Mathematics? Nope. I use the trigonometric functions like sin(x) to draw nice graphics in my spare time but I never use them at work. I used logarithmic last year to round a number but that’s about it. Add, multiply, subtract and divide is all the math that I ever do and most of that is “x = x + 1”. If I have to do statistics, I use a library. No need to find the maximum of a list of values myself.
So what do we do? Really?
We translate mumble into Programming Language of the Year(TM).
Or more diplomatic: We try to translate the raw and unpolished rambling of clients into the strict and unforgiving rules of a programming language.
We’re translators. Like those people who translate between human languages. We know all the little tricks how to express ourselves and what you can and can’t easily express. After a while, we can distinguish between badly written code and the other kind, just like an experienced journalist.