Quite a random guy here. 90% an engineer (Electrical Power Engineering student) and 10% a physicist. My favorite formula in mathematics:

$\int_{0}^{\infty}x^{-x}\ dx=1.9954...$

Favorite quote from mathematics:

In the theory of probability generating functions have been used since DeMoivre and Laplace, but the power and the possibilities of the method are rarely fully utilized.

(William Feller)