(if you can understand all of them, you have taken too many math classes)

Several students were asked the following problem:

Prove that all odd integers are prime.

Well, the first student to try to do this was a math student. Hey says "Hmmm... Well, 1 is prime, 3 is prime, 5 is prime, and by induction, we have that all the odd integers are prime."

Of course, there are some jeers from some of his friends. The physics student then said, "I'm not sure of the validity of your proof, but I think I'll try to prove it by experiment." He continues, "Well, 1 is prime, 3 is prime, 5 is prime, 7 is prime, 9 is ... uh, 9 is an experimental error, 11 is prime, 13 is prime... Well, it seems that you're right."

The third student to try it was the engineering student, who responded, "Well, actually, I'm not sure of your answer either. Let's see... 1 is prime, 3 is prime, 5 is prime, 7 is prime, 9 is ..., 9 is ..., well if you approximate, 9 is prime, 11 is prime, 13 is prime... Well, it does seem right."

Not to be outdone, the computer science student comes along and says "Well, you two sort've got the right idea, but you'd end up taking too long doing it. I've just whipped up a program to REALLY go and prove it..." He goes over to his terminal and runs his program. Reading the output on the screen he says, "1 is prime, 1 is prime, 1 is prime, 1 is prime...."

Mathematician: 3 is a prime, 5 is a prime, 7 is a prime, 9 is not a prime - counter-example - claim is false.

Physicist: 3 is a prime, 5 is a prime, 7 is a prime, 9 is an experimental error, 11 is a prime, ...

Engineer: 3 is a prime, 5 is a prime, 7 is a prime, 9 is a prime, 11 is a prime, ...

Computer scientist: 3's a prime, 5's a prime, 7's a prime, 7's a prime, 7's a prime, ...

Computer scientist using Unix: 3's a prime, 5's a prime, 7's a prime, segmentation fault

Gosh, they all overlooked that even 2's a prime!! I figure that 2 is the oddest prime of all, because it's the only one that's even!

Theorem: a cat has nine tails.

Proof:

No cat has eight tails. A cat has one tail more than no cat. Therefore, a cat has nine tails.

My geometry teacher was sometimes acute, and sometimes obtuse, but always, he was right.

And now, for some really bad picture jokes (that I heard at Cal Poly SLO) :

Q: What's the title of this picture?

.. .. ____ .. .. \\===/======\\== || | | || || |____| || || ( ) || || \____/ || || || || || || || || || || || || || || || || || || || || (\ || || ) ) || || //||\\ ||

A: Hypotenuse

Q: What quantity is represented by this?

/\ /\ /\ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ /______\ /______\ /______\ || || || || || ||

A: 9, tree + tree + tree

Q: A dust storm blows through, now how much do you have?

A: 99, dirty tree + dirty tree + dirty tree

Q: Some birds go flying by and leave their droppings, one per tree,
how many is that?

A: 100, dirty tree and a turd + dirty tree and a turd + dirty tree and
a turd

I saw the following scrawled on a math office blackboard in college:

1 + 1 = 3, for large values of 1

___ lim \/ 8 = 3 8->9

Along the same lines:

___ lim \/ 3 = 2 3->4

Asked how his pet parrot died, the mathematician answered "Polynomial. Polygon."

Lumberjacks make good musicians because of their natural logarithms.

Q: What is Quayle-o-phobia?

A: The fear of natural logarithms. (Hint: Quayle and the letter "e"
made news.)

Pie are not square.

Pie are round.

Cornbread are square.

"The integral of e to the x is equal to f of the quantity u to the n."

/ x n | e = f(u ) /

A physics joke:

"Energy equals milk chocolate square"

Russell to Whitehead: "My Godel is killing me!"

A doctor, a lawyer and a mathematician were discussing the relative merits of having a wife or a mistress.

The lawyer says: "Certainly a mistress is better. If you have a wife and want a divorce, it causes all sorts of legal problems.

The doctor says: "It's better to have a wife because the sense of security lowers your stress and that is good for your health.

The mathematician says: " You're both wrong. It's best to have both so that when the wife thinks you're with the mistress and the mistress thinks you're with your wife --- you get some peace and quiet so that you can do some mathematics.

