LOBACHEVSKY, NIKOLAY IVANOVICH

born , Dec. 1 [Nov. 20, Old Style], 1792, Nizhny Novgorod, Russia died Feb. 24 [Feb. 12, Old Style], 1856, Kazan Russian mathematician and founder of non-Euclidean geometry, which he developed independently of Jnos Bolyai and Carl Gauss. (Lobachevsky's first publication on this subject was in 1829, Bolyai's in 1832; Gauss never published his ideas on non-Euclidean geometry.) Valentin A. Bazhanov Additional reading A good book for the study of Lobachevsky's geometry, with biographical and bibliographical references, is Roberto Bonola, Non-Euclidean Geometry (1912, reissued 1955; originally published in Italian, 1906). Much biographical and bibliographical information is presented in Alexander Vucinich, Nikolai Ivanovich Lobachevskii: The Man Behind the First Non-Euclidean Geometry, Isis, vol. 53, part 4, no. 174, pp. 465481 (December 1962). Two recent surveys of Lobachevsky's work are A.P. Norden and A.P. Shirokov, The heritage of N.I. Lobachevskii and the activity of Kazan geometers, Russian Mathematical Surveys, 48 (2): 4774 (MarchApril 1993); and V.Ya. Perminov, The Philosophical and Methodological Thought of N.I. Lobachevsky, Philosophia Mathematica: Series III, vol. 5, first third, pp. 320 (February 1997). Valentin A. Bazhanov