Is it rude to use the phrase "so called" in mathematics?

I'm a native English speaker and mathematician.

You're right that it does have a negative connotation. The phrase "so called" suggests that the name you are referring to is misleading. For example I might say "the so-called irrational numbers" if I wanted to remind the audience that there's no connection between the numbers and the common English meaning of "irrational" (irrational numbers aren't illogical). I don't think the phrase "so-called" can be used without this negative connotation, even if some people try. Despite this, the audience will almost certainly work out the intended meaning after a moment's thought.

The phrase I'd use instead is "known as". For example "the result known as The Theorem of Highest Weight". It conveys that the name you've given is the one that people commonly use, which I think is what you want to say.

It is common use, even in written mathematics, even in text books. Examples from this site include

So-called Artin-Schreier Extension

Is “:” so-called Frobenius inner product?

Inversion of so-called probability-generating functional

Show that f solves the so called wave equation

EDIT. See "this is the so-called representation theory" in Rotman J.J. Introduction to the theory of groups.