Before Penrose, the chief tool of general relativity was differential equations. They gave detailed predictions, but only for idealized situations. From solving differential equations, it had been known that if a perfectly spherical star collapsed, it would form a black hole.

But no real star is perfectly symmetrical! Solving the exact differential equations for an arbitrarily-shaped star was impossible. One could at best study stars that were almost spherical. Penrose brought a new mathematical tool to bear on this problem - topology.