Dana Angluin's List of Proof Techniques
- 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
- Proof by personal communication:
- 'Eight-dimensional colored cycle stripping is NP-complete'
[Karp, personal commmunication].
- 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
- 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 meta-proof:
- 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
- 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.
- Proof by elimination of the counterexample:
- 'Assume for the moment that the hypothesis is true. Now, let's
suppose we find a counterexample. So what? QED.' (from Don Woods