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Nikolai Ivanovich Lobachevskii

Lobachevskii was a Russian mathematician who had little influential impact on the mathematical world. He published a few works that included some papers that were about the fifth postulate and his ideas of geometry.Nikolai was born on December 1, 1792 in Nizhny Novgorod, Russia. Later in his life he would move to Kazan , Russia. He would die on February 24, 1856. Nikolai's fatherIvan Maksimovich Lobachevskii, worked as a clerk in an office which was involved in land surveying while Nikolai Ivanovich's mother was Praskovia Alexandrovna Lobachevskaya. Nikolai Ivanovich was one of three sons in this poor family. When Nikolai Ivanovich was seven years of age his father died and, in 1800, his mother moved with her three sons to the city of Kazan in western Russia on the edge of Siberia. There the boys attended Kazan Gymnasium, financed by government scholarships, with Nikolai Ivanovich entering the school in 1802. In 1807 Lobachevskii graduated from the Gymnasium and entered Kazan University as a free student. Kazan State University had been founded in 1804, the result of one of the many reforms of the emperor Alexander I, and it opened in the following year, only two years before Lobachevskii began his undergraduate career. His original intention was to study medicine but he changed to study a broad scientific course involving mathematics and physics.Lobachevskii received a Master's Degree in physics and mathematics in 1811. In 1814 he was appointed to a lectureship and in 1816 he became an extraordinary professor. In 1822 he was appointed as a full professor. The University of Kazan flourished while Lobachevskii was rector, and this was largely due to his influence. There was a vigorous programme of new building with a library, an astronomical observatory, new medical facilities, and physics, chemistry, and anatomy laboratories being constructed. He pressed strongly for higher levels of scientific research and he equally encouraged research in the arts, particularly developing a leading centre for Oriental Studies. There was a marked increase in the number of students and Lobachevskii invested much effort in raising not only the standards of education in the university, but also in the local schools. His major work, Geometriya completed in 1823, was not published in its original form until 1909. On 11 February 1826, in the session of the Department of Physico-Mathematical Sciences at Kazan University, Lobachevskii requested that his work about a new geometry was heard and his paper A concise outline of the foundations of geometry was sent to referees. The text of this paper has not survived but the ideas were incorporated, perhaps in a modified form, in Lobachevskii's first publication on hyperbolic geometry. He published this work on non-euclidean geometry, the first account of the subject to appear in print, in 1929. It was published in the Kazan Messenger but rejected by Ostrogradski when it was submitted for publication in the St Petersburg Academy of Sciences. The story of how Lobachevskii's hyperbolic geometry came to be accepted is a complex one and this biography is not the place in which to go into details, but we shall note the main events. In 1866, ten years after Lobachevskii's death, HoûÄl published a French translation of Lobachevskii's Geometrische Untersuchungen together with some of Gauss's correspondence on non-euclidean geometry. Beltrami, in 1868, gave a concrete realisation of Lobachevskii's geometry. Weierstrass led a seminar on Lobachevskii's geometry in 1870 which was attended by Klein and, two years later, after Klein and Lie had discussed these new generalisations of geometry in Paris, Klein produced his general view of geometry as the properties invariant under the action of some group of transformations in the Erlanger Programm. There were two further major contributions to Lobachevskii's geometry by PoincarêÂin 1882 and 1887. Perhaps these finally mark the acceptance of Lobachevskii's ideas which would eventually be seen as vital steps in freeing the thinking of mathematicians so that relativity theory had a natural mathematical foundation. BY MIGUEL MACARENO