To do theoretical physics, you're gonna need to know at least Abstract Algebra, Lie Groups/Algebras, Topology, Complex Analysis and Differential Geometry.

Do theories use math?

The explanations (if they are really explanations) are mathematical explanations (as opposed to physical explanations). ... It is then possible (since actual) to give wholly mathematical explanations for physical theories and, as a special case, wholly mathematical explanations for physical phenomena.

What kind of math do theoretical physicists use?

A strong mastery of basic high-school level algebra, trigonometry, analytic and synthetic geometry, and single-variable calculus is required at the very least if one wishes to do serious research in the physical sciences.