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

**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

**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.”