Economics, for instance, has been stuck since Marshall[1] in Newton's method of fluxions/ Liebnitz calculus. (Well, their elaborations perhaps. And leavened with a little game theory. Probability and statistics have contributed nothing significant to the core theory.)

Economics has been crying out for a better mathematical foundation since the 1960s at least.

1. https://en.wikipedia.org/wiki/Principles_of_Economics_(Marsh...