Survey of proof techniques
--------------------------

Proof by accumulated evidence:
  Long and diligent search has not revealed a counterexample.

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

Proof by cosmology:
  The negation of the proposition is unimaginable or meaningless.  Popular
  for proofs of the existence of God.

Proof by cumbersome notation:
  Best done with access to at least four alphabets and special symbols.

Proof by eminent authority:
  'I saw Karp in the elevator and he said it was probably NP-complete.'

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 exhaustion:
  An issue or two of a journal devoted to your proof is useful.

Proof by funding:
  How could three different government agencies be wrong?

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 ghost reference:
  Nothing even remotely resembling the cited theorem appears in the reference
  given.

Proof by importance:
  A large body of useful consequences all follow from the proposition in
  question.

Proof by intimidation:
  'Trivial.'

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 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 obfuscation:
  A long plotless sequence of true and\or meaningless syntactically related
  statements.

Proof by omission:
  'The reader may easily supply the details.'
  'The other 253 cases are analogous.'
  '...'

Proof by personal communication:
  'Eight-dimensional colored cycle stripping is NP-complete [Karp, personal
  commmunication].
 
Proof by picture:
  A more convincing form of proof by example.  Combines well with proof by
  omission.

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 semantic shift:
  Some standard but inconvenient definitions are changed for the statement
  of the result.

Proof by vehement assertion:
  It is useful to have some kind of authority relation to the audience.

Proof by vigorous handwaving:
  Works well in a classroom or seminar setting.

Proof by wishful citation:
  The author cites the negation, converse, or generalization of a theorem
  from the literature to support his claims.


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Proof Techniques

Methods for getting people to believe you (as good as, if not better than,
proof).  A collection of proof techniques that will prove invaluable to
both mathematicians and members of the general public.

PROOF TECHNIQUE #1 - 'Proof By Induction'

     1.  Obtain a large power transformer.
     2.  Find someone who does not believe your theorem.
     3.  Get this person to hold the terminals on the HV side of the
         transformer.
     4.  Apply 25000 volts AC to the LV side of the transformer.
     5.  Repeat step (4) until they agree with the theorem.

PROOF TECHNIQUE #2 - 'Proof By Contradiction'

     1.  State your theorem.
     2.  Wait for someone to disagree.
     3.  Contradict them.

PROOF TECHNIQUE #3 - Fire Proof

     1.  Summon all your inferiors for a departmental meeting.
     2.  Present your theorem.
     3.  Fire those who disagree.

PROOF TECHNIQUE #4 - The Famous Water Proof

     1.  State your theorem.
     2.  Wait for someone to disagree.
     3.  Drown them.

     NB.  This is closely related to the 'bullet' proof, but is easier
     to make look like an accident.

PROOF TECHNIQUE #5 - Idiot Proof

     1.  State your theorem.
     2.  Write exhaustive documentation with glossy colour pictures
         and arrows about which bit goes where.
     3.  Challenge anyone to not understand it.

PROOF TECHNIQUE #6 - Child Proof

     1.  State your theorem.
     2.  Encapsulate it in epoxy and shape it into an ellipsoid.
     3.  Put it in a jar with all the other proofs (one with one of
         those Press-to-Open lids).
     4.  Give it to a professor and challenge him to open it.

PROOF TECHNIQUE #7 - Rabbit Proof

     1.  Generate theorems at an altogether startling rate, much
         faster than anybody is able to refute them. Use up every
         body else's paper.  Run away at the slightest sign of danger.
     2.  Leave any crap in small, easily identified piles, in
         prominent places where you no longer are, and it cannot in
         fact be proven that you ever were.

PROOF TECHNIQUE #8 - Fool Proof

     1.  State your theorem.
     2.  Invite colleagues to comment.
     3.  If they don't agree, exclaim loudly, "You Fools!"

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