Friday, November 30, 2007

The proof is in the proving...

S sent me this link today, about the various techniques of proving theorems.

Vidhya had already told me one:
Proof by intimidation, which according to her, was proving by throwing tons of math at the reviewer :-) [read "abstract nonsense" below]

But this one has some more true gems. Here is a sample:
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 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 be correct?


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 personal communication
``Eight-dimensional colored cycle stripping is NP-complete [Karp, personal communication].''


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 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?

Seriously.. go read the article :-).
P.S. Still down with a terrible cold .. gah!

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