It would have saved me a ton of frustration and wasted effort if it were a lot less than currently. In high school I remember hating math - it was obvious some people were far better at grinding through computations than I could ever hope to be, and it made me resentful being forced to go through what seemed a pointless exercise.

In university I made a late switch to computer science, and took real analysis thinking it would be very painful, but would make up for having no calculus. I actually enjoyed so much I switched to math, and so did sort of a math crash course over a year to prepare for grad school. Some of the math was hell. Studying differential equations, complex variables (computation oriented), and bits of differential geometry, etc. would leave me with so frustrated, wondering why I was putting myself through this. On the other hand, measure theory, complex analysis, functional analysis, algebra, and galois theory were so illuminating. I could just sit there for hours working through proofs, and not burn out.

However, this would not work for everyone (or most even). It shocked me that everyone else didn't see it my way, so it was very interesting observing how others studied/thought about math. I had a friend in all my pure math classes whom I worked on assignments with. He was a computational wizard who could flawlessly plow through pages of computations. My rate of errors - flipping a sign, carelessly misapplying a rule, etc. - was so much higher than his I had to conclude our brains were just wired in a totally different way. I noticed, when trying to prove something, we'd proceed very differently. He'd take what he knew to be true, and just begin enumerating some logical consequences of that, and go in the direction which seemed to have the smallest blowup in data. I'd usually assume the statement was false, and think and think and think about why that would be so absurd. Then, when I came up with the abstract explanation in my mind, in my mind I'd shape it into something concrete enough to write down (or even describe).

I identify a lot with the mathematician Alexander Grothendieck (at least before he became a little eccentric), because he's one of the rare examples (I know of) of an outstanding mathematician who seems to have approached math the way I do, and derives value from it for similar reasons. AG was reknowned for thinking about math in an extremely abstract way: many people learn by taking specific examples and then playing around with them mechanically until they get a general 'feel' for what's going on. Instead AG would describe the phenomenon being observed in the most abstract and general way possible, sometimes building an entire new theory of which the solution to the original problem was merely a trivial consequence.

Here is a two part piece biographical essay that, regardless of your interest in math, you'll probably find very interesting. He led an extraordinary life:

http://www.ams.org/notices/200409/fea-grothendieck-part1.pdf

http://www.scribd.com/doc/35435936/As-If-Summoned-from-the-V...

EDIT: Hmm, I sort of went off on a general rant instead of making the point I intended (this tiny text field makes that so easy, haha). I wanted to point out it's a common distinction in math made between the "problem solvers" and the "theory builders" (AG, mentioned above, epitomizes the latter). Most subjects in pure math are populated by people in one field or the other, and I believe that by forcing a computational approach on people early in their development, you're completely turning people off of math who could have fallen in love with the abstract theory. How prevalent this is, I don't know.