Math Jokes: Methods of Mathematical Proof
(From Dick A. Wood in The Mathematics Teacher November 1998 and from Steve Phipps)
If the proof of a theorem is not immediately apparent, it may be because you are trying the wrong approach. Below are some effective methods of proof that may aim you in the right direction.
* Proof by Obviousness: "The proof is so clear that it need not be mentioned."
* Proof by General Agreement: "All in Favor?..."
* Proof by Imagination: "Well, We'll pretend its true."
* Proof by Convenience: "It would be very nice if it were true, so ..."
* Proof by Necessity: "It had better be true or the whole structure of mathematics would 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 so 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: " For any epsilon> 0 there exists a corresponding delta > 0 s.t. f(x) − L < epsilon whenever x − a < delta"
* Proof by Profanity: (example omitted)
* Proof by Definition: "We'll define it to be true."
* Proof by Tautology: "It's true because it's true."
* Proof by Plagiarism: "As we see on page 238 ..."
* Proof by Lost Reference: "I know I saw this 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: " ¥ ª Ð Þ þæ"
* 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 just the same as the last."
* Proof by Divine Word: "And the Lord said, 'Let it be true,' and it came to pass."
* 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 t approaches infinity.
* Proof by Design: "If it's not true in today's math, invent a new system in which it is."
* Proof by Intuition: "I just have this gut feeling ..."
* Proof by Authority: "Well, Bill Gates says it's true, so it must be."
* Proof by Vigorous Assertion: "And I REALLY MEAN THAT!"
* Proof by A.F.K.T. Theorem: "Any Fool Knows That!"
* Proof by vigorous handwaving: Works well in a classroom.
* Proof by seduction: "Convince yourself that this is true!"
* Proof by accumulated evidence: "Long and diligent search has not revealed a counterexample."
* Proof by Divine Intervention: "Then a miracle occurs ..."
* 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 funding: How could three different government agencies be wrong?
* 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 omission: "The reader may easily supply the details" or "The other 253 cases are analogous"
* Proof by deferral: "We'll prove this later in the course".
* Proof by picture: A more convincing form of proof by example. Combines well with proof by omission.
* Proof by intimidation: "Trivial."
* Proof by adverb: "As is quite clear, the elementary aforementioned statement is obviously valid."
* 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 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 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 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 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 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.
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