And, let's not forget, the mathematical prowess of a civilization determines how fast other knowledge fields advance.
What do you mean by that statement?
If the math is already done, you don't have to wait for mathematicians to solve certain types of problems in order to progress through those fields. And with sufficient mathematical background, one can go through the implications of an hypothesis much quicker. Hence, mathematical prowess is one of the indicators of how fast one can advance in relevant fields. I didn't mean to imply it was the only one, if that's what you are suggesting.
As a practical example, the math behind black holes was mostly done by the time physicists proposed their existence.
Also, regarding "theoretical" vs "practical" knowledge, it's kind of pointless to make that distinction. Specially when most research can be dependent on its results to see which is which. As an example, there's the computer science problem of
P vs NP. If the answer is P != NP, then the practical application of this doesn't seem to be much (at least compared with the alternative), and it's what most researchers lean towards. However if the answer is P = NP...