I come from a country which had a strong Soviet influence, and in school basically we were taught that behind every hard formula lies an intuitive explanation. As otherwise, there’s no way to come up with the formula in the first place.

This statement is not true, there are counter examples I encountered in my university studies but I would say that intuition will get you very far. Einstein was able to come up with special theory of relativity by just manipulating mental models after all. Only when he tried to generalize it, that’s when he hit the limit of the claim I learned in school.

That being said after abandoning intuition, relying on pure mathematical reasoning drives you to a desired place and from there you usually can reason about the theorem in an intuitive way again.

Math in this paper is not that hard to learn, you just need someone to present you the key idea.