[mcphage]

We spend years learning "spelling", because the mathematical equivalent (arithmetic, up through calculus, linear algebra, differential equations, discrete math, etc) is incredibly valuable on its own—and that that value doesn't really require familiarity with the proof-based foundations underpinning it. Learning real analysis is valuable if you're going to be a mathematician, but as an engineer it won't help you get more out of calculus (at least, not compared to the cost of learning it).

[paxcoder]

I believe you have adopted your opinion of what should go into the first set of brackets of yours.

An engineer is expected to allot too much time to math to turn out unfamiliar with it. I think we should spend less effort on practicing cleaning fish and more on learning to forage for fish.

[mcphage]

> I believe you have adopted your opinion of what should go into the first set of brackets of yours.

I'm not really sure what you mean by that.

Certainly I'm not of the opinion that proof-based math is useless; I studied math in grad school, and stayed as far away from anything applied as I could. But I don't think it offers much value to engineers or scientists. Let mathematicians establish the foundations, and let scientists and engineers build on top of that. They're different skill sets, with different goals.