> Mathematics and programming are not really all that related to each other

I may be wrong but I believe the Curry-Howard correspondence disproves your claim. One can translate between the two and find that they are equivalent.

The difficulty is that some programming languages are hard to model mathematically due to the way they were designed and implemented. Some, like Idris or Agda, make it easy to see the correspondences. Others like C or Javascript are harder.

The key to solving hard problems is being able to think concretely in abstractions. The best language we have for abstraction is pure mathematics.