Von Neumann and Norbert Wiener were both the subject of many dotty professor stories. Von Neumann supposedly had the habit of simply writing answers to homework assignments on the board (the method of solution being, of course, obvious) when he was asked how to solve problems. One time one of his students tried to get more helpful information by asking if there was another way to solve the problem. Von Neumann looked blank for a moment, thought, and then answered, "Yes".

Wiener was in fact very absent minded. The following story is told about him: When they moved from Cambridge to Newton his wife, knowing that he would be absolutely useless on the move, packed him off to MIT while she directed the move. Since she was certain that he would forget that they had moved and where they had moved to, she wrote down the new address on a piece of paper, and gave it to him. Naturally, in the course of the day, an insight occurred to him. He reached in his pocket, found a piece of paper on which he furiously scribbled some notes, thought it over, decided there was a fallacy in his idea, and threw the piece of paper away. At the end of the day he went home (to the old address in Cambridge, of course). When he got there he realised that they had moved, that he had no idea where they had moved to, and that the piece of paper with the address was long gone. Fortunately inspiration struck. There was a young girl on the street and he conceived the idea of asking her where he had moved to, saying, "Excuse me, perhaps you know me. I'm Norbert Wiener and we've just moved. Would you know where we've moved to?" To which the young girl replied, "Yes daddy, mommy thought you would forget."

The capper to the story is that I asked his daughter (the girl in the story) about the truth of the story, many years later. She said that it wasn't quite true -- that he never forgot who his children were! The rest of it, however, was pretty close to what actually happened...

The USDA once wanted to make cows produce milk faster, to improve the dairy industry.

So, they decided to consult the foremost biologists and recombinant DNA technicians to build them a better cow. They assembled this team of great scientists, and gave them unlimited funding. They requested rare chemicals, weird bacteria, tons of quarantine equipment, there was a horrible typhus epidemic they started by accident, and, 2 years later, they came back with the "new, improved cow." It had a milk production improvement of 2% over the original.

They then tried with the greatest Nobel Prize winning chemists around. They worked for six months, and, after requisitioning tons of chemical equipment, and poisoning half the small town in Colorado where they were working with a toxic cloud from one of their experiments, they got a 5% improvement in milk output.

The physicists tried for a year, and, after ten thousand cows were subjected to radiation therapy, they got a 1% improvement in output.

Finally, in desperation, they turned to the mathematicians. The foremost mathematician of his time offered to help them with the problem. Upon hearing the problem, he told the delegation that they could come back in the morning and he would have solved the problem. In the morning, they came back, and he handed them a piece of paper with the computations for the new, 300% improved milk cow.

The plan began:

"A Proof of the Attainability of Increased Milk Output from Bovines:

Consider a spherical cow......"

An engineer, a mathematician, and a physicist went to the races one Saturday and laid their money down. Commiserating in the bar after the race, the engineer says, "I don't understand why I lost all my money. I measured all the horses and calculated their strength and mechanical advantage and figured out how fast they could run..."

The physicist interrupted him: "...but you didn't take individual variations into account. I did a statistical analysis of their previous performances and bet on the horses with the highest probability of winning..."

"...so if you're so hot why are you broke?" asked the engineer. But before the argument can grow, the mathematician takes out his pipe and they get a glimpse of his well-fattened wallet. Obviously here was a man who knows something about horses. They both demanded to know his secret.

"Well," he says, between puffs on the pipe, "first I assumed all the horses were identical and spherical..."

Theorem : All positive integers are equal.

Proof :

Sufficient to show that for any two positive integers, A and B, A = B. Further, it is sufficient to show that for all N > 0, if A and B (positive integers) satisfy (MAX(A, B) = N) then A = B.

Proceed by induction.

If N = 1, then A and B, being positive integers, must both be 1. So A = B.

Assume that the theorem is true for some value k. Take A and B with MAX(A, B) = k+1. Then MAX((A-1), (B-1)) = k. And hence (A-1) = (B-1). Consequently, A = B.

A bunch of Polish scientists decided to flee their repressive government by hijacking an airliner and forcing the pilot to fly them to a western country. They drove to the airport, forced their way on board a large passenger jet, and found there was no pilot on board. Terrified, they listened as the sirens got louder. Finally, one of the scientists suggested that since he was an experimentalist, he would try to fly the aircraft.

