You say that as if it's a given you can only do one or the other. FWIW, I'm a pure mathematician by training - not exactly a shortage of experience in thinking

You say that as if it's a given you can only do one or the other. FWIW, I'm a pure mathematician by training - not exactly a shortage of experience in thinking things through. But I would have very low confidence in any code I had just written down, instead of building it iteratively, using a REPL.