Funny Proof Techniques

Quite often I read articles and papers where the authors use the phrase “Trivial”. This post summarizes my frustation in more generality :P

Shamelessly borrowed from http://www.cs.northwestern.edu/~riesbeck/proofs.html. A more complete list has been compiled here. Also, this medium article has a more pictoral representation.

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:

    '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 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 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.
  

• 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 <DON@SU-AI.ARPA>)