[RiderOfGiraffes]

Studying higher math does not automtically mean you miss out on practicality and people skills. Perhaps in your case it did, but a good engineer will be dealing with some of that.

It's important to have a balance - there are infinitely many things that you could advise would be useful, and time is limited. When solving problems it's important not to dive in immediately, but also to ask "What of this has already been done?"

But even then, solving some of the problem first gives an appreciation of what has been done, and often makes you better understand the strengths and limitations of existing solutions. Your example of an IDE is one where re-doing it from scratch is unlikely to give a better result, but Linus re-did the source control idea, and did it better.

[mathgladiator]

That's very true.

Part of the culture of learning higher math however rewards/tolerates esoteric behavior where practicality is just not valued.

I think it is all about related rates. If you are studying abstract algebra now hard-core, then you are missing out on doing some cool Kinect hacks now. Or, you are missing out on chatting up the girls over at the pub.

I found math very ... addicting, and I wish I had learned balance sooner. Instead, I thought it was a lot of fun to sit down every evening and grind on problems from "Berkeley Problems in Mathematics"

[dfox]

In most mathematicians and theoretical physicist I know this tolerance for "esoteric behavior" probably caused exactly opposite effect: they are probably too much sociable and cool.