Some Non-Mathematical Proofs

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

1. Proof by example:
   The author gives only the case n = 2 and suggests that it contains most of the ideas of the general proof.

2. Proof by intimidation:
   'Trivial.'

3. Proof by vigorous handwaving:
   Works well in a classroom or seminar setting.

4. Proof by cumbersome notation:
   Best done with access to at least four alphabets and special symbols.

5. Proof by exhaustion:
   An issue or two of a journal devoted to your proof is useful.

6. Proof by omission:
   'The reader may easily supply the details.'
   'The other 253 cases are analogous.'
   '...'

7. Proof by obfuscation:
   A long plotless sequence of true and/or meaningless syntactically related statements.

8. Proof by wishful citation:
   The author cites the negation, converse, or generalization of a theorem from literature to support his claims.

9. Proof by funding:
   How could three different government agencies be wrong?

10. Proof by eminent authority:
    'I saw Karp in the elevator and he said it was probably NP-complete.'

11. Proof by personal communication:
    'Eight-dimensional colored cycle stripping is NP-complete [Karp, personal communication].'

12. Proof by reduction to the wrong problem:
    ' To see that infinite-dimensional colored cycle stripping is decidable, we reduce it to the halting problem.'

13. 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.

14. Proof by importance:
    A large body of useful consequences all follow from the proposition in question.

15. Proof by accumulated evidence:
    Long and diligent search has not revealed a counterexample.

16. Proof by cosmology:
    The negation of the proposition is unimaginable or meaningless.
    Popular for proofs of the existence of God.

17. 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.

18. Proof by metaproof:
    A method is given to construct the desired proof. The correctness of the method is proved by any of these techniques.

19. Proof by picture:
    A more convincing form of proof by example. Combines well with proof by omission.

20. Proof by vehement assertion:
    It is useful to have some kind of authority in relation to the audience.

21. Proof by ghost reference:
    Nothing even remotely resembling the cited theorem appears in the reference given.

22. Proof by forward reference:
    Reference is usually to a forthcoming paper of the author, which is often not as forthcoming as at first.

23. Proof by semantic shift:
    Some standard but inconvenient definitions are changed for the statement of the result.

24. Proof by appeal to intuition:
    Cloud-shaped drawings frequently help here.