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 claim.
- 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 coloured cycle stripping is NP-complete (Karp,
personal communication)."
- Proof by reduction to the wrong problem
- "To see that infinite-dimensional coloured 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 accumulation of 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 by the author.
- 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.
Dana Angluin, Sigact News, Winter-Spring 1983, Volume
15 #1
(Source courtesy of Dietrich Neuman)
