> But there's a difference between trying to understand, say, a theorem by applying it in concrete situations and by studying its proof. There may be a differe

> But there's a difference between trying to understand, say, a theorem by applying it in concrete situations and by studying its proof. There may be a difference or there may not. You could study a proof within the context of a specific example. That is how I usually would do it. But yes of course it's possible not to do like that (many people don't study proofs that way). In any case, I don't really understand your point.