http://paul.merton.ox.ac.uk/science/maths-proofs.html


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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. 



(based on an unoriginal email forwarded by Richard Green, Mar 1997)