I'm a cs student and I'm soon getting my bachelor degree. These three years were mainly practical, but by reading GEB this summer I realized how much I'd like to learn about theory of computation, algorithmic information theory, metamathematics and logic.
In my country I didn't really find appropriate cs courses, so I decided to just read in my free time. Should I just get into math? And, more importantly, are these active areas of research or are there just borderline philosiphy?

Also, what do you think about viewing maths as a quasi-empirical science?