A couple of weeks ago a teacher of mine (I'm taking mathematics) was giving a final inspiring lecture about how fundamental Math is to every possible universe. During the lecture though, he said that what the current physics theories tell us is that the Universe originated from a point. Not a really small point, but an actual mathematical point, one with 0 dimensions. I've heard the concept of a singularity before, but even in theory, can it happen in Nature?
EDIT: My question is not the same as Did the Big Bang happen at a point?. I'm not interested in how the Universe expanded, I want to know if the Universe was compressed into an actual point.