I mean how someone goes from a student to become a teacher or a professor ? What is that state feel like ? Are you confident of the knowledge you have conquered over the years ?or there is part of doubt in there ?
I am current in the 3rd year out of 4 to get my degree, and I am struggling to learn the subjects to the fullest, always questions about things that confuse me and I can't answer , I can't solve problems with confidence (a lot of times I can't solve them at all), I don't have much confidence about my solution etc. I have a feeling that even if I get my degree those doubts and confusion won't go away like that, if there is someone who felt that way their opinion and point of view are more that welcome . You can imagine you are giving advice to your old self , an advise you never got but you needed.
For example because you did good on your finals doesn't mean you know abstract algebra , it's like the piano, you can't call your self a pianist because you know how to play well 5-10 songs. So when someone can be called a mathematician ? Or even that at least he knows abstract algebra. Also, I can observe that my knowledge on statistics and probabilities are a bit weaker over the pure math like real analysis number theory etc(because i study them more and give them more attention). Does every professor know deeply all the subjects ?