Useful Proofs

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 hand-waving:
    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.

The above material is by Dana Angluin and was published in Sigact News, Winter-Spring, 1983, Volume 15  #1.