Lobachevsky was born at Nizhny Novgorod in Russia. Throughout his life he was associated with the University of Kazan; he was a student there and held various posts, including the chair in mathematics and finally the rectorship. Later he was deprived of his position for political reasons.

Lobachevsky's fame is due to his epoch-making discovery, announced in 1826 and published in 1829, that there could be consistent systems of geometry based on other postulates than those of Euclid. In particular Lobachevsky constructed and studied a type of geometry in which Euclid's parallel postulate is false (the postulate states that through a point not on a certain line only one line can be drawn not meeting the first line). Janós Bolyai had, at the same time though quite independently, come to a similar result and the same discovery had in fact been made decades earlier by Karl Friedrich Gauss, but he never published his work.

For centuries the status of Euclid's geometry and in particular of his parallel postulate had been a matter of controversy. Attempts had been made to show that it followed from the other axioms and it was widely held that Euclid's geometry described the necessary structure of space. By revealing the coherence of a non-Euclidean geometry Lobachevsky showed that Euclidean geometry has no such privileged position, helped mathematicians to break free from undue reliance on intuition, and paved the way for the systematic study of different kinds of non-Euclidean geometry in the work of Bernhard Riemann and Felix Klein.

Although it was not well received at first the value of Lobachevsky's work was fully appreciated once Riemann began his investigations into the fundamental concepts of geometry. Perhaps his fullest vindication came with the advent of Einstein's theory of relativity when it was demonstrated experimentally that the geometry of space is not described by Euclid's geometry.

Apart from geometry, Lobachevsky also did important work in the theory of infinite series, algebraic equations, integral calculus, and probabilty.