Proof notes

Reading a proof line by line is not the same as understanding it. A mathematician who understands a proof can say what it is trying to show, the plan in a sentence, which step does the real work, and which hypotheses are used where. The rest is bookkeeping. These notes make that structure visible.

The habit behind them is old and widely taught: restate the theorem in your own words, name the technique (induction, contradiction, contrapositive, construction, pigeonhole, diagonalization), justify every step, check where each hypothesis is used, and then poke at the result by weakening a hypothesis or trying a special case.

When to use it