
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'' or ``obvious.''
 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? Or, to
play the game a different way: how could anything funded by those bozos
be correct?
 Proof by democracy
 A lot of people believe it's true: how could they all be wrong?
 Proof by market economics
 Mine is the only theory on the market that will handle the data.
 Proof by eminent authority
 ``I saw Ruzena in the elevator and she said that was tried in
the 70's and doesn't work."
 Proof by cosmology
 The negation of the proposition is unimaginable or
meaningless. Popular for proofs of the existence of God
and for proofs that computers cannot think.
 Proof by personal communication
 ``Eightdimensional colored cycle stripping is NPcomplete
[Karp, personal communication].''
 Proof by reference to talk
 ``At the special NSA workshop on computer vision, Binford proved
that SHGC's could be recognized in polynomial time.''
 Proof by reduction to the wrong problem
 ``To see that infinitedimensional 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 Icelandic
Philological Society, 1883. This works even better if the paper
has never been translated from the original Icelandic.
 Proof by ghost reference
 Nothing even remotely resembling
the cited theorem appears in the reference given. Works well
in combination with proof by reference to inaccessible literature.
 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 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 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. A strong background in programming language
semantics will help here.
 Proof by picture
 A more convincing form of proof by example. Combines well
with proof by omission.
 Proof by flashy graphics
 A moving sequence of shaded, 3D color models will convince
anyone that your object recognition algorithm works. An SGI
workstation is helpful here.
 Proof by misleading or uninterpretable graphs
 Almost any curve can be made to look like the desired
result by suitable transformation of the variables and
manipulation of the axis scales. Common in experimental work.
 Proof by vehement assertion
 It is useful to have some kind of authority relation to the
audience, so this is particularly useful in classroom settings.
 Proof by repetition
 Otherwise known as the Bellman's proof: ``What I say three
times is true.''
 Proof by appeal to intuition
 Cloudshaped drawings frequently help here.
 Proof by vigorous handwaving
 Works well in a classroom, seminar, or workshop setting.
 Proof by semantic shift
 Some of the standard but inconvenient definitions are changed
for the statement of the result.
 Proof by cumbersome notation
 Best done with access to at least four alphabets, special
symbols, and the newest release of LaTeX.
 Proof by abstract nonsense
 A version of proof by
intimidation. The author uses terms or theorems from advanced
mathematics which look impressive but are only tangentially related to
the problem at hand. A few integrals here, a few exact sequences
there, and who will know if you really had a proof?
 Disproof by finding a bad apple
 One bad apple spoils the whole bunch. Among the many proponents of
this theory, we have found one who is obviously loony; so we can
discredit the entire theory.
(Often used in political contexts.)
 Disproof by slippery slope (or thin end of wedge, if you are British)
 If we accepted [original proposal], we'd have to accept [slightly
modified proposal], and eventually this would lead to [radically different
and clearly objectionable proposal].
 Disproof by ``not invented here''
 We have years of experience with this equipment at MIT and we
have never observed that effect.

