I don't think the accurate analogy is with mathematics itself.
Consider the belief that the universe must be fundamentally mathematical in nature, that if some aspect of it appears not to admit of mathematical description that's just because we don't understand it well enough yet, or our tools can't handle the complexity or somesuch, not because of any fundamental incompatibility.
That belief (to which I and probably most readers here subscribe) is an ideology as the term is being used here.
I will suggest that belief is to rationalism as mathematics is to rationality.
I will suggest that belief is to rationalism as mathematics is to rationality.
Is the "that" a conjunction or a determiner?
I feel that the term "rationalism", as opposed to "rationality", or "study of rationality", has undesirable connotations. My concerns are presented well by Eric Drexler in the article For Darwin’s sake, reject "Darwin-ism" (and other pernicious terms):
So, my suggestion is to use "rationality" consistently and to avoid using "rationalism". Via similarity to "scientist" and "physicist", "rationalist" doesn't seem to have the same problem. Discuss.
(Typical usage on Less Wrong is this way already, 3720 Google results for "rationality" and 1210 for "rationalist", against 251 for "rationalism". I've made this post as a reference for when someone uses "rationalism".)