If you don't see the massive structural difference between the practice of pure mathematics and the practice of software, that means you misunderstand both software development and mathematics.
Programming and mathematics are many things. Sure, it might be hard to see how maintaining a web site has has do with mathematics, but if you need to design a novel algorithm it is worth actually working out the proofs to show that it works (and if you want to publish it in a journal that is often essential).
Computer science is a branch of math, but programming is not. People frequently confuse the two. The difference between using mathematical constructs to inform your engineering and discovering new mathematical constructs is fundamental and the practices do not intersect much at all.
