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: • 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: • 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."