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 constrait, 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: 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 plagarism: "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: 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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