razvan jigorea & friends: the blog

HOW TO PROVE IT, PART 1

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.

HOW TO PROVE IT, PART 2

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’
‘…’

HOW TO PROVE IT, PART 3

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.’

HOW TO PROVE IT, PART 4

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.

HOW TO PROVE IT, PART 5

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.

HOW TO PROVE IT, PART 6

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.

HOW TO PROVE IT, PART 7

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.

(Thanks, steju)