The following is a list of some common proof techniques that are often extremely useful.

  1. Proof by passion: The author gives the proof with a lot of passion, expressive eyes and vigorous movements...
  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 intimidation: 'Trivial.'
  4. Proof by vigorous handwaving: Works well in a classroom or seminar setting.
  5. Proof by cumbersome notation: Best done with access to at least four alphabets and special symbols.
  6. Proof by exhaustion: An issue or two of a journal devoted to your proof is useful.
  7. Proof by omission:
    • 'The reader may easily supply the details.'
    • 'The other 253 cases are analogous.'
    • '...'
  8. Proof by obfuscation: A long plotless sequence of true and/or meaningless syntactically related statements.
  9. Proof by wishful citation: The author cites the negation, converse, or generalization of a theorem from literature to support his claims.
  10. Proof by funding: How could three different government agencies be wrong? Proof by personal communication: 'Eight-dimensional colored cycle stripping is NP-complete [Karp, personal communication].'
  11. Proof by reduction to the wrong problem: 'To see that infinite- dimensional colored cycle stripping is decidable, we reduce it to the halting problem.'
  12. Proof by reference to inaccessible literature: The author cites a simple corollary of a theorem to be found in a privately circulated memoir of the Slovenian Philological Society, 1883.
  13. Proof by importance: A large body of useful consequences all follow from the proposition in question.
  14. Proof by accumulated evidence: Long and diligent search has not revealed a counterexample.
  15. Proof by cosmology: The negation of the proposition is unimaginable or meaningless. Popular for proofs of the existence of God.
  16. Proof by mutual reference: In reference A, Theorem 5 is said to follow from Theorem 3 in reference B, which is shown from Corollary 6.2 in reference C, which is an easy consequence of Theorem 5 in reference A.
  17. Proof by metaproof: A method is given to construct the desired proof. The correctness of the method is proved by any of these techniques.
  18. Proof by picture: A more convincing form of proof by example. Combines well with proof by omission.
  19. Proof by vehement assertion: It is useful to have some kind of authority in relation to the audience.
  20. Proof by ghost reference: Nothing even remotely resembling the cited theorem appears in the reference given.
  21. Proof by forward reference: Reference is usually to a forthcoming paper of the author, which is often not as forthcoming as at first.
  22. Proof by semantic shift: Some standard but inconvenient definitions are changed for the statement of the result.
  23. Proof by appeal to intuition: Cloud-shaped drawings frequently help here.