Many years ago, I received an email listing these wonderful ways to prove theorems. I am sure the mail would still be circulating in some form or the other. This is my small attempt to preserve the best mathematical lesson I had for posterity. Thanks to the anonymous author.
The author gives only the case n = 2 and suggests that it contains most of the ideas of the general proof.
"Trivial."
Works well in a classroom or seminar setting.
Best done with access to at least four alphabets and special symbols.
An issue or two of a journal devoted to your proof is useful.
"The reader may easily supply the details."
"The other 253 cases are analogous."
"..."
A long plotless sequence of true and/or meaningless syntactically related statements.
The author cites the negation, converse, or generalization of a theorem from literature to support his claims.
How could three different government agencies be wrong?
"I saw Karp in the elevator and he said it was probably NP-complete."
"Eight-dimensional colored cycle stripping is NP-complete [Karp, personal communication]."
"To see that infinite-dimensional colored cycle stripping is decidable, we reduce it to the halting problem."
The author cites a simple corollary of a theorem to be found in a privately circulated memoir of the Slovenian Philological Society, 1883.
A large body of useful consequences all follow from the proposition in question.
Long and diligent search has not revealed a counterexample.
The negation of the proposition is unimaginable or meaningless. Popular for proofs of the existence of God.
In reference A, Theorem 5 is said to follow from Theorem 3 in reference B, which is shown from Corollary 6.2 in reference C, which is an easy consequence of Theorem 5 in reference A.
A method is given to construct the desired proof. The correctness of the method is proved by any of these techniques.
A more convincing form of proof by example. Combines well with proof by omission.
It is useful to have some kind of authority in relation to the audience.
Nothing even remotely resembling the cited theorem appears in the reference given.
Reference is usually to a forthcoming paper of the author, which is often not as forthcoming as at first.
Some standard but inconvenient definitions are changed for the statement of the result.
Cloud-shaped drawings frequently help here.
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