Checklist for finding and writing proofs
(Stolen from Barbara Kaiser)
- Be sure you have a clear statement to prove
- Understand what you're proving
- Figure out the logical structure.
- Rephrase the statement in several logically equivalent ways.
- Make sure you know the definitions of the mathematical terms.
- Think about what theorems, concepts, etc. that involve those terms.
- Decide how you might prove it
- Which proof techniques seem likely? Best?
- What can you assume? What is your goal?
- Find the proof
- Compare what you can assume with the theorems and definitions you know.
- Figure out what theorems would get you to your goal.
- Stuck? Try an alternative proof technique.
- Still stuck? See if you can prove the theorem is false.
Write rough draft, check for logical errors
- Did you use all of the hypotheses?
- Did you assume the conclusion? (This is bad.)
- Are there clear steps in your proof that lead directly to the conclusion?
- Does each step follow logically from the previous one?
- Are the steps consistently sized?
Write first draft
- Check that you just prove one thing. If necessary, prove some
propositions or lemmas first.
- Check for content.
- Check spelling, punctuation, grammar, and writing style.
- Check for readability - format, spacing, visual appeal.
Write the final draft
- Be sure to state the theorem you're proving.
- Be sure to leave room in the margins and between proofs for my comments.