The more complex mathematics appears, the more it is just simplifying otherwise very complicated compounds of algebraic functions.
For instance, calculus is actually a simplification of maths. It takes algebra to new heights without having to constantly do algebra to algebra every step of the way just to get one solution set. Calculus eliminates a lot of tedium.
One example of a sophisticated process, that is at its heart simplifying, is a Fourier transform. It is a simplification of chaotic waves combined in an indecipherable (to algebra) wave function, into a group of individualized functions as fundamental frequencies. In essence, it teases out one trigonometric function from a group of combined trig functions. It’s simply complex!