When you go into battle to solve a computational mathematics problem, the problem sometimes doesn't care about these boundaries. E.g., you might think that you're solving a problem in "computer algebra", but a sufficiently fast solution might end up involving numerical linear algebra in surprising ways. (E.g., enumerating elliptic curves over the rational numbers is reduced to exact linear algebra because of a Wiles work on Fermat's last theorem, and often exact linear algebra can be done via clever tricks much more efficiently using floating point matrices, which happen to be insanely fast to work with due to GPU's...). It's thus valuable, at least for research, to have large mathematical software systems that span these boundaries.