Other examples include quantum mechanics, Fourier analysis(I'm a speaker buff, so yeah), actuarial science(insurance and so forth), statistics(this one is HUGE).

A lot of great discoveries are made when someone makes a crazy claim, someone else formulates it mathematically and makes predictions with it, and then it's tested and proven. Schrodinger wasn't proud of his now famous equation. The 'poisson' spot in diffraction was an attempt by Poisson to discredit Fresnel wave theory of light. Einstein developed a lot of the ideas used in QM, yet didn't take it seriously enough.