36 Methods of Mathematical Proof

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 might 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 it's true..."

· Proof by convenience: "It would be very nice if it were true, so..."

· Proof by necessity: "It had better be true, or the entire 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 long and arduous, so it is given to you in the appendix."

· Proof by accident: "Hey, what have we here?!"

· Proof by insignificance: "Who really cares anyway?"

· Proof by mumbo-jumbo:

· 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:

· Proof by logic: "If it is on the problem sheet, 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 reduced 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 have this gut feeling."

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