How to prove it?
(Anonymous)
- 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'
- '...'
- '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-
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 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 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.
