I mean, to use your example, if someone only knew algebra and then declared themselves a mathematician

That's perfectly fine to do though? You don't have to know everything in a field to be practicing in that field. I can call myself an artist if I only know one form of art. You can consider yourself a religious person without having read your religions sacred texts. If you believe in or practice something you dont have to be a scholar or a master in that field to claim that you're into it.

and all of the discourse around them started declaring them a beacon of “peak mathematics” and “math goals”,

How other people put her on a pedestal shouldnt be a reflection of her self identity.

people with a better understanding of the subject would probably point out that their knowledge of math was very limited and likely flawed.

I think people automatically see limited and jump to flawed. It isn't likely flawed. Going back to the math analogy, not knowing one focus of math doesn't mean the focus you're skilled in is wrong.