1820s–1830sReputable sourceWell documented
Non-Euclidean Geometry
On the timeline · around 1820s–1830s · The Modern Age
What happened
For two thousand years mathematicians had tried in vain to prove Euclid's parallel postulate. In the early 19th century, Gauss, Bolyai, and Lobachevsky realized it could not be proved — and that entirely consistent geometries exist in which it is false, describing curved rather than flat space.
Why it matters
Non-Euclidean geometry shattered the belief that Euclid described the only possible space, freeing mathematics to explore abstract structures — and, decades later, giving Einstein the geometry he needed for general relativity and curved spacetime.