Compiled from experience by many at Cambridge University and someone called Dana Angluin who I know nothing about. "Proof by a woman" was removed as it was blantantly sexist. [] means "End of Proof"

Things start to go wrong at school, when you are first introduced to the "Proof by Division by Zero". By University, you have gotten a little wiser, so _they_ introduce some variants:

Proof by Bullshit - Write down hundreds of symbols in a fast and frenzied manner while mumbling a constant stream of vaguely technical jargon. Ensure that at least one line looks vaguely like the answer, and underline it several times. Move quickly onto the next question.

Proof by Misdirection - Waffle on until the students become disinterested and start staring into space, and then write anything you fancy on a piece of paper, which you quickly cast aside, asking "Do you see that now?"

Proof by Writing the Answer Down - Scribble down the answer without any working whatsoever, while hinting at how trivial the question is. (A crib sheet under the desk may be useful.)

Proof by Changing the Question - This is a very slick method for use with questions containing fancy mathematical terminology - by declaring sagely that the wording of the question implies some cunning simplification, you can make the hardest problems completely trivial.

Proof by "Surely You Can See That Makes..." - Plough through the problem until you are completely stuck and then do as for Proof by Writing the Answer Down.

Proof by "See if You Can Take it From There..." - As above, but leave the last part to the students. (I sometimes think that some lecturers would give this proof for the 4-colour theorem, given half a chance.)

Proof by Precognition - Use a result you are going to prove in "just a few days" with the assurance that all will be clear when you look back at your notes for revision. Then in "just a few days, you prove the result, using what you have already shown from it.

Proof by Example - Demonstrate that it works for a few carefully chosen numbers you know in advance will not give the students even a hint of the difficulty in finding a general proof. Alternatively, state WLOG (without loss of generality) and then prove a specific example that you know works.

Proof by Intimidation - Ask the audience if anybody can't see how to prove it. Nobody will put their hand up.

Proof by Omission - Cultivate such a tedious lecturing style during the first lecture, so that no-one arrives for any subsequent lectures, so that proofs are not required.

Proof by TeX - Apologize for not being a TeX wizard, but claim that a random series of squiggles, and diverse other marks on the handout constitute a proof.

Proof by Indirection - Find a book which contains the proof, and explain that the proof is trivial, but dedicated students can find it in <%EXPENSIVE MATHEMATICAL TEXT>

Proof by Xerox - As for proof by TeX, except that you rely on the run- down toner cartridge in the photocopier to hide the errors.

Proof by Reduction - Take any four A4 sheets of lines of mathematical working, and use a photocopier to reduce to 1/4 size, with the contrast set incorrectly, and assert that these sheets constitute an elegant, if lengthy proof.

Proof by Intuition - Promise a proof to be given next year, and next year say that the thing is intuitively obvious and something you've known for years.

Proof by Non-existent Reference - Claim the proof is available in Chapter 9 of the excellent well-known book by Prof. Schraufen Zieger which should be available in any respectable library. The book either has 8 chapters, or does not exist.

Proof by Honesty - This really is true. Honest!

Proof by Change of Direction - State A >= B, waffle about until everybody has forgotten the theory, then prove A <= B.

Proof by Jumping into Heavens - State premises. Then say "and this clearly implies <ANY MEANINGLESS STATEMENT> which is obviously equivalent to". State conclusion.

Proof by Pure Maths - State that the result is proved in Analysis III/ Linear Analysis and go to them if you really want to know.

Proof by Axiom - We can see that <%EXPRESSION> ... therefore <%SAME EXPRESSION>.

Proof by Cross-breeding - Start off with an equation which is patently false, and gradually annotate it with more and more corrections as the audience points out the mistakes. Eventually you will end up with something so completely intractable that you can claim "This can be simplified to <%WHATEVER YOU WANT>" and nobody will be able to work out that it can't.

Proof by Lecturer - "Your lecturer will prove this result later in the course."

Proof by Supervisor - "Your supervisor will prove this if you ask him about this part of the lecture course."

Proof by Other Supervisor - " Your <%COURSE> supervisor will deal with this.

Proof by Introduction of Terminology - "Theorem: Every planet is an orange. Proof: Define: A round ball is a stellar object. Define: A ball is an orange citrus fruit from which one can make orange juice. Clearly every planet is a round ball, hence surely a ball and therefore an orange. []"

Proof by Tedium - this elegant method is was actually used by Dr. XXX in Algebra III. He wrote down a theorem and chalked underneath it. Proof: Boring! []

Proof by Blackmail - If you don't believe this is true, then I'll write down the long, incredibly excruciatingly boring proof after the lecture - does anyone want to see it? (Pause) Right, I won't bother.

Proof by Convenience - This isn't strictly speaking true, but that remark makes all our calculations meaningless, so we'll assume it is. (This requires courage)

Proof by Example Sheet - Derive some result looking vaguely similar to the required one and then say, "which is correct modulo a sign or two and a couple of powers of alpha, so it's just an algebraic mistake - you can easily do it yourself."

