This is manifestly NOT true in math, and is less true in the more mathematical areas of CS. But for much of it, we don't even know what the right questions are. In theory we have P vs NP as an overriding question and also concerns about quantum computation (yet another area that is intensely mathematical), but in networks, we don't even know what the right questions are. In software engineering, we are feeling around in the dark, and in user interfaces, we just keep throwing things against the wall and hoping they stick. (note that these are broad generalizations, and practitioners in each of these could certainly find counterexamples, but I think the broad gist is true).
If you know some computer science and come up with a question that combines concerns in disparate subfields, the chances are good that your question has never been asked before, much less answered, that both the question and answer may be interesting to more people than just you, and that you may have all the tools you need to solve it just from your undergrad education. Are there any other fields where this is true?