>Hmm, that's completely different from my experience in mechanical engineering school. We were always complaining we were taking more math than we needed to know to get the job done. But our profs said we needed to understand how the formulas were arrived at, so we would have faith in them - in many cases lives are at stake.

It could be just the professors there going for quantity instead of quality, i.e. stuffing more material than they have the time for. And then I've accidentally leafed through some of their math books, which is where I got that impression. They did have some places where logic was skipped, approximations were used without a proper explanation (which I hated in the physics course - just how can they replace sin(x) with x in a pendulum, out of the blue?).

>One summer job, shortly after spring exams I was working at a semi-remote fishing resort. This was 1979, no Internet, no TV nor VCR/videotapes. One day, someone idly wondered how much the 500m hill behind the resort weighed. Everyone looked at me, I said "No problem, it's roughly coned-shaped, I'll just use the formula for the volume of a cone". Except I couldn't remember that formula.

Some guys on that mechanical engineering sat a whole day to calculate the amount of work required for pressing an h on a mechanical typewriter.