TITLE: Is it bad to resort to numerical examples to understand the idea behind a proof?
QUESTION [21 upvotes]: When reading proofs, I often get confused and need to devise my own examples to understand what's going on. Is this practice ok or should I train myself to think in abstract terms?
As an example, here's something that I'd need a sketch on paper to understand.

REPLY [12 votes]: I would say that, not only is it normal, it is recommended and also something that some people have to be taught to do. John Conway said that he worked out numerous examples with physical tokens when he was inventing his game of Life, and I got the sense he thought that kind of concreteness was important in other more conventional mathematical contexts too.