 Not infrequently this opposition is debated in terms of which approach is “the right one”,  with the implication that only one of them but not the other is legitimate. (This started with Dedekind and Kronecker. We already noted that Dedekind explicitly rejected constructivist strictures on his work, although he did not rule out corresponding projects as illegitimate in themselves. Kronecker, with his strong opposition to the use of set-theoretic and infinitary techniques, went further in the other direction.) But another question is more basic: Can the contrast between the two approaches to algebraic number theory, or to mathematics more generally, be captured more sharply and insightfully; and in particular, what is its methodological and epistemological significance?