the Greeks had proposed three problems in elementary geometry: with compass and straight-edge to trisect any angle, to construct a cube with a volume twice the volume of a given cube, and to construct a square equal in area to that of a given circle. For more than 2,000 years unsuccessful attempts were made to solve these problems; at last, in the nineteenth century it was proved that the desired constructions are logically impossible.
Ancient Greek mathematicians were amazing. Imagine the kind of stuff they spoke when they got together without realizing they are at cusp of revolutionary advances.
