Main differences between analytic number theory and algebraic number theory What are some of the big differences between analytic number theory and algebraic number theory?
Well, maybe I saw too much of the similarities between those two subjects, while I don't see too much of analysis in analytic number theory.

The main difference is that in algebraic number theory one typically considers questions with answers that are given by exact formulas, whereas in analytic number theory one looks for good approximations of quantities we don't expect to find a formula for.
