Proof Techniques. (author unknown)

This is a list of proof techniques that are very powerful, but unfortunately not valid. -- from a copy posted on unknown professor's door.

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

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

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

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

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

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

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

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

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

10. 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.

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

12. Proof by accumulated evidence :
    Long and dilligent search has not revealed a counterexample.

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

14. Proof by mutual reference :
    In reference A, Theorem 5 is said to follow from Theorem 3 in reference B, which is shown to follow from Corollary 6.2 in reference C, which is an easy consequence of Theorem 5 in reference A.

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

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

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

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

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

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

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