Lobachevsky, Nikolai Ivanovich (nyĭkəlĪˈ ēväˈnəvĭch ləbəchĕfˈskē) [key], 1793–1856, Russian mathematician. A pioneer in non-Euclidean geometry, he challenged Euclid's fifth postulate that one and only one line parallel to a given line can be drawn through a fixed point external to the line; he developed, independently of János Bolyai, a self-consistent system of geometry (hyperbolic geometry) in which that postulate was replaced by one allowing more than one parallel through the fixed point. Lobachevsky first announced his system in 1826; he subsequently wrote several expositions of it, including Geometrical Researches on the Theory of Parallels (originally pub. 1840 in German; tr. 1891, 1914), and a statement of his completed work, Pangéométrie (issued 1855 in Russian and French). A graduate of the Univ. of Kazan, he remained there as teacher (1812), professor (1816), and rector (1827). Despite his efficient and devoted service, in 1846 he was relieved by the government of his posts of professor and rector.