I am occasionally astounded how nodes in PM align with things I have been pondering in my day-to-day life.
This node is an excellent example of that alignment.
Just yesterday I was discussing some of our Perl programming for our work and we were both quietly (and somewhat conspiratorially) noting that we both occasionally need to "geek out"...I tend to "geek out" with my fascination for Perl and all that it can do, he "geeks out" on learning new things that apply to our work...e.g., the mathematics behind Convolutional encoding of communication transmission.
My background was in Math and Physics (in school); his is electrical engineering. We are close friends and continually provide mutually-reinforcing challenges to each other. It turns out that Perl is a strong backbone of that friendship. He learned Perl several years before I undertook it; I watched him using it and we talked a lot about it and I "caught the bug."
What we both experience with Perl is that it is both powerful and easy. He tends to stick with the basics and crafts Perl into some outstanding applications and tools. I am attracted to its intrace twists and twirls and craft applications and tools.
What we have both found is that inspite of programming experience with quite a few other languages, Perl has never ceased to provide all the power and capability that we need. We use if for testing and exploring the behavior and performance of spacecraft and for a lot of space mission supporting activities (e.g., simulating navigation, guidance and control schemes, testing new ideas or exercising existing ideas in a variety of space mission challenges, and simulating both environmental influences on spacecraft and the spacecrafts' reaction to various influences.
The nature of our work results in a non-stop need to grow and learn...especially mathematically. So, between the two of us, we are almost always in positive-feedback loop of mathematical interests and testing our knowledge of what we understand and have learned.
Perl is such a powerful catalyst for our learning and growth...both in terms of providing such a rich environment for trying ideas and testing our understanding and as a medium in which we can translate the knowledge into real-world applications and tools.
I think that, at least for me, I had a strong mathematical background coming out of college; but I have also found that rarely did any of the organization of mathematics and mathematical knowledge in college, prepare me well for how to find the mathematics we often need to accomplish work. I had a lot of theory and the organization of the "learning" in college was topically motivated rather than "you've got a problem, how do you find the math to solve it". This is especially notable in my work where almost every problem is not redicible to a single mathematical solution...it requires blending, meshing, and sometimes abstracting to bring the right mathematics to bear.
So I would have to say that, in my case, the mathematics I was taught in college prepared me well in the sense of having seen and understood the theory, but ill-prepared me for how to wade through the morass of theory to find solutions to my day-to-day problems.
I don't have a formal CS background, so there isn't much I can add in terms of your interesting inquiries. When I went to graduate school they did not have (at least at my college) an formal courses in *any* aspects of CS. The closest was to study electrical engineering where we at least got to see, build, design, and work with computers. So, over the years, I have to try to self-educate myself on topics that for most of today's graduates I would presume is almost second nature. Of course now I've truly place myself into the dinosaur era! ;-)
My friend and I, yesterday, were musing over almost the exact topic that you inquired about. Deja Vu all over again (as some brilliant person once noted)!