Engineer comes from ingenius or genius, the one who generates, invents. Most to all of the engineers I have met in my life are mere calculators, equipped with some knowledge about finite element method and such. What they lack in general is intuition, the female part of life.
Probably one of the reasons I ended up in the rubber industry. The most advanced math I do anymore is multiplication and division (usually just by 25.4 anyway...)
Rubber design is kind of a dark art, you either have a grasp of what's going on or you don't. Once the arcane incantations are uttered, the part goes out into the field and we see what happens. A customer once asked me to do FEA and I told her that it can't possibly tell you anything you don't already know because of the degree you need to babysit it and ensure that the non-linear effects come out the way they should. Maybe it makes a cleaner presentation to management, that'd be the upside.
That said, there are a lot of good solutions out there already, our company probably sends a dozen jobs out the door for each one that even comes near my desk, but the ones that I end up getting stuck in on are often some really oddball stuff, and I wouldn't have it any other way.