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How to Prove It

Occasionally, it is useful for the researchers at The Mill (YSA's research laboratories) to remind everyone about how one should go about proving a proposition. It is quite important that scientific proofs be properly constructed so ensure their veracity. Listed here are the generally accepted forms of proof for use in scientific papers along with additional notes. You should use these forms of proof in all your future work.

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

"And this result is, of course, trivial to prove."

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 generalisation 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."

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 accumulated evidence

Long and diligent search has not revealed a counter-example.

proof by cosmology

The negation of the proposition is unimaginable or meaningless.

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 meta-proof

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.

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The Researchers at The Mill are interested in hearing about your unpublished research or new and interesting theories. If you have something in which you think our team would be interested, send it to us by email or snail mail to your YSA Chapter. Prizes will be awarded to good contributions as judged by the senior researchers.

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Last Modified: Monday, 08-Sep-2003 10:24:09 EST