Funny ways to prove things guide for lecturers

Proof by vigorous handwaving:

Works well in a classroom or seminar setting.


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 funding:

How could three different government agencies be wrong?


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 omission:

“The reader may easily supply the details” or “The other 253 cases are analogous”
Proof by deferral:

“We’ll prove this later in the course”.


Proof by picture:

A more convincing form of proof by example. Combines well with proof by omission.


Proof by intimidation:



Proof by adverb:

“As is quite clear, the elementary aforementioned statement is obviously valid.”


Proof by seduction:

“Convince yourself that this is true! ”


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 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 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 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 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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