If you want to do anything cool in science, you gotta learn some math. Here is the bare minimum I think everyone should know.
Classical mechanics
Probability theory, random variables, and statistical inference
Real analysis, limits, continuity, and calculus foundations
Group theory, symmetry, and abstract algebra
Vector spaces, matrices, eigenvalues, and linear transformations
Ordinary and partial differential equations, solutions, and applications
Multivariable calculus, gradients, divergence, curl, and integration