From: cate3.osbunorth@xerox.com (Henry Cate III)
Subject: How to prove something



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Survey of proof techniques

This survey was written by Dana Angluin.  Not really sure where it came from.

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.'
  '...'

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
  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 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 standard but inconvenient definitions are changed for the statement
  of the result.

Proof by appeal to intuition:
  Cloud-shaped drawings frequently help here.

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Henry Cate III
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  (ucbvax!xerox.com!cate3.osbunorth)  OR  (cate3.osbunorth@Xerox.Com)
Everyone complains of his memory, no one of his judgment.