The math in computer science may not be much like the usual idea of science, but neither is it what people ordinarily mean when they say "pure mathematics." It's much more nearly "applied mathematics," like statistics or signal processing or control theory: more likely to be interested in, e.g., the development of wavelets than in a proof of the Poincare conjecture.

Maybe it would've been more logical if the applied math end of the CS field had ended up with an applied-math-y name comparable to "statistics", e.g. "algorithmics" or "algorithmic analysis," and much of the rest of the CS field had ended up "software engineering" or "computer engineering" or "computational engineering" or "information system engineering" by analogy with "electrical engineering." But naming of technical fields is not necessarily systematically logical, sometimes because of old idiosyncratic reasons to avoid ambiguity with other pursuits: "astronomy" vs. "astrology," anyone?