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.

## 1. Proof by obviousness

## "The proof is so clear that it need not be mentioned."

## 2. Proof by general agreement

## "All in favor?..."

## 3. Proof by imagination

## "Well, we'll pretend it's true..."

## 4. Proof by convenience

## "It would be very nice if it were true, so..."

## 5. Proof by necessity

## "It had better be true, or the entire structure of mathematics would crumble to the ground."

## 6. Proof by plausibility

## "It sounds good, so it must be true."

## 7. Proof by intimidation

## "Don't be stupid; of course it's true!"

## 8. Proof by lack of sufficient time

## "Because of the time constraint, I'll leave the proof to you."

## 9. Proof by postponement

## "The proof for this is long and arduous, so it is given to you in the appendix."

## 10. Proof by accident

## "Hey, what have we here?!"

## 11. Proof by insignificance

## "Who really cares anyway?"

## 12. Proof by plagiarism

## "As we see on page 289,..."

## 13. Proof by clever variable choice

## "Let A be the number such that this proof works..."

## 14. Proof by divine word

## "...And the Lord said, 'Let it be true,' and it was true."

## 15. Proof by hasty generalization

## "Well, it works for 17, so it works for all reals."

## 16. Proof by avoidance

## "Limit of proof by postponement as it approaches infinity."

## 17. Proof by design

## "If it's not true in today's math, invent a new system in which it is."