Maths Humour

Quick Reference

• Math Riots
• Noah's Maths
• Quotes from Oxbridge Maths Lectures
• 13 Misunderstandings in the History of Maths
• Polly Nomial
• Maths Through the Decades
• Mathmo Quiz

Math Riots

MATH RIOTS PROVE FUN INCALCULABLE

Yes, admittedly, there was rioting and vandalism last week during the celebration. A few bookstores had windows smashed and shelves stripped, and vacant lots glowed with burning piles of old dissertations. But overall we can feel relief that it was nothing -- nothing -- compared to the outbreak of exuberant thuggery that occurred in 1984 after Louis DeBranges finally proved the Bieberbach Conjecture.

"Math hooligans are the worst," said a Chicago Police Department spokesman. "But the city learned from the Bieberbach riots. We were ready for them this time."

When word hit Wednesday that Fermat's Last Theorem had fallen, a massive show of force from law enforcement at universities all around the country headed off a repeat of the festive looting sprees that have become the traditional accompaniment to triumphant breakthroughs in higher mathematics.

Mounted police throughout Hyde Park kept crowds of delirious wizards at the University of Chicago from tipping over cars on the midway as they first did in 1976 when Wolfgang Haken and Kenneth Appel cracked the long-vexing Four-Color Problem. Incidents of textbook-throwing and citizens being pulled from their cars and humiliated with difficult story problems last week were described by the university's math department chairman Bob Zimmer as "isolated."

Zimmer said, "Most of the celebrations were orderly and peaceful. But there will always be a few -- usually graduate students -- who use any excuse to cause trouble and steal. These are not true fans of Andrew Wiles."

Wiles himself pleaded for calm even as he offered up the proof that there is no solution to the equation x^n + y^n = z^n when n is a whole number greater than two, as Pierre de Fermat first proposed in the 17th Century. "Party hard but party safe," he said, echoing the phrase he had repeated often in interviews with scholarly journals as he came closer and closer to completing his proof.

Some authorities tried to blame the disorder on the provocative taunting of Japanese mathematician Yoichi Miyaoka. Miyaoka thought he had proved Fermat's Last Theorem in 1988, but his claims did not bear up under the scrutiny of professional referees, leading some to suspect that the fix was in. And ever since, as Wiles chipped away steadily at the Fermat problem, Miyaoka scoffed that there would be no reason to board up windows near universities any time soon; that God wanted Miyaoka to prove it.

In a peculiar sidelight, Miyaoka recently took the trouble to secure a U.S. trademark on the equation "x^n + y^n = z^n " as well as the now-ubiquitous expression "Take that, Fermat!" Ironically, in defeat, he stands to make a good deal of money on cap and T-shirt sales.

This was no walk-in-the-park proof for Wiles. He was dogged, in the early going, by sniping publicity that claimed he was seen puttering late one night doing set theory in a New Jersey library when he either should have been sleeping, critics said, or focusing on arithmetic algebraic geometry for the proving work ahead.

"Set theory is my hobby, it helps me relax," was his angry explanation. The next night, he channeled his fury and came up with five critical steps in his proof. Not a record, but close.

There was talk that he thought he could do it all by himself, especially when he candidly referred to University of California mathematician Kenneth Ribet as part of his "supporting cast," when most people in the field knew that without Ribet's 1986 proof definitively linking the Taniyama Conjecture to Fermat's Last Theorem, Wiles would be just another frustrated guy in a tweed jacket teaching calculus to freshmen.

His travails made the ultimate victory that much more explosive for math buffs. When the news arrived, many were already wired from caffeine consumed at daily colloquial teas, and the took to the streets en masse shouting, "Obvious! Yessss! It was obvious!"

The law cannot hope to stop such enthusiasm, only to control it. Still, one has to wonder what the connection is between wanton pillaging and a mathematical proof, no matter how long-awaited and subtle.

The Victory Over Fermat rally, held on a cloudless day in front of a crowd of 30,000 (police estimate: 150,000) was pleasantly peaceful. Signs unfurled in the audience proclaimed Wiles the greatest mathematician of all time, though partisans of Euclid, Descartes, Newton, and C.F. Gauss and others argued the point vehemently.

A warmup act, The Supertheorists, delighted the crowd with a ragged song, "It Was Never Less Than Probable, My Friend," which included such gloating, barbed verses as --- "I had a proof all ready / But then I did a choke-a / Made liberal assumptions / Hi! I'm Yoichi Miyaoka."

