The following is a list of some common proof techniques that are often
- Proof by passion: The author gives the proof with a lot of passion,
expressive eyes and vigorous movements...
- 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
- 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
- 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 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
- 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
- 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.