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.
