Well it's not a spectrum really, you need a mix to do anything. Scientists need developers (or need to be developers too) if they want to do experiments related to their theories, or if they want to push them to the world. Developers need to understand what scientists say, or they need to be partly scientists, to be able to build up their own small theories whenever a problem is difficult enough. And so on.

Back to your original question, maths is an extremely useful tool both for CS research and development. A pure mathematician is providing material for all of CS to work. But CS people, programmers, and so on need to know some math too.