### Methods of proof: a guide for lecturers

**Proof by vigorous handwaving.**

Works well in a classroom or seminar setting.

**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 funding.**

How could three different government agencies be wrong?

**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 omission.**

Examples include: "The reader may easily supply the details," or "The other 253 cases are analogous," etc.

**Proof by deferral.**

"We'll prove this later in the course."

**Proof by picture.**

A more convincing form of proof by example. Combines well with proof by omission.

**Proof by intimidation.**

"Trivial."

**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 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 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 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 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.