Lobachevsky

Nikolai Ivanovich Lobachevsky (1792–1856) was a Russian mathematician renowned for founding non-Euclidean geometry, in particular the branch now known as hyperbolic geometry. He was born in the Nizhny Novgorod region of the Russian Empire and spent most of his career at Kazan University, where he rose to the position of professor of mathematics.

Lobachevsky is best known for his work on the parallel postulate. In the 1820s and 1830s he developed a coherent geometric system in which Euclid’s fifth postulate is replaced by an alternative: through a given point not on a line, there exist infinitely many lines that do not meet the original line. This work demonstrated that consistent geometries other than Euclidean could describe space, laying the foundations for what is now called Lobachevsky geometry or hyperbolic geometry. He also derived trigonometric relations and geometric methods appropriate to spaces of constant negative curvature and proposed models in which these geometries could be realized, helping to translate abstract axioms into concrete constructions.

Despite initial skepticism, Lobachevsky’s ideas influenced contemporaries and subsequent generations, contributing to the broader 19th-century expansion of geometry. His work, alongside that of Bolyai and Gauss, helped reshape the understanding of space and laid important groundwork for future developments in differential geometry and mathematical physics.

See also: hyperbolic geometry, Lobachevsky plane, Lobachevsky function.