As a counterpoint I'd like to claim that pen and paper is a massively underrated tool for programming, and furthermore that the parts that you can do on pen and paper are more mathematically interesting than the parts that can't be done without a computer.
Math is a broad field. Of the many branches of math, the one that programmers engage in, is programming. But I've observed that programmers tend to have the same proficiency in general math as anybody else, i.e., most people forget the math that they learned in school.
At the places where I've worked, general math or quantitative problems that go beyond the capabilities of Excel are brought to the "math person."
Nah. Programming is its own thing. Math is lovely and all, but programming isn't applied mathematics any more than playing the cello is applied physics.
Sounds like a case of:
"The math that is "real" to them is just what they happened to learn, the way they learned it"
Programming is doing mathematics, and computers do a great job of enabling one to program.