Proof by Mendacity - As above, but the rubric goes, "and on the example sheet, there's a mistake of a couple of signs and the odd power of alpha."

Proof by Construction - a good one for engineers. "This looks wrong, but it works if you build it."

Proof by Physical Intuition - Look, I could prove this formally, but you can see that it's got to be true physically anyway, and since you're a scientist and not a mathematician (ouch!), that should be good enough.

Proof by Contradiction - Assume result ... long incomprehensible working ... hence a contradiction, hence result.

Proof by Necessity - If this result isn't true, then I've been talking balls all week. - As an extension, the negation of the proposition is unimaginable or meaningless. Popular for proofs of the existence of a God.

Proof by Authority - This result is due to <%EMININENT MATHEMATICIAN> (preferably a head of department).

Proof by Thinly Veiled Threat - If this isn't obvious to you, you shouldn't be taking this course.

Proof by Number-Crunching - This result follows immediately from 1.4 along with Corollaries 2.4(b) and 2.6(a), using the same method we used in 1.6(b), replacing alpha with 4 pi q / episolon nought where required, then substitute the answer into 3.3 to give the result.

Proof by Prevarication - Has your <%COURSE> lecturer covered <%TOPIC> yet? Some geek : 'No!' Oh well, this is actually a trivial <%TOPIC> problem, and the proof will be obvious to you when you cover it.

Proof by Variation of Statement - Ah yes, b was supposed to equal 3 rather than 1. Just change it all the way through and you'll see it comes out all right.

Proof by Reduction and Confusion - We'll omit some of the hypotheses for the moment and add them later when we see what they need to be to make the result work.

Proof by Simplification - We'll prove continuity: differentiability is harder.

Proof by Illegibility - Is that a z or a 2? Doesn't really matter as we get something useful either way.

Proof by Chronometry - Well, we'll finish the proof next time... Last time we proved that...

Proof by Invisible Blue Chalk - We now integrate along the blue contour.

Proof by Erasure - By the lemma which I've just rubbed off...

Proof by Practicality - This isn't true in general, but you'll see by a few examples that it's true for all reasonable functions.

Proof by "I think that's not on the/your syllabus" - you don't really need this to pass the exam, so we won't bother with it.

Proof by Obviousness - This is obvious.

Proof by a Hint - simply write down the hint, followed by the desired result. The hint is obviously true, and the result follows clearly from it.

Proof by Integration by Inspection - Simply write down the answer with no hint as to how you arrived at it. Any fool can differentiate it to discover it is right; hence the problem is solved.

Proof by Dodgy Assumption - "We assume a generalized version of the Riemann Hypothesis..."

Proof by Circular Reference - Prove the result using an assumption proved later in the course. When proving this, assume the result previously proven.

Proof by looking like Basil Fawlty - !

Proof by the Clock - Waffle on until the hour is up, and then run out the door as you have another supervision to give halfway across Cambridge.

Proof by Feynman - Invent a new functional integral and say that it takes care of all the problems.

Proof by Illegibility - Use u, v and y in a proof. Give the v a rounded bottom and run the tail of the y into the divide by line. Do NOT read out the equations and write small. - Alternatively, resort to Greek or Cyrilic alphabets. Students will never differentiate (nu) and v, or (ioto) and i.

Proof by Squaring - Ideal to hide that missing +/- sign. Square the equations half way through, and then take the root at the end. This allows you to assume whichever sign you want.

Proof by OHP - On an overhead projector - now we can write down five conditions here (shows transparency) and it is easy to verify that Aimpliesbimpliescwhichisequivalenttodandtoe (removes transparency while students still writing down a). Write down complicated equation with subscripts, then say "Oops, there's a mistake there" and proceed to smudge out half the equation so that you can write a single subscript ridiculously large in thick black pen.

Proof by Hospital - Get taken to hospital suffering from a stress related condition before proving anything, but after setting the examination questions. Leave the students to try to find something in the library.

Proof by Vigorous Handwaving - works well when teaching to a small number.

Proof by Obfuscation - A long plotless sequence of true and/or meaningless syntactically related statements.

Proof by Wishful Citation - The lecturer cites the negation, converse, or generalization of a theorem from the literature.

Proof by Accumulated Evidence - Long and diligent search has not revealed a counter-example.

Proof by Metaproof - A method is given to construct a desired proof.

Proof by Picture - More convincing than proof by example.

Proof by Semantic Shift - Some standard but inconvenient definitions are changed for the statement of the result.

Proof by Clarity - (fairly controversial) Know you subject. Check your proof in several book. Explain the strategy of the proof to your audience. Write clearly and speak loudly. Justify each step. Use a minimum of notation and draw a useful diagram. Reach a conclusion with the theorem clearly proved. This fails in the long term as the first couple of lectures take 90% of the course leaving the lecturer sprinting through the rest and leaving everyone stranded.

Go Back