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Lobachevsky published the first account of non-Euclidean geometry to appear in print.
When Lobachevsky was seven his father died and the family moved to Kazan on the edge of Siberia. Lobachevsky received a public scholarship to attend school and then entered Kazan University as a free student. He was going to study medicine. At Kazan he was taught by Johann Bartels, who had taught Gauss. A skilled teacher, Bartels soon interested Lobachevsky in mathematics. He received a Master's Degree in physics and mathematics in 1811. In 1814 he was appointed to a lectureship and in 1816 he became a professor.
His major work, Geometriya , completed in 1823, was not published in its original form until 1909. In 1829 he published his non-Euclidean geometry, the first account of the subject to appear in print. It was published in the Kazan Messenger but rejected by Ostrogradski when it was submitted for publication in the St Petersburg Academy of Sciences.
In 1834 he found a method for the approximation of the roots of algebraic equations. In 1837 he published his article Géométrie imaginaire and a summary of his new geometry Geometrische Untersuchungen zur Theorie der Parellellinien was published in Berlin in 1840. This last publication greatly impressed Gauss.
Since Euclid work, mathematicians had been trying to deduce Euclid's fifth postulate as a theorem. It states that given a line and a point not on the line, a unique line can be drawn through the point parallel to the given line. Lobachevsky did not try to prove this postulate as a theorem. Instead he studied geometry in which the fifth postulate does not necessarily hold. Lobachevsky categorised euclidean as a special case of this more general geometry.
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