How to prove anything 
                              How to prove anything

                              HOW TO PROVE ANYTHING (source unknown)6-15-89

                              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."
                              "Intuitively obvious to the most casual observer."

                              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 
                              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."

                              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 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.

                              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.

                              Now, the lab session: A group of scientists of all 
                              kinds gathered one day
                              to prove that all odd numbers were prime numbers.

                              The mathematician was first: "One is a prime 
                              number, three is a prime
                              number, five is a prime number, seven is a prime 
                              number. Thus by induction,
                              all odd numbers are prime."

                              Then came the physicist: "One is a prime number, 
                              three is a prime number,
                              five is a prime number, seven is a prime number. 
                              Nine is NOT a prime number.
                              Eleven is a prime nummber, thirteen is a prime 
                              number. Well, nine falls within
                              experimental error, so all odd numbers are prime."

                              Finally the chemist: "One is a prime number, three 
                              is a prime number, five
                              is a prime number, seven is a prime number, nine 
                              is a prime number . . .



                               
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