Proof Methods

The following is a list of some common proof techniques that are often extremely useful.

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 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 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 in 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.