This list has been compiled by Dana Angluin and was originally published in SIGACT News, Winter-Spring, 1983, Volume 15 #1.
- 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
- 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 claim.
- 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 accumulation of 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 by the author.
- 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.
The following methods have been used successfully and have been consequently submitted by fellow readers and members.
- Proof by lack of imagination
How could a life form not be carbon based?