What a coincidence that this post popped just when I have been dealing with an integral that resulted in a special function. Erf(x) in this case, if anyone was interested. Didn't like the look of resulting mess (Erf with imaginary arguments) and decided to go straight to numerical integration. But as a general rule, integrals of weighted Gaussians don't turn out to be nice... [Mutter] Stupid exp(-x^2). [/Mutter]
No, I didn't find the clip amusing either.
I guess it goes down to differences between people, I know a bunch of people who cannot solve a linear equation on paper, but it really doesn't affect their lives either. Although, they might be really quick to answer such questions as "Considering a drink that costs 5€ in a bar, do I have money to buy a round for my buddies or not?" which is actually not that far from solving the equation itself...
It probably goes down to the fact that life rarely throws you an equation and asks you to solve it, but deals with above kind of questions. Maths itself is an abstract product of mind, and actually differs radically from equation solving, which unfortunately is an image one tends to get from schools before University. It is not uncommon that Physicists and Engineers are actually a lot better at solving equations (Calculus) than Mathematicians themselves, but it is the Mathematicians who first research the problem and check if it can be solved at all, and what methods can be used.
