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IlyaShpitser comments on Stupid Questions May 2015 - Less Wrong Discussion
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"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.