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.