What might happen, though, is that the person develops considerable experience and expertise in programming whilst holding a job that isn't about programming. For example, the person could be doing some research work but makes use of programming to solve the problems at hand. Provided she has become competent in programming as a by-product, she can then market herself as a Programmer even though she doesn't have the background in CS or Mathematics.

I think two factors are at work here. Because of the availability of overseas coders, native coders are being expected to meet higher standards. I also think that CYA principles are being applied by HR personnel and managers, i.e. bureaucrats. If they can point to a degree, they can't be faulted. It is rarer and rarer that a boss is a programmer.

That said, I have never had a problem getting a job in either EE or CS-related fields in spite of the fact that my academic career stopped with a BA in Sociology from a mid-range state university. I have been denied the chance a number of times, so degree-consciousness IS a factor at many companies. What I am ranting about is that it should never be a reason not to be proud of one's abilities or to try for a position. IMNSHO, the companies that have hired me have been far better off for doing so, and, yes, I have taken jobs away from degreed programmers several times.

Programming stands much further away from CompSci than Mathematics. Programming has as much to do with CompSci as building telescopes has to do with astronomy.

"... looking for a Programmer with Perl and MySQL experience"

??? Funny how people see different questions. Do I detect a bit of nose-in-the-air, Mr. A-M?

At any rate, abstraction is a discipline in itself, whatever framework/notation one uses.

I was in a 'gifted' program in high school ('73) where I visited with a junior math professor at the university, and we spent Monday afternoons discussing equations and their solutions from both mathematical and algorithmic perspectives. You're correct in that it wasn't about programming.

A more pertinent question would be, "was it useful?" Since the OP's specifics were about a job requiring a degree, it would seem to me that that would be the question to ask. It was useful in that it stretched my brain, but I wouldn't say that I have ever gotten close to that kind of algorithmic expression again.

Which is not to say that I don't value the fields of computer science or math... if you look at my posts, I've repeatedly stated that I have read gobs of both, among other things. What I object to is the blind assumption that someone with an undergrad degree in CS or math (or anything else except perhaps an engineering degree) is going to be better at a {name your specialty} computer-related job than a non-degreed person.

I cannot emphasize enough that most programming jobs ...

That's why we have two separate words for CS and programming.

To be fair, we have two separate words just for Computer Science.

Yoda would agree with Perl design: there is no try{}