The vast majority of people that design and write rigorously formal systems to express complex real world ideas and behaviours are programmers.
They are rigorous, not in the sense that anything is ever proven about their formal systems, but in the sense that they are interpreted rigorously as to their formal consequences by computers. This is really different to how I as a physicist might use equations to express ideas to other physicists, and if I can't exactly formalize what the equation means that isn't always relevant.
This is of course an unorthodox way to frame what programmers do, but I think it's relevant to your last comment. What is a good foundation for formal systems is an empirical question, and empirically, type theory is extremely important to programmers. Set theory not at all.
They are rigorous, not in the sense that anything is ever proven about their formal systems, but in the sense that they are interpreted rigorously as to their formal consequences by computers. This is really different to how I as a physicist might use equations to express ideas to other physicists, and if I can't exactly formalize what the equation means that isn't always relevant.
This is of course an unorthodox way to frame what programmers do, but I think it's relevant to your last comment. What is a good foundation for formal systems is an empirical question, and empirically, type theory is extremely important to programmers. Set theory not at all.