What does random mean? Are you asking why the universe appears to be consistent and intelligible at all? Where would we be if it weren’t?

The weak anthropic principle covers this nicely. Perhaps it is an unsatisfying answer, but scientists and mathematicians aren’t usually in the business of answering ontological questions.

Maybe a good place to start thinking about this problem would be to read Wigner's work "The Unreasonable Effectiveness of Mathematics in the Natural Sciences".

I have studied all of this. Wigner’s account is very important for the debates it inspired but it’s far from the last word on the topic. There have been numerous replies addressing all of Wigner’s claims. Try reading Hamming’s replies to start.