What is it like to sit in your office, do advanced math with real?
I managed a group composed of individuals who did just what you describe. I was chosen to run the group because I was presumed to understand their clients, not their math. (If I could understand what they were going to tell a client, presumably so could the client) The math was kinematics, applied probability, finite element analysis, monte carlo, statics and dynamics. Here is how that Math Newsletter from the University of Rochester describes what one of theirs did for us: "For three years she worked in applied probability (a subject unrelated to her thesis,) .... About nine years ago, the company was concerned that it was taking too long to turn good ideas into viable products. She determined that a major part of the problem was that engineers were not able to deal with variability. All components of and inputs to a system vary somewhat from the norm, and this is the primary cause of failures. A system designed to be fail safe ends up being "overdesigned," so that it is much more costly than it needs to be."Jean Parks joins faculty (this blurb would get pained looks from our engineers. It is none the less presumably how a mathematician described it to other muggles) Alas, this group is no longer needed but the companies from which the specialists came included: Boeing, US Steel, IBM. I would think that today, getting yourself noticed by the right potential employers would be the hard part. User-11089291636160371577 described a position with a different kind of subject domain. Your comment implied a narrow interpretation of your personal skill set. Understanding the basics of Black-Scholes for example is not that hard. It only gets complicated when trying to extend the technique to Levy-Stable distributions and the like. Similarly math applications to engineering problems may require a modicum of cramming to absorb the terminology and basics but once the links are established, powerful math can provide extremely useful solutions to problems the clients did not even know they could solve.