# 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.