The Russian mathematician Nikolai Ivanovich Lobachevskii (1792-1856) was one of the first to found an internally consistent system of non-Euclidean geometry. His revolutionary ideas had profound implications for theoretical physics, especially the theory of relativity.

Nikolai Lobachevskii was born on Dec. 2 (N.S.; Nov. 21, O.S.), 1792, in Nizhni Novgorod (now Gorkii) into a poor family of a government official. In 1807 Lobachevskii entered Kazan University to study medicine. However, the following year Johann Martin Bartels, a teacher of pure mathematics, arrived at Kazan University from Germany. He was soon followed by the astronomer J. J. Littrow. Under their instruction, Lobachevskii made a permanent commitment to mathematics and science. He completed his studies at the university in 1811, earning the degree of master of physics and mathematics.

In 1812 Lobachevskii finished his first paper, "The Theory of Elliptical Motion of Heavenly Bodies." Two years later he was appointed assistant professor at, occupying...