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Methods of Proof

Top 10 Proof Techniques

  1. Proof by throwing in the kitchen sink: The author writes down every theorem or result known to mankind and then adds a few more just for good measure. When questioned later, the author correctly observes that the proof contains all the key facts needed to actually prove the result. Very popular strategy on exams. Known to result in extra credit with sufficient whining.
  2. Proof by example: The author gives only the case n = 2 and suggests that it contains most of the ideas of the general proof.
  3. Proof by vigorous hand waving: A faculty favorite. Works well in any classroom or seminar setting.
  4. Proof by cumbersome notation: Best done with access to at least four alphabets and special symbols. Helps to speak several foreign languages.
  5. Proof by exhaustion: An issue or two of a journal devoted to your proof is useful. Works well in combination with proof by throwing in the kitchen sink and proof by cumbersome notation.
  6. Proof by omission: “The reader may easily supply the details.” “The other 253 cases are analogous.” “…”
  7. Proof by picture: A more convincing form of proof by example. Combines well with proof by omission.
  8. Proof by vehement assertion: It is useful to have some kind of authority in relation to the audience.
  9. Proof by appeal to intuition: Cloud-shaped drawings frequently help here. Can be seen on exams when there was not time to include a complete proof by throw-ing in the kitchen sink.
  10. Proof by reference to eminent authority: “I saw Fermat in the elevator and he said he had a proof . . .” Continue Reading →