This happened to me (math background, now write software), so I decided to fix it : I read most of the classic textbooks over the course of a few years, and tried to apply what I learned in them at my day job (provided that it was useful to my company obviously). Three things happened :

- I got a lot better at my job because my toolbox was a lot bigger

- I developed a much 'broader' view of the field, which became unified instead of a collection of subfields

- I realized that there was even more that I didn't know about, and that I should keep reading !