In the speeches from the stage, there was talk of a dynasty, specifically that next year Wiles will crack the great unproven Riemann Hypothesis ("Rie-peat! Rie-peat!" the crowd cried), and that after the Prime-Pair Problem, the Goldbach Conjecture ("Minimum Goldbach," said one T-shirt) and so on.

They couldn't just let him enjoy his proof. Not even for one day. Math people. Go figure 'em.

Noah's Maths

Noah, being the resourceful man he was, immediately got busy cutting down trees and building a large table with the unfinished lumber therefrom. And he saw that it was good. The snakes were overjoyed when Noah picked them up and placed them on it. Noah and the snakes both knew that even adders could multiply on a log table.

• "Graphs of higher degree polynomials have this habit of doing unwanted wiggly things."
• "I don't want to go into this in detail, but I would like to illustrate some of the tedium."
• "If I am incomprehensible then stop me, but if it's simply wrong then I don't think that it matters."
• "If you've got a problem with this then go back, write the whole thing out using sigma notation and convince yourself that it's better not to have problems."
• "A one by one matrix has one column and one row, and the same number in both. "
• "Any questions? [pause] You all look asleep - what is it, hyperglucocemia? Too much sugar on your cornflakes? Not any cornflakes? Never mind - I'm bright eyed and bushy tailed, so let's continue."
• "Damn! I'm running out of integers!"
• "When you stick your fingers in the mains, its not the imaginary component which you will feel."
• "I'll give you a clue - it begins with `f' and rhymes with `factor'..."
• "The object of this lecture is to frighten half of you away."
• "I wrote my first program in 1954, and that didn't work either."
• "That is the total and absolute generalisation ... well, almost."
• "Dr. X hasn't lectured a Cambridge group before, so he might be quite interesting."
• "Some students may feel that the contents of Question 33 are both dull and useless. I must confess that my first impulse is to reply that it serves them right for doing the fast course."
• "I've never tried dividing both sides by infinity before, so here goes."
• "It's OK to divide by zero, provided you don't cancel it."
• "It's a real integer, not just any old integer."
• "To a mathematician, PI is 1 and PI^2 is 10. 2*PI we're not quite sure about."
• "This is the simple form. [pause] Well, it's simple in the sense that it leaves out all the really important bits."
• "This is obvious. But don't look at it too carefully, or it becomes unobvious, until you look at it for a long time when it becomes obvious again."
• "FORTRAN... Then, as now, the language used by scientists with real problems."
• Supervisor (drawing a graph): "This function has no nodes."
  (Pause)
  "How does it smell?"
• "Theoretical physicists tend to assume that Nature isn't as malevolent as our pure mathematical examiners."
• "A sphere isn't that simple when you get into higher dimensions - it's a bit non-flat."
• "Mathmos think of engineers a bit like lemmings... ...they're both wooly and jump to the wrong conclusions."
• "I don't see the point of lecturers talking, except to resolve some of the ambiguities in their handwriting."
• "Various people with suicidal tendencies can even integrate elliptic functions."
• "This course could be viewed as 1001 things to do with your favourite matrix"
• "For non-deterministic read 'Inhabited by pixies'."
• "Unless x is a banana or some other such object that commutes with A."
• "I know you all have very innocent minds, but occasionally a word should be allowed to wander through before reaching the paper."
• "The prime leaps on to the other factor in a most convenient fashion."
• "This is rigorous. Well, it's rigorous in the sense that ... All right, it's not rigorous."
• "A real gentleman never takes bases unless he really has to."
• "This book fills a well needed gap in the literature."
• "Trying to solve differential equations is a youthful aberration that you will soon grow out of."
• "Nature abhors second order differential equations."
• "Of course,this isn't really the best way to do it. But seeing as you're not quite as clever as I am -- in fact none of you are anywhere near as clever as I am -- we'll do it this way."
• "Now we'll prove the theorem. In fact, I'll prove it all by myself."
• "If you haven't enjoyed the material in the last few lectures then a career in chartered accountancy beckons."
• "Any theorem in Analysis can be fitted onto an arbitrarily small piece of paper if you are sufficiently obscure."
• "This must be wrong by a factor that oughtn't to be too different from unity."
• "I'm not going to say exactly what I mean because I'm not absolutely certain myself."
• "If you play around with your fingers for a while, you'll see that's true."
• "To do this we use a special theorem... the theorem that says that secretly this is an applied maths course."
• "In the sort of parrot-like way you use to teach stats to biologists, this is expected minus observed."
• "You could define the subspace topology this way, if you were sufficiently malicious."
• "This handout is not produced for your erudition but merely so I can practice the TeX word-processor."
• "Just because they are called 'forbidden' transitions does not mean that they are forbidden. They are less allowed than allowed transitions, if you see what I mean."
• "If you find bear droppings around your tent, it's fairly likely that there are bears in the area."
• "This isn't true in practice - what we've missed out is Stradivarius's constant. For those of you who don't know, that's been called by others the fiddle factor..."
• "Graphs of higher degree polynomials have this habit of doing unwanted wiggly things."
• "This is a one line proof... if we start sufficiently far to the left."
• "Sorry, I should have made that completely clear. This is a shambles."
• "I'm not going to get anything more useful done in this lecture, so I might as well talk."
• "Before I started this morning's lecture I was going to tell you about my third divorce but on reflection I thought I'd better tell my wife first."
• "I can see T is tending to infinity for you as well."
• "If I am incomprehensible then stop me, but if it's simply wrong then I don't think that it matters."
• "I shall explain this by waving my hands about in an appropriate manner."
• "There's a number down here which, for the sake of argument, we can call 1."
• "I'm going to make a small point in the corner of the board [does so], and come back to it later!" And later...
  "The thing which caused me to write 'lies' in extremely small letters in the corner of the board was..."
• "Proof left as an exercise for your supervisor."
• "This principle is sometimes known as assuming the CIA is paying our computing bills."
• "You could sort a sequence by assigning 1,2,3... to it. That's the fastest sort routine I know of!"
• "This is the stage where I start to pray."
• "I have a personality disorder: I don't like to assume things are measurable."
• "Integration by parts is not economical on paper."
• "I worked it out last night - let's see if it works in the daylight."
• "'3+1' is physicists' notation for '4'."
• "Has anyone got it out yet? (Pause) You're not doing it are you?"
• "It looks an incredibly integrable function."
• "The proof is not required for Finals, but I'm going to give you it anyway because it's nice."
• "Tonelli would tell us..." (undergraduate) "No he wouldn't, he's dead."
• "If you want to cut corners, an intelligent corner to cut is not to learn the proofs of any of these theorems."
• "I am falling into a trap. I assume I know it's there - I want to fall into it"
• "We could do it if we could pull the sum sign through and that's what God gave us the monotone convergence theorem for."
• "I'm going to use this diagram. It's not completely silly."
• "Let's fall into the trap - let's do the obvious thing."
• "It will enable you to pull derivatives through integrals, which you have wanted to do all your life - and some of you have been. This tells you when you can legally do it."
• "Watch this proof carefully - it looks like a confidence trick."
• A lecturer trying to justify an obscure step in a proof: "(pause) because it isn't."

