I am a junior in Caltech's mathematics department.
I keep being harassed by some non-mathematicians and fellow students that I do not have what it takes to do mathematics. They say that one must have done something by the age of 20 years old to actually do something in mathematics.
Also, they kept harassing me that I don't know what I'm doing, because the only reason I gave them for why I'm doing math is that it is fun. They don't think that's a valid reason, and think that there is a problem.
They keep telling me that I need to reasses my plans. Has anyone been in these situations before? What should I do?