But the same could be said of math, couldn't it?
So, you see, in mathematics your unconscious assumptions are sometimes wrong, and there's nothing that would tip this off to you, like a compiler. In fact, very few areas of mathematics are the sort where you can easily tell when you're wrong.
I suspect you think of your high school math classes when you think of mathematics. That's really a very poor representative. Mathematics is about proofs, not answers. To be fair, though, the original post makes a similar misconception. Computer programming : computer science :: high school math : mathematics.
Also, this is somewhat unorthodox, but I've read that Godel proposed a new method of doing mathematics based on the experimental method, due to the implications of his incompleteness theorem. If that were the case, then math becomes more like computer science, or perhaps computer science is this new way of doing math.
Absolutely. I don't think the degree is very useful for developing skills at all. I'm sure there are plenty who would disagree, but mathematics courses don't set a very high bar for how much you have to think about a topic. I learned more in the past month preparing for my algebra qual than I did during an entire year of an undergrad class at Northwestern (of course, I drew heavily on the basic knowledge I had).
I'm learning COQ (proof assistant), to make some aspects of it automatically checkable.
The feedback of programming is also encouraging and satisfying, and this makes it more easily self-taught, like a (computer) game. Unit testing builds on this.
PS: My proofs are part of my compsci PhD, which began without any maths; so I choose a supervisor has some knowledge of proofs but isn't very experienced in them. Perhaps more guidance with proofs could really help...? Things are finally coming together for, but I keep stumbling on what I think are extremely elementary proof ideas (e.g. that f(AUB) = f(A) U f(B) ). My feeling is that rigorously understanding takes effort, no matter how good the guidance.
To be a financially successful programmer, you often just need a few books, courage to step outside your comfort zone, and a good idea. There are lots of examples of this, but for me the embodiment is Ken Williams of Sierra fame who made out pretty well, and I don't recall that he had a degree in CS.