He sat down at the controls and tried to figure them out. The sirens got louder and louder. Armed men surrounded the jet. The would be pilot's friends cried out, "Please, please take off now!!! Hurry!!!!!!"

The experimentalist calmly replied, "Have patience. I'm just a simple pole in a complex plane."

A group of Polish tourists is flying on a small airplane through the Grand Canyon on a sightseeing tour. The tour guide announces: "On the right of the airplane, you can see the famous Bright Angle Falls." The tourists leap out of their seats and crowd to the windows on the right side. This causes a dynamic imbalance, and the plane violently rolls to the side and crashes into the canyon wall. All aboard are lost. The moral to this episode is: always keep your poles off the right side of the plane.

**Hiawatha Designs an Experiment**

Hiawatha, mighty hunter,

He could shoot ten arrows upward,

Shoot them with such strength and swiftness

That the last had left the bow-string

Ere the first to earth descended.

This was commonly regarded

As a feat of skill and cunning.

Several sarcastic spirits

Pointed out to him, however,

That it might be much more useful

If he sometimes hit the target.

"Why not shoot a little straighter

And employ a smaller sample?"

Hiawatha, who at college

Majored in applied statistics,

Consequently felt entitled

To instruct his fellow man

In any subject whatsoever,

Waxed exceedingly indignant,

Talked about the law of errors,

Talked about truncated normals,

Talked of loss of information,

Talked about his lack of bias,

Pointed out that (in the long run)

Independent observations,

Even though they missed the target,

Had an average point of impact

Very near the spot he aimed at,

With the possible exception

of a set of measure zero.

"This," they said, "was rather doubtful;

Anyway it didn't matter.

What resulted in the long run:

Either he must hit the target

Much more often than at present,

Or himself would have to pay for

All the arrows he had wasted."

Hiawatha, in a temper,

Quoted parts of R. A. Fisher,

Quoted Yates and quoted Finney,

Quoted reams of Oscar Kempthorne,

Quoted Anderson and Bancroft

(practically in extenso)

Trying to impress upon them

That what actually mattered

Was to estimate the error.

Several of them admitted:

"Such a thing might have its uses;

Still," they said, "he would do better

If he shot a little straighter."

Hiawatha, to convince them,

Organised a shooting contest.

Laid out in the proper manner

Of designs experimental

Recommended in the textbooks,

Mainly used for tasting tea

(but sometimes used in other cases)

Used factorial arrangements

And the theory of Galois,

Got a nicely balanced layout

And successfully confounded

Second order interactions.

All the other tribal marksmen,

Ignorant benighted creatures

Of experimental set-ups,

Used their time of preparation

Putting in a lot of practice

Merely shooting at the target.

Thus it happened in the contest

That their scores were most impressive

With one solitary exception.

This, I hate to have to say it,

Was the score of Hiawatha,

Who as usual shot his arrows,

Shot them with great strength and swiftness,

Managing to be unbiased,

Not however with a salvo

Managing to hit the target.

"There!" they said to Hiawatha,

"That is what we all expected."

Hiawatha, nothing daunted,

Called for pen and called for paper.

But analysis of variance

Finally produced the figures

Showing beyond all peradventure,

Everybody else was biased.

And the variance components

Did not differ from each other's,

Or from Hiawatha's.

(This last point it might be mentioned,

Would have been much more convincing

If he hadn't been compelled to

Estimate his own components

>From experimental plots on

Which the values all were missing.)

Still they couldn't understand it,

So they couldn't raise objections.

(Which is what so often happens

with analysis of variance.)

All the same his fellow tribesmen,

Ignorant benighted heathens,

Took away his bow and arrows,

Said that though my Hiawatha

Was a brilliant statistician,

He was useless as a bowman.

As for variance components

Several of the more outspoken

Make primeval observations

Hurtful of the finer feelings

Even of the statistician.

In a corner of the forest

Sits alone my Hiawatha

Permanently cogitating

On the normal law of errors.

Wondering in idle moments

If perhaps increased precision

Might perhaps be sometimes better

Even at the cost of bias,

If one could thereby now and then

Register upon a target.

