Is computer science a branch of mathematics? I have been wondering, is computer science a branch of mathematics? No one has ever adequately described it to me. It all seems very math-like to me. My second question is, are there any books about computer science/programming that are very rigorous and take an axiomatic approach? Basically, putting computer science and programming on a rigorous foundation.
Theoretical computer science could certainly be considered a branch of mathematics. This branch of computer science deals with computers and computer programs as mathematical objects. Theoretical computer scientists could be described as computer scientists who know little about computers.

However, when people say "computer science" they usually include many things which would not be considered mathematics, for instance computer architecture, specific programming languages, etc.
I say that computer science is a branch of mathematics, but it has many branches connected to other sciences or fields of study as well. Many of the founding contributors to the field were mathematicians. The analogy of a musician to sports has no bearing because the person's sports accomplishments weren't necessarily any by-product of this person's musical talents. Computer science was fostered from mathematical carving.