Only by looking at the discovery theorem, putting forward propositions and proving conjectures that contribute to mathematical theory and application can we be called mathematicians.
Can mathematicians do math problems? Not necessarily, or rather, definitely not. Because mathematics is a very big category, a concise mathematics manual is as thick as a modern Chinese dictionary. Do you think scholars in China know the meaning of all Chinese characters?
To say the least, what kind of "home" do you think a person who can recite Modern Chinese Dictionary is? No, because Chinese studies are far more than this dictionary. Similarly, mathematics is far more than a manual, and this one is only for college students to learn.
Mathematicians are all specialized, but for ordinary people, they are generally called mathematicians.