Proofs
                          ==========
 
The following is a list of some common proof techniques that
are often extremely useful.
 
1  Proof by example:
 
      The author gives only the case n = 2 and suggests that
      it contains most of the ideas of the general proof.
 
2  Proof by intimidation:
      'Trivial.'
 
3  Proof by vigorous handwaving:
 
      Works well in a classroom or seminar setting.
 
4  Proof by cumbersome notation:
 
      Best done with access to at least four alphabets
      and special symbols.
 
5  Proof by exhaustion:
 
      An issue or two of a journal devoted to your proof is
      useful.
 
6  Proof by omission:
 
      'The reader may easily supply the details.'
      'The other 253 cases are analogous.'
      '...'
 
7  Proof by obfuscation:
 
      A long plotless sequence of true and/or meaningless
      syntactically related statements.
 
8  Proof by wishful citation:
 
      The author cites the negation, converse, or generalization
      of a theorem from literature to support his claims.
 
9  Proof by funding:
 
      How could three different government agencies be wrong?
 
10 Proof by eminent authority:
 
      'I saw Karp in the elevator and he said it was probably
      NP-complete.'
 
11 Proof by personal communication:
 
      'Eight-dimensional colored cycle stripping is NP-complete
      [Karp, personal communication].'
 
12 Proof by reduction to the wrong problem:
 
      ' To see that infinite-dimensional colored cycle stripping
      is decidable, we reduce it to the halting problem.'
 
13 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.
 
14 Proof by importance:
 
      A large body of useful consequences all follow from the
      proposition in question.
 
15 Proof by accumulated evidence:
 
      Long and diligent search has not revealed a counterexample.
 
16 Proof by cosmology:
 
      The negation of the proposition is unimaginable or meaningless.
      Popular for proofs of the existence of God.
 
17 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.
 
18 Proof by metaproof:
 
      A method is given to construct the desired proof. The
      correctness of the method is proved by any of these techniques.
 
19 Proof by picture:
 
      A more convincing form of proof by example. Combines well
      with proof by omission.
 
20 Proof by vehement assertion:
 
      It is useful to have some kind of authority in relation to
      the audience.
 
21 Proof by ghost reference:
 
      Nothing even remotely resembling the cited theorem appears
      in the reference given.
 
22 Proof by forward reference:
 
      Reference is usually to a forthcoming paper of the author,
      which is often not as forthcoming as at first.
 
23 Proof by semantic shift:
 
      Some standard but inconvenient definitions are changed for
      the statement of the result.
 
24 Proof by appeal to intuition:
 
      Cloud-shaped drawings frequently help here.