How to Prove It

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 generalisation 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 coloured cycle stripping is NP-complete [Karp, personal communication]."

Proof by reduction to the wrong problem - "To see that infinite-dimensional coloured 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.