At the Austrian Institute of Advanced studies there was a professor that got real good at stochastic differential equations and made a career out of applying them to anything and all in economics. One big advantage was that almost no other economist can actually follow it. Those few that can are obviously super invested in the technique

Stochastic differential equations is fundamental knowledge to do option pricing (black-scholes) among other things. I would expect an average guy educated in that field to be able to understand

In functional analysis, it is somewhat of a sport to attach indices to all four corners of a symbol. I remember overhearing a discussion between two big players in the field, and they obviously did not share the same starting point for reading the indices out loud. For sure, I didn't understand what they were talking about, but neither did they.