TITLE: Is 'Algebraic Number Theory' the study of the theory of algebraic numbers, or is it the study of the theory of numbers from an algebraic viewpoint?
QUESTION [15 upvotes]: Asked differently: Is Algebraic Number Theory the study of the theory of algebraic numbers? Or is it Number Theory from an algebraic viewpoint?
Or is it both?
I know I can just find a wiki article but I figure answers from the MSE community would be more intuitive and instructive.

REPLY [4 votes]: Not only are the answers from the Mathematics StackExchange community "more intuitive and instructive," they're much more valid than anything you will find on Wikipedia. Although it's true that a lot of the "community" here are also active on Wikipedia, their talents and insights are mostly wasted over there.
There is much tighter control here than there. And not just anyone with an account here can edit the tag list (for example, I can't, however much the lower-case "diophantine" may bother me). That tag list defines algebraic-number-theory thus:

Questions related to the algebraic structure of algebraic integers

Seems very clear to me. For the sake of comparison, look at elementary-number-theory

Questions on congruences, linear diophantine equations, greatest
  common divisor, divisibility, etc.

analytic-number-theory

Questions on the use of the methods of real/complex analysis in the
  study of number theory.

and p-adic-number-theory

In mathematics the p-adic number system for any prime number p extends
  the ordinary arithmetic of the rational

I would adjust the punctuation of that last one, but, like I said, I can't edit the tag descriptions. But I can go on Wikipedia right now and insert all manners of nonsense and wrongheadedness.