13 Misunderstandings in the History of Maths

In the interest of historical accuracy let it be known that...

1. Fibonacci's daughter was not named "Bunny."
2. Michael Rolle was not Danish, and did not call his daughter "Tootsie."
3. William Horner was not called "Little-Jack" by his friends.
4. The "G" in G. Peano does not stand for "grand."
5. Rene Descartes' middle name is not "push."
6. Isaac Barrow's middle name is not "wheel."
7. There is no such place as the University of Wis-cosine, and if there was, the motto of their mathematics department would not be "Secant ye shall find."
8. Although Euler is pronounced oil-er, it does not follow that Euclid is pronounced oi-clid.
9. Franklin D. Roosevelt never said "The only thing we have to sphere is sphere itself."
10. Fibonacci is not a shortened form of the Italian name that is actually spelled: F i bb ooo nnnnn aaaaaaaa ccccccccccccccccccccccccccccccccccc iiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiii.
11. It is true that August Mobius was a difficult and opinionated man. But he was not so rigid that he could only see one side to every question.
12. It is true that Johannes Kepler had an uphill struggle in explaining his theory of elliptical orbits to the other astronomers of his time. And it is also true that his first attempt was a failure. But it is not true that after his lecture the first three questions he was asked were "What is elliptical?" What is an orbit?" and "What is a planet?
13. It is true that primitive societies use only rough approximations for the known constants of mathematics. For example, the northern tribes of Alaska consider the ratio of the circumference to the diameter of a circle to be 3. But it is not true that the value of 3 is called Eskimo pi. Incidentally, the survival of these tribes is dependent upon government assistance, which is not always forthcoming. For example, the Canadian firm of Tait and Sons sold a stock of defective compasses to the government at half-price, and the government passed them onto the northern natives. Hence the saying among these peoples: "He who has a Tait's is lost."

