In one of her TEDx Talks (https://www.youtube.com/watch?v=QQTUtBJE5fs), a Stanford professor of Math Education, Jo Boaler, claimed to be a "mathematician" when in fact, her work lies solely in math education (she in fact, likely has not even taken intro to proof course or any of the upper-division courses). What would be in general, a potential legal consequence for misrepresenting academic expertise in public?
Here are some lingering questions:
The word "mathematician" does not seem to me to be legally protected, so does that mean anyone can claim to be a "mathematician" if they say that they like doing math?
To abstract further, is there any legal accountability of individuals with degrees in a field X, but claims an expertise in fields X', X'' which look superficially similar to X but in reality, very different? Let's also say that the individual does not claim a specific degree in fields X', X'' etc. - merely expertise (e.g. French major claims expertise in European history, or medical doctor claims expertise in evolutionary biology).
Does Stanford University (or in general, any other top universities) have policies against faculty members misrepresenting credentials or others' research (as Boaler has done in several occasions), or is it protected under "academic freedom"?
Boaler runs several online courses, and if say, students signs up for a course believing that Boaler is a "mathematician" and later finds out that she isn't, what recourse would a student have against Boaler? Is there no legal recourse due to reasons in 1)?
Are there anything legal-related that I'm missing from this?