Olbers' paradox (H. Olbers; 1826):
If the Universe is uniform, infinite & unchanging then the whole sky at night would be bright regarding as bright as the Sun. The further you looked out to space, the more stars there would be, and therefore in any direction wherein you looked your line-of-sight would impinge upon a star eventually. The paradox is resolved through the big bang theory, which puts forth that the Universe is dynamic, non-uniform and (probably) finite.