| Harvard09, to engineers, math is a tool. For my graduate work, I needed to know how to do tensor calc, tops. A lot of matrix manipulation. The stuff I needed to know how to do, I knew how to do well. Engineers don't need to know math to the degree that math majors know how to do math because there is an exorbitant amount of *other* stuff that engineers have to learn that *math* majors don't. Saying that engineering majors need to be well-versed in mathematical proofs in order to understand what we're doing as engineers is kind of like saying that in order for mathematicians to understand the implications of the math that they're doing, then they need to be well-versed in what engineers do... and if you were, you wouldn't be quite so incensed that we don't know math backwards and forwards!
For your carpenter analogy counterexample, when a house falls down (or when your math falls down) you don't even ask the carpenter what happened. You call in a structural engineering forensicist. Likewise, in the rare case that an engineer encounters math that they (or Mathematica) can't handle, they'll call in a mathematician, who can help out with highly abstract math, which engineers run into probably a few times in a lifetime. That's why we specialize in different things. It's unreasonable to expect an engineer to be highly versed in how to do proofs, since that's not what they're being trained to do. It's not my job to do mathematical research in my engineering field. It's my job to do *engineering* research in my engineering field. There's a lot more to engineering than just math. Rest assured that while we may not know *everything* in math, we know a heck of a lot about engineering.
(To your original statement, I'd have to dredge out my vector calc book, but I'm reasonably sure I could prove that a particular function describes a cone. It wouldn't be pretty, kind of like how my programming's always horribly inefficient... which is another reason why I'm an engineer and not a programmer, and probably ties into the reasons why I'm not a mathematician either... but it'd get the job done. My engineering's at least really pretty.) |