<p>pmvd, I would say the “average mathematician” is closer to a genius than to your everyday intellectual. Math majors or graduates (below PhD, and even some PhD’s and professors) are not mathematicians in the usual sense of the word.</p>
<p>And about Fourier transforms - anything can look difficult when you don’t have the background. Which is a reason I see the “math is too theoretical” argument as a little bit questionable. Engineers get fed a lot of math without a rationale. Math majors are not introduced to anything that isn’t defined or proven rigorously, so you understand where mostly everything is coming from. Which makes it a hell of a lot easier to remember, if not outright reproduce.</p>