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Wednesday, January 2, 2008

36 Methods of Mathematical Proofs

36 Methods of Mathematical Proof
Author unknown

Proof by obviousness - "Proof is so clear it need not be mentioned."
Proof by general agreement - "All in favor?. . . "
Proof by imagination - "Well, we'll pretend it's true. . .
Proof by convenience - "It would be very nice if it were true, so . . .
Proof by necessity - "It’d better be, or the entire structure of mathematics will crumble to the ground."
Proof by plausibility - "It sounds good, so it must be true."
Proof by intimidation - "Don't be stupid; of course it's true."
Proof by lack of sufficient time - "Because of the time constraint, I'll leave the proof to you."
Proof by postponement - "The proof for this is long and arduous, so it is given in the appendix."
Proof by accident - "Hey, what have we here?!"
Proof by insignificance - "Who really cares, anyway?"
Proof by mumbo-jumbo - " (B Ì P ) , $ (C Î W )
Proof by profanity - (example omitted)
Proof by definition - "We define it to be true."
Proof by tautology - 'It's true because it's true."
Proof by plagiarism - "As we see on page 289......"
Proof by lost reference - "I know I saw it somewhere......"
Proof by calculus - "This proof requires calculus, so we'll skip it."
Proof by terror - When intimidation fails ...
Proof by lack of interest - "Does anyone really want to see this?"
Proof by illegibility - (scribble, scribble) QED
Proof by logic - "If it is on the problem sheet, then it must be true!"
Proof by majority rule - Only to be used if general agreement is impossible
Proof by clever variable choice - "Let A be the number such that this proof works. . "
Proof by tessellation - "This proof is the same as the last."
Proof by divine word - "And the Lord said, 'Let it be true,' and it was true."
Proof by stubbornness - "I don't care what you say-it is true!"
Proof by simplification - "This proof reduces to the statement 1 + 1 = 2."
Proof by hasty generalization - "Well, it works for 17, so it works for all reals."
Proof by deception - "Now everyone turn their backs. . ."
Proof by supplication - "Oh please, let it be true."
Proof by poor analogy - "Well, it's just like . . . "
Proof by avoidance - Limit of proof by postponement as it approaches infinity
Proof by design - If it's not true in today's math, invent a new system in which it is.
Proof by authority - "Well, Don Knuth says it's true, so it must be!"
Proof by intuition - "I just have this gut feeling. . ."

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