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I'm a CS PhD, and I agree. I always tell people I'm studying math because it gives them much more of a flavor for what I'm actually doing everyday. When I say computer science, people think I'm just programming something.

Also, when people ask me, "So What do you actually do studying math?" I reply, "Sit and stare at the wall for several hours a day. Occasionally I write something down."

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It does depend a lot on the sub-field of CS.

For systems work you spend a lot of time implementing ideas and running experiments. In a lot of cases it isn't necessarily that difficult to find an interesting idea that's probably viable. The real work is spending a lot of time writing code and work out all the annoying details to get to the point where you have a decent proof of concept.

Presumably, when you tell people you're doing research in math they imagine you're multiplying long numbers all day.

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