- 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
- 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
- ``Eight-dimensional colored cycle stripping is NP-complete
[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 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 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
- 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
- Cloud-shaped 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.