"There is no royal road to geometry."
The way we teach proofs and mathematical sophistication is ad hoc and subject specific. I wish I knew a better general way, but barring that, perhaps start with a mathematical subject close to programming. For instance logic or complexity theory. I wouldn't bother with proof assistants until you are pretty comfortable with proofs.
This thread is for asking any questions that might seem obvious, tangential, silly or what-have-you. Don't be shy, everyone has holes in their knowledge, though the fewer and the smaller we can make them, the better.
Please be respectful of other people's admitting ignorance and don't mock them for it, as they're doing a noble thing.
To any future monthly posters of SQ threads, please remember to add the "stupid_questions" tag.