And we also suck in messages from everything from the television, to advertising, to marketing, etc. These are hugely powerful forces that define what we want and how we view ourselves. When we're told that banking is a very respectable profession, a lot of us want to go into banking. When banking is no longer so respectable, we lose interest in banking. We are highly open to suggestion.
Mathematics is not a deductive science—that's a cliché. When you try to prove a theorem, you don't just list the hypotheses and then start to reason. What you do is trial and error, experimentation, guesswork.