with regards to my topic, i mean that in a sense that the subject is not some sort of prodigy/genius, but an average human being with a strong interest in mathematics who wants to pursue a career in math. do most people who graduate with a math degree have a strong knowledge in all math fields, or do you come out being stronger in one particular math field and choose to pursue that route? when i hear the word 'mathematician' i think of someone who when asked a math question, no matter what field it relates to, can answer it fully, if not then to a certain extent. the reason i ask is because math just seems so overwhelming, like it would take my life 10 fold just to know half the stuff relating to math. also, there are some fields i really enjoy and others not so much. and how important is it to know definitions word by word?