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How to Prove It (humor)

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

  • proof by intimidation: 'Trivial'.

  • proof by vigorous handwaving: Works well in a classroom or seminar setting.

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

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

  • proof by omission: 'The reader may easily supply the details'
    'The other 253 cases are analogous'

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

  • proof by wishful citation:

    The author cites the negation, converse, or generalization of a theorem from the literature to support his claims.

  • proof by funding: How could three different government agencies be wrong?

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

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

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

  • 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.

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

  • proof by accumulated evidence: Long and diligent search has not revealed a counterexample.

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

  • 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.

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

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

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

  • proof by ghost reference: Nothing even remotely resembling the cited theorem appears in the reference given.

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

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

  • proof by appeal to intuition: Cloud-shaped drawings frequently help here.