Subject: Rigorous Proof... NOT!
Date: Mon, 18 Nov 1996 23:26:50 -0500

My good friend Heather writes:
             "Math is good.  Math is your friend.  We like math."

Heather
.......
"A mathematician is a device for turning coffee into theorems."
                                          -- P. Erdos


                               HOW TO PROVE IT

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 communication].'

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 metaproof:
       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 of the standard but inconvenient definitions are changed
       for the statement of the result.

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

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