Many "tricks" that we use to solve mathematical problems don't correspond nicely to theorems or lemmas, or anything close to that rigorous. Instead they take the form of analogies, or general methods of proof more specialized than "induction" or "reductio ad absurdum" but applicable to a number of problems. These can often be summed up in a "slogan" of a couple of sentences or less, that's not fully precise but still manages to convey information. What are some of your favorite such tricks, expressed as slogans?
(Note: By "slogan" I don't necessarily mean that it has to be a well-known statement, like Hadamard's "the shortest path..." quote. Just that it's fairly short and reasonably catchy.)
Justifying blather: Yes, I'm aware of the Tricki, but I still think this is a useful question for the following reasons:
- Right now, MO is considerably more active than the Tricki, which still posts new articles occasionally but not at anything like the rate at which people contribute to MO.
- Perhaps causally related to (1), writing a Tricki article requires a fairly solid investment of time and effort. The point of slogans is that they can be communicated without much of either. If you want, you can think of this question as "Possible titles for Tricki articles," although that's by no means its only or even main purpose.