On 3/21/2013 3:52 PM, Kaba wrote: > > what you already know. The book then becomes a reference. In practice > this means you won't be looking at proofs anymore, or spending much time > with the book itself. What you do instead is to look up some small > details.
I admit that I do not do as much mathematics as I would like to do. And, for many things what you describe here is absolutely correct.
For mathematics, if I were actively involved with some specific area of study and frequently investigating the same cluster of results, what you say would also be true.
But, generally, the conditions of the premises and any "known" results not forming the logic of the proof for some given statement of interest involve more. There is usually a hierarchy of definitions that are not apparent without deeper investigation. Since I tend to be careful about such things, I shall politely disagree with you on this point in so far as one might take it as a general rule.