It wasn't until the 1920's when Edwin Hubble, thanks to a brilliant idea proposed by Henrietta Swan Leavitt, was able to measure the distance to a Cepheid variable in what was suspected to be either a weird part of the Milky Way, or an altogether different galaxy. The measurements made it clear that the universe was orders of magnitude larger than we had suspected.
Could it, in fact, be infinite? Does space go on forever? Or does it have to have an edge? If it has an edge, what's on the other side? More universe? And if it's infinite, and there are an infinite number of stars, why isn't the night sky as bright as it is during the day?
In the following documentary, Professor Jim Al-Khalili traces the history and the science behind these and other similarly fascinating questions that scientists, especially with the help of brilliant minds like Gauss, Reimann and Einstein, are just beginning to solve.
I would have thought that a finite amount of stars would solve the problem much more easily, but maybe Professor Al-Khalili hasn't heard of Ockham's Razor? :)