HOW TO PROVE IT
By Dana Angluin with apologies to G. Polya
and contributions from the Yale Computer Science Department.

  • 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 standard but inconvenient definitions are changed for the statement of the result.
  • proof by appeal to intuition:
    Cloud-shaped drawings frequently help here.