Original: The century's most significant development in geometry occurred when, around 1830, JÃ nos Bolyai and Nikolai Ivanovich Lobachevsky separately published work on non-Euclidean geometry, in which the parallel postulate is not valid.
Simplified: These are non-Euclidean. Carl Friedrich Gauss, JÃ nos Bolyai, and Nikolai Ivanovich Lobachevsky were some people that developed such geometries.