>if/when mathematics provides a complete map to that territory which is "the world",
Then it will encode all the information that exists in the universe. Which will not fit in your head, and thus will not be mathematics. Just because a territory is trivially a map of itself doesn't mean it is useful to call it a map.
>The description of the state of it as it is before us is monstrously large, but the initial conditions and rules might not be.
Reality isn't just the initial rules. It has state. That state must be described for you to have a complete description of reality. Yes, we could mathematically describe the complete laws of nature. But reality is necessarily more than just that, because the state is really damn relevant. You can't just ignore it because it doesn't fit your argument.
If reality is deterministic, then all the state is derivable from the rules and the initial state, and it's possible we could figure out the rules and initial state and become relatively sure of them. (We probably wouldn't be able to calculate the future, since evaluating the rules within reality probably necessarily takes more steps than reality takes during that time. But we might be able to calculate enough to see that it matches up with what we think the early universe must have looked like. We might notice that even the smallest of tweaks to the rules or initial state creates an avalanche of changes that doesn't line up with what we believe the early universe looked like, so we can be sure there are no free parameters.) It's fully possible that the rules and initial state could fit in someone's head. They might be ridiculously simple, like Conway's game of life in a few more dimensions.
(If you think "reality can't be deterministic because true randomness or quantum events exist", well you can fit true randomness into a deterministic theory by having the world branch of every random event outcome. The Many-Worlds Interpretation could be viewed as doing something like this for quantum events; it's a deterministic theory.)
I am not at all! We do math with symbols and diagrams, but those symbols and diagrams are about something: they are maps, and there is a territory that they are about. When I say "math", I include the concepts, not just the symbolic, graphical and other representations.
So what I'm saying is that if/when mathematics provides a complete map to that territory which is "the world", that territory must then be made of exactly the same stuff as other described-by-math territory-entities like "ellipse", "pi", "finite field", "Hilbert space", ... the map of mathematics doesn't describe any other kind of territory.
I'm not saying that the symbols and pictures used to carry out math (the "maps") are the world.
> you will never find a complete description of the entire universe that fits in a network of human brains
The description of the state of it as it is before us is monstrously large, but the initial conditions and rules might not be. E.g. the Mandelbrot set is just iterating on z^2 + c for various c. To describe isn't necessarily to evaluate.