his ideas in a lecture for the Kazan faculty in 1826.
Publishes "Imaginary Geometry" Findings
In 1829, the first complete published account of non-Euclidean geometry appeared in a Kazan-based publication called the Kazan Messenger after the leading scientific journals in Russia declined to print it. In 1837 he published his article "Géométrie imaginaire" ("Imaginary Geometry"), and the most important and full version of his new geometry was published in 1840 as Geometrische Untersuchungen zur Theorie der Parellellinien("Geometric Investigations of the Theory of Parallel Links"). In these articles, Lobachevsky demonstrated that logical possibility of non-Euclidean geometry, which he called "imaginary geometry," as an analogy to imaginary numbers. In particular, Lobachevsky proved that Euclid's Fifth postulate was not a deducible result of the rest of Euclid's postulates.
Lobachevsky did not marry until he was 40 years old in 1832. He married the daughter of an aristocrat, Lady Varvara Aleksivna Moisieva. It was a generally unhappy marriage, and, although she came into the marriage with wealth, their economic situation deteriorated over the rest of Lobachevsky's life.
Lobachevsky also published in other areas of mathematics. In 1834, Lobachevsky devised a way to approximate the roots of algebraic equations. He also published a paper called "Algebra ili ischislenie konechnykh" ("Algebra, or Calculus of Finites"), which concerned the theory of infinite series, and a paper on the convergence of trigonometric series in which he proposed a general definition of a function similar to that later suggested by Peter Gustav Lejeune Dirichlet.
Though much of his work was dismissed in his lifetime, Lobachevsky was given a heredity nobility in 1837. Perhaps this honor was bestowed on him in part for such actions as personally saving lives during the cholera epidemic of 1830.
Forced from the University of Kazan
Despite his valiant actions as administrator, teacher, and citizen of the university, Lobachevsky was relieved of his professorship in 1846. Some sources suggest this event occurred for political reasons. In that year, Lobachevsky became a government official, working in the Kazan educational district as an assistant trustee (or assistant guardian), where he remained until 1855 when he left because of his deteriorating health. Lobachevsky was not limited to his many university activities. He was a longtime member of the Kazan Economic Society, and was interested in agriculture as a hobby, which tied in with the society.
Lobachevsky's last publication of note, Pangéométrie (1855-56) was dictated by him in both French and Russian. (He spent the last years of his life blind or nearly so, because of cataracts.) The title means Pangeometrybecause he rightly thought non-Euclidean geometry had universal characteristics and applications. The text sums up his work in this field.
Receives Acclaim Only After Death
Lobachevsky died in Kazan, on February 24, 1856. After his death, his work continued to be reprinted and translated elsewhere, which helped to spread his work and his reputation. Finally, Lobachevsky was given his due and put in a canon with other scientific greats. In the beginning of a book on his life and work, the author quotes W.K. Clifford: "What Vesalius was to Galen, what Copernicus was to Ptolemy, that was Lobachevsky to Euclid. There is, indeed, a somewhat instructive parallel between the last two cases. Copernicus and Lobachevsky were both of Slavic origin. Each of them has brought about a revolution in scientific ideas so great that it can only be compared with that wrought by the other. And the reason of the transcendent importance of these two changes is that they are changes in the conception of the Cosmos."
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