Finding tactics in proofs

Abstract This is a note about writing and appreciating proofs by examining their middle level between strategy and specific details in order to discern “tactics”, i.e., key ideas or methods that might appear in many proofs. Doing so may help the intuition of the author or reader, or it may lend itself to new applications of a tactic from a proof. Explicitly pointing out tactics should produce more illuminating and memorable proofs. A core illustrative tactic is connected to broad research in topology and dynamics, the tactic of “following curves”, and we end with examples suitable for direct adoption in an undergraduate analysis course.