What does it mean to call something "Naive" in mathematics? I've seen the term "naive" come up repeatedly in mathematics textbooks and lectures without any knowledge of what it indicates.
There is always the dictionary definition, but my impression of the word based on how I've seen it used is that it's similar to "trivial," where it has connotations in mathematics that differ significantly from those in natural language, even if it doesn't have a formal definition as such.
Can anyone who's spent more time immersed in the jargon of mathematics give me an impression of what naive means in this context?
 A: Among other uses, there are two quite specific uses that have become almost formalized themselves: "naive set theory" and "naive category theory". For naive set theory, it means not axiomatized, and not worrying too much about potential paradoxes (such as "the set of all sets that do not contain themselves as elements"), but focusing more on the positive possibilities. Similarly, beginning several decades later, "naive category theory" (a less universal convention) again avoids too much concern for foundations, either from set theory (Grothendieck universes, large cardinals, ...?!?), or more innately category-theoretic, as from Lawvere et al.
There is also a related-but-different "naivete", of physicists' computations that mathematicians could only genuinely justify after Schwartz and Grothendieck, using distributions and function-valued and operator-valued functions, etc. In these cases, in the happy outcomes, the computations could eventually be justified (and had matched physical facts all along!), but required much-more-sophisticated viewpoints to achieve the justification, or even to understand what might go wrong... but doesn't :)
