These are non-Euclidean . Carl Friedrich Gauss , JÃ nos Bolyai , and Nikolai Ivanovich Lobachevsky were some people that developed such geometries . 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 .