Polly Nomial

Now Polly was convergent and her mother had made it an absolute condition that she must never enter an array without her brackets on. Polly, however, who had changed her variables that morning and was feeling particularly badly behaved, ignored this condition on the grounds that is was insufficient and made her way in amongst the complex elements. Rows and columns envoloped her on all sides, Tangents approached her surface - she became tensor and tensor. Quite suddenly three branches of a hyperbola touched her at a single point. She oscillated violently, lost all sense of directrix, ane went completely divergent. As she reached a turning point she tripped over a square root which was protruding from the erf and plunged headlong down a steep gradient. When she was differential once more, she found herself, apparently, in a non-Euclidean space.

She was being wathced however. That smooth operator Curly Pi, was lurking inner product. As his eyes devoured her curvilinear coordinate a circular expression crossed his face. "Was she convergent?", he wondered. He decided to integrate improperly at once. Hearing a vulgar fraction behind her, Polly turned round and saw Curly Pi approaching her with his power series extrapolated. She could see at once by his degenerate conic and his dissipative terms that he was bent on no good.

"Eureka" she gasped.

"Ho, ho" he said, "What a symmetric little Polly Nomial you are. I can see you're absolutely bubbling over with secs."

"O Sir", she protested, "keep away from me. I haven't got my brackets on."

"Calm yourself, my dear", said our smooth operator.

"i, i" she thought, "perhaps he's homogeneous then?"

"What order are you?", the brute demanded.

"17", replied Polly.

Curly leered, "I suppose you've never been operated on before?" he said.

"Of course not", Polly replied indignantly, "I'm absolutely convergent".

"Come, come", said Curly, "let's take off to a decimal place I know, and I'll take you to the limit."

"Never" gasped Polly.

"P1000", he swore, using the vilest oath he knew. His patience was gone.

Coshing her over the coefficient with a lot until she was powerless, Curly removed her discontinuities. He stared at her significant places and began smoothing her points of inflection. Poor Polly was all up. She felt her hand tending to her asymptotic limit. Her convergence would soon be gone for ever.

There was no mercy, for Curly was a Heavyside operator. He integrated by partial fractions. The complex beast even went all the way round and did a contour integration; Curly went on until he was absolutely orthogonal.

When Polly got home that evening, her mother noticed that she had been truncated in several places. But it was too late to differentiate now. As the months went by, Polly increased monotonically. Finally she generated a small but pathological function which left surds all over the place until she was driven to distraction.

The moral of our sad story is this: never, if you want to keep your expressions convergent, allow them a single degree of freedom.

Maths Through the Decades

1970 maths question:
"A logger sells a load of timber for $100. His production costs are 3/4 of the selling price, in other words $75. What profit does he make?"

1980 maths question:
"A logger sells a load of timber for $100. His production costs are 3/4 of the selling price, or $75, leaving $25 profit. Underline the number twenty-five.

1990 maths question:
"A logger cuts down some beautiful trees to in order to make $25 profit. What do you think of this way of earning a living, and how do you think the squirrels feel?"

