Non-Euclidean Geometry

Lobachevsky, Bolyai and Riemann show that geometry also works on curved spaces, later the language of relativity.

For two thousand years Euclid's parallel postulate was considered untouchable. Gauss, Lobachevsky (1829) and Bolyai showed that consistent geometries exist in which it fails. Riemann generalized this to arbitrarily curved spaces in 1854, and Einstein needed exactly this mathematics for general relativity.