                            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. 
