My sense of this mapping is that it only exists for a small subset of mathematics. It might be the case that you're only interested in learning math insofar as it has practical applications (relevant to some technical field), but most higher-level mathematics (topology, analysis, algebra, logic) have an unclear relation to technical fields, i.e. there are fields that use concepts drawn from those subject areas but have no 1-1 connection as there might be for mechanics/calculus.

I'm not aware of any such mapping, but just off the top of my head:

economics: calculus, optimization problems, probability theory

computer science: computability theory, complexity theory

physics: calculus, differential equations

It might also be useful to go through a course catalog to familiarize yourself with the existence of various technical fields/mathematics. You *might* be able to explicitly trace dependencies to figure out what the connected fields are, but I don't expect this to work in general. Caltech's course catalog can be located: catalog.caltech.edu/documents/3199/caltech_catalog-1819.pdf

My sense is that if you want to learn math so you can *do* stuff with it, you should learn slightly more than the minimum amount required to be able to do what you want. Anything else is probably wasted effort. I consider most of the value of the amount of math I've learned to be in making my brain into a different shape and giving me more abstractions than any concrete knowledge I now possess; it's not clear to me what I can do now that I couldn't do before, but it is clear that I can think about problems from more angles.

If it is interesting to you, the level hierarchy for mathematics in my brain looks something like:

Level 1: calculus, probability/statistics, linear algebra, number theory

Level 1.5: differential equations [technically a subfield of calculus, but it's usually split off because it involves a bunch of techniques] [aka an entire class on "how to solve fewer differential equations using more time than Mathematica"]

Level 2: abstract algebra, analysis [with probability as a subfield], topology, logic + intuitive set theory (model theory?) [technically, this contains computability theory and complexity theory as a subfield, but it's pretty independent] [technically, category theory also lives here]

Level 3: algebraic topology, algebraic number theory, descriptive set theory, even abstracter algebra, topology but like weirder, logic but you chart the implications of various assumptions in excruciating detail, <things that combine 2 or more things for level 2>, <things that build on level 2 things more deeply>

Level 4: this is too far above my current level to even figure out what's happening. I have a fairly strong belief that the value of math starts to rapidly diminish the higher the "level" and that this level is almost completely aesthetic.

This was a helpful answer. Thank you!