## How to Prove Everything

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.

Sent by: posted on 02 December 2006