1. You first went out with your other half (for lunch) on January 5th.
   When's your one-month anniversary?
   1. Your what?
   2. The day that you get back from work to find your other half in a terminal sulk and refusing to speak to you.
   3. February 5th.
   4. February 2nd.
   5. Around midnight on February 4th/5th.
2. You're sitting at home on the sofa together when your other half suddenly asks "What are you thinking?"
   You reply:
   1. "There's got to be a simpler way to solve Taniyama-Shimura than Wiles' approach."
   2. "Uh?"
   3. "You'll regret having asked me if I tell you."
   4. "Do you really want to know, or is this one of those social convention things?"
   5. "How wonderful it would be if we moved in together and had kids."
3. What do you buy your beloved for her birthday?
   1. Chocolate
   2. Cuddly toy
   3. Tom Lehrer CD
   4. Jewellery
   5. Whatever the corner shop's selling when you're almost home from work and suddenly remember what day it is.
4. And what does she buy you?
   1. A pocket calculator
   2. A pocket calculator that uses RPN
   3. Pretty much the most tasteful, best-fitting piece of clothing that you have owned or will ever own
   4. Alcohol
   5. "Men are from Mars, Women are from Venus"
5. Okay, it's the first time you're buying her underwear. After having orbited the store a few times to build up courage, you make it over the threshold and make a beeline for a helpful assistant.
   "No problem," she says cheerfully when you explain the situation. "What size is she?"
   1. You have no idea, and have to leave to find out
   2. You have no idea, but try to approximate by pointing at various other people in the store
   3. You have no idea, and make the figures up on the spot
   4. You hand over the piece of paper with the numbers on
   5. You hand over the piece of paper with the parameters of the spline for her Y-Z axis profile.
6. Your home PC says a lot about you. What kind is it?
   1. A Mac
   2. A battered early Pentium
   3. A 1-3 year old reasonably-specc'd P2/P3 or equivalent
   4. Brand new top-of-the range P4/Athlon with ridiculously high specs
   5. Don't you mean 'What kinds are they?'
7. What OS are you running?
   1. MacOS =20
   2. Win 3.1
   3. Win 95/98/ME
   4. Win NT/2000/XP
   5. Unix flavour
   6. At least 3 of the above on a multi-boot configuration that no-one else can figure out how to use
8. And what do you normally use it for?
   1. Word processing and household accounts
   2. Mathematica / LaTeX
   3. Quake/Unreal Tournament/Half Life
   4. Email / web browsing
   5. Controlling pretty much every piece of electrical equipment in the house
9. Your choice of clothing in the morning is primarily dictated by:
   1. The people you'll be seeing throughout the day and the impression you want to make on them
   2. Your other half
   3. A list of valid colour combinations painstakingly worked out over many years and pinned on your wall
   4. What's on top in the clothes drawer
   5. What's least offensive-smelling in the laundry basket
10. You're in a restaurant and have ordered a main course of fish. The waiter asks whether you would like red or white wine.
    You answer:
    1. "Red"
    2. "White"
    3. "Rose"
    4. "No"
    5. "Yes"
11. How many Pratchett books do you have on your shelves?
    1. None, they're superficial and pointless fantasy
    2. 1-4
    3. 5-10
    4. 11-40
    5. None, they're all piled on your bedside table
12. It's time to buy your first house, and you're meeting your mortgage advisor.
    You ask for:
    1. advice on fixed rate vs. discount mortgages
    2. recommendations for conveyancing agencies
    3. the mortgage repayment formula
    4. clarification as to why their repayment calculations don't match the ones you've derived from first principles
    5. their job
13. How many of your mathmo mates became accountants?
    1. Mathmo mates?
    2. A couple
    3. About half
    4. Nearly all of them
    5. None; accountancy was too exciting so they became actuaries
14. Is the glass half-full or half-empty?
    1. Half-empty
    2. Half-full
    3. What glass?
    4. Define 'full'
    5. Define 'is'
15. y. dy/dx = 2x^3 +1. Solve to get y = sqrt(x^4/2 + x + c).
    How?
    1. Multiply both sides by dx and integrate.
    2. Find a mathmo and ask them.
    3. By inspection.
    4. Apply the Chain Rule, Product Rule and FCT to derive a valid solution in the space of Riemann-integrable functions
    5. The answer is in the question and is clearly valid by substitution therefore it's trivial.

Scoring:

1. a=4 b=3 c=0 d=1 e=5
2. a=4 b=1 c=2 d=3 e=-5
3. a=1 b=1 c=4 d=1 e=3
4. a=2 b=4 c=2 d=1 e=3
5. a=2 b=2 c=3 d=0 e=5
6. a=-1 b=3 c=3 d=1 e=5
7. a=-1 b=2 c=0 d=-1 e=3 f=5
8. a=0 b=3 c=2 d=1 e=4
9. a=0 b=3 c=2 d=1 e=5
10. a=2 b=0 c=2 d=1 e=4
11. a=0 b=1 c=2 d=3 e=4
12. a=0 b=-1 c=2 d=4 e=1
13. a=0 b=1 c=2 d=3 e=4
14. a=1 b=1 c=2 d=3 e=5
15. a=1 b=0 c=5 d=3 e=4

-8 - 0

Maths-illiterate

1 - 10

Maths-phobic

11 - 20

Probably a normal human being

21 - 34

Recovering from a maths degree

35 - 44

In maths nerd territory

45 - 54

Desperately in need of a life

55 - 65

Probably a danger to society.

My personal score was 40, so that's your baseline...
Original by Adrian Hilton

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