How important is knowing how to program for TCS?

Coming from a more mathematical background, I never really learned how to code. I am starting a PhD in TCS and many people were surprised by how little I knew about programming (and about computer in general). I can write algorithms in pseudo-code, but I don't really know any programming language. I can imagine that someday I may have to implement some algorithms for my work, but then can I wait for this moment? Or is there something more? How important is knowing how to code in TCS (in fields where programming is not directly involved)? Are there reasons which could bring a CS theorist (for example) to know how to code? Is it worth spending a lot of time learning how to code? And if there are, is there a category (functional, imperative, object-oriented...) of programming language that would be more suited?