How to prove it
- 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
- 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-
- 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
- Proof by metaproof:
A method is given to construct the desired proof. The
correctness of the method is proved by any of these
- 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
- 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.