I am a new postdoc in mathematics. I feel that I often lack even basic knowledge in fields even closely related to mine. This is primarily because I tend to "wing it" rather than sit down and do homework, memorize proofs, etc.

However, I tend to bristle with indignation when people point out my lack of "polish" in mathematics, and have solved problems that even my advisor couldn't. This I essentially did out of spite, and actually working hard for a change.

Am I good enough to get a tenure track job?