these might not be 100% complete, but i think this does a reaaalllly good job at capturing the vast majority of mathematics.

i'm sure you could come up with another breakdown, but these also have the benefit of tracking roughly with history. numbers and geometry (euclid), then eventually algebra. probability was a fundamentally new way of looking at the world. analysis comes via newton/leibniz and then dynamics tries to tackle complex systems (kinda where newton left off, e.g., 3-body problem type stuff).

also: dimension reduction is not a bad thing. this is like a decomposition: we can decompose so much of what research mathematics is doing into 6 different basis elements. that's pretty darn neat.

(edit: liebnitz -> leibniz)