I can readily believe that they're (currently working as) programmers, but where do you get "not mathematicians" from? If you're spending 8 hours a day writing

I can readily believe that they're (currently working as) programmers, but where do you get "not mathematicians" from? If you're spending 8 hours a day writing mathematical code and understand the mathematics, then in my book you're being both a programmer and a mathematician. Incidentally, my experience is that plenty of people who are programmers are ashamed of a lot of their code too, at least in the sense that they wouldn't want anyone else reading it and judging them. Writing code that looks good as well as getting the job done is hard, whoever's doing it, and it's by no means always worth the effort.