Proof Techniques

written by Armen H. Zemanian, published in The Physics Teacher, May 1994.

The usual techniques for proving things are often inadequate because they are merely concerned with truth. For more practical objectives, there are other powerful - but generally unacknowledged - methods. Here is an (undoubtedly incomplete) list of them:

Proof of Blatant Assertion:

Use words and phrases like "clearly...,""obviously...,""it is easily shown that...," and "as any fool can plainly see..."

Proof by Seduction:

"If you will just agree to believe this, you might get a better final grade."

Proof by Intimidation:

"You better believe this if you want to pass the course."

Proof by Interruption:

Keep interrupting until your opponent gives up.

Proof by Misconception:

An example of this is the Freshman's Conception of the Limit Process: "2 equals 3 for large values of 2." Once introduced, any conclusion is reachable.

Proof by Obfuscation:

A long list of lemmas is helpful in this case - the more, the better.

Proof by Confusion:

This is a more refined form of proof by obfuscation. The long list of lemmas should be arranged into circular patterns of reasoning - and perhaps more baroque structures such as figure-eights and fleurs-de-lis.

Proof by Exhaustion:

This is a modification of an inductive proof. Instead of going to the general case after proving the first one, prove the second case, then the third, then the fourth, and so on - until a sufficiently large n is achieved whereby the nth case is being propounded to a soundly sleeping audience.

References: I don't have any.

Prove Anything

Methods for getting people to believe you (as good as, if not better than, proof). A collection of proof techniques that
will prove invaluable to both mathematicians and members of the general public.

     PROOF TECHNIQUE #1 - 'Proof By Induction'
        1.Obtain a large power transformer.
        2.Find someone who does not believe your theorem.
        3.Get this person to hold the terminals on the HV side of the transformer.
        4.Apply 25000 volts AC to the LV side of the transformer.
        5.Repeat step (4) until they agree with the theorem.
     PROOF TECHNIQUE #2 - 'Proof By Contradiction'
        1.State your theorem.
        2.Wait for someone to disagree.
        3.Contradict them.
     PROOF TECHNIQUE #3 - Fire Proof
        1.Summon all your inferiors for a departmental meeting.
        2.Present your theorem.
        3.Fire those who disagree.
     PROOF TECHNIQUE #4 - The Famous Water Proof
        1.State your theorem.
        2.Wait for someone to disagree.
        3.Drown them.
     This is closely related to the 'bullet' proof, but is easier to make look like an accident.
     PROOF TECHNIQUE #5 - Idiot Proof
        1.State your theorem.
        2.Write exhaustive documentation with glossy colour pictures and arrows about which bit goes where.
        3.Challenge anyone to not understand it.
     PROOF TECHNIQUE #6 - Child Proof
        1.State your theorem.
        2.Encapsulate it in epoxy and shape it into an ellipsoid.
        3.Put it in a jar with all the other proofs (one with one of those Press-to-Open lids).
        4.Give it to a professor and challenge him to open it.
     PROOF TECHNIQUE #7 - Rabbit Proof
        1.Generate theorems at an altogether startling rate, much faster than anybody is able to refute them. Use up
          every body else's paper. Run away at the slightest sign of danger.
        2.Leave any crap in small, easily identified piles, in prominent places where you no longer are, and it cannot
          in fact be proven that you ever were.
     PROOF TECHNIQUE #8 - Fool Proof
        1.State your theorem.
        2.Invite colleagues to comment.
          If they don't agree, exclaim loudly, "You Fools!"