But there is a whole world between being able to do the math necessary to rotate a 3D vector in a 4D space and the proof of the Poincaré-conjecture.
Also a plumber doesn't need to be able to do the math of the Chapman-Kolmogorov equation to find out when the laminar flow in a water tube turns chaotic. But he should know that changing one parameter (e.g. the length of the tube or the diameter or the flowing speed) will move the limit and can turn the actual flow back to laminar, even though he's not able to write down all the integrals.
So yes, knowing math is fine for programming, and there are many task in programming which require some special knowledge about some obscure math problem and its solutions, but it is not necessary to study the whole field of mathematics surrounding that math problem, nor is it necessary to be able to solve the math problem on your own.