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
- 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
- Proof by Plausibility: "It sounds good so it must
- 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
- Proof by Accident: "Hey, what have we here?"
- Proof by Insignificance: "Who really cares
- 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
- Proof by Tautology: "It's true because it's
- Proof by Plagiarism: "As we see on page 238 ..."
- Proof by Lost Reference: "I know I saw this
- 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
- 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
- Proof by Supplication: "Oh please, let it be
- 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