W. E. Mientka, "Professor Leo Moser -- Reflections of a
Visit"

American Mathematical Monthly, Vol. 79, Number 6 (June-July, 1972)

See also "Applied Dynamic Programming" by Bellman and Dreyfuss, prior to 1962.

An assemblage of the most gifted minds in the world were all posed the following question:

"What is 2 x 2 ?"

The engineer whips out his slide rule (so it's old) and shuffles it back and forth, and finally announces "3.99".

The physicist consults his technical references, sets up the problem on his computer, and announces "it lies between 3.98 and 4.02".

The mathematician cogitates for a while, oblivious to the rest of the world, then announces: "I don't what the answer is, but I can tell you, an answer exists!".

Philosopher: "But what do you *mean* by 2 x 2 ?"

Logician: "Please define 2 x 2 more precisely."

Accountant: Closes all the doors and windows, looks around carefully,
then asks "What do you *want *the answer to be?"

Computer Hacker: Breaks into the NSA super-computer and gives the answer.

Economist: Someone who is good with numbers but lacks the personality to be an accountant.

Old mathematicians never die; they just lose some of their functions.

During a class of calculus my lecturer suddenly checked himself and stared intently at the table in front of him for a while. Then he looked up at us and explained that he thought he had brought six piles of papers with him, but "no matter how he counted" there was only five on the table. Then he became silent for a while again and then told the following story:

"When I was young in Poland I met the great mathematician Waclaw Sierpinski. He was old already then and rather absent-minded. Once he had to move to a new place for some reason. His wife didn't trust him very much, so when they stood down on the street with all their things, she said: - Now, you stand here and watch our ten trunks, while I go and get a taxi.

She left and left him there, eyes somewhat glazed and humming absently. Some minutes later she returned, presumably having called for a taxi. Says Mr. Sierpinski (possibly with a glint in his eye): - I thought you said there were ten trunks, but I've only counted to nine. - No, they're TEN! - No, count them: 0, 1, 2, ..."

What's non-orientable and lives in the sea?

Mobius Dick.

Philosopher: "Resolution of the continuum hypothesis will have profound implications to all of science."

Physicist: "Not quite. Physics is well on its way without those mythical `foundations'. Just give us serviceable mathematics."

Computer Scientist: "Who cares? Everything in this Universe seems to be finite anyway. Besides, I'm too busy debugging my Pascal programs."

Mathematician: "Forget all that! Just make your formulae as aesthetically pleasing as possible!"

Definition:

Jogging girl scout = Brownian motion.

limsin(x)= 6 n->oo n

Proof: cancel the n in the numerator and denominator.

Two male mathematicians are in a bar.

The first one says to the second that the average person knows very little about basic mathematics.

The second one disagrees, and claims that most people can cope with a reasonable amount of math.

The first mathematician goes off to the washroom, and in his absence the second calls over the waitress.

He tells her that in a few minutes, after his friend has returned, he will call her over and ask her a question. All she has to do is answer one third x cubed.

She repeats `one thir -- dex cue'? He repeats `one third x cubed'.

Her: `one thir dex cubed'? Yes, that's right, he says. So she agrees, and goes off mumbling to herself, `one thir dex cubed...'.

The first guy returns and the second proposes a bet to prove his point, that most people do know something about basic math.

He says he will ask the blonde waitress an integral, and the first laughingly agrees.

The second man calls over the waitress and asks `what is the integral of x squared?'.

The waitress says `one third x cubed' and while walking away, turns back and says over her shoulder `plus a constant'!

- 1) Have you ever been excited about math?
- 2) Had an exciting dream about math?
- 3) Made a mathematical calculation?
- 4) Manipulated the numerator of an equation?
- 5) Manipulated the denominator of an equation?
- 6) On your first problem set?
- 7) Worked on a problem set past 3:00 a.m.?
- 8) Worked on a problem set all night?
- 9) Had a hard problem?
- 10) Worked on a problem continuously for more than 30 minutes?
- 11) Worked on a problem continuously for more than four hours?
- 12) Done more than one problem set on the same night (i.e. both started and finished them)?
- 13) Done more than three problem sