When I first saw integration techniques in calculus, I thought they were a waste of time because software packages could do any integral I could do by hand. Besides, you can always just use Simpson’s rule to compute integrals numerically.

In short, I thought symbolic integration was useless and numerical integration was trivial. Of course **I was wrong on both accounts**. I’ve solved numerous problems at work by being able compute an integral in closed form, and I’ve had a lot of fun cracking challenging numerical integration problems.

Many of the things I thought were impractical when I was in college have turned out to be very practical. And many things I thought would be supremely useful I have yet to apply. Paying too much attention to what is “practical” can be self-defeating. Pragmatism is impractical.