The most famous example is probably Euclid's Fifth Postulate, aka the Parallel Postulate, which states that given a line and a point, there's a single line thro

The most famous example is probably Euclid's Fifth Postulate, aka the Parallel Postulate, which states that given a line and a point, there's a single line through the point parallel to the first line. http://en.wikipedia.org/wiki/Parallel_postulate http://en.wikipedia.org/wiki/Parallel_postulate For 2000 years, it was conjectured that it followed from Euclid's other postulate. Lobachevsky, however, disproved it. (As with many 19th Century results, there are questions of precedence -- in part because Gauss claimed to have thought of everything first himself -- but his name is most commonly attached to the result.) Riemannian Geometry depends on the Parallel Postulate being false. General Relavity depends upon Riemannian Geometry.