Roger Penrose, in 1965. He used the way light cones behave in general relativity, and the fact that gravity is always attractive, to show that a star that collapses under its own gravity is trapped in a region whose boundary eventually shrinks to zero size. This means that all the matter in the star will be compressed into a region of zero volume, so the density of matter and the curvature of space-time become infinite. In other words, one has a singularity contained within a region of space-time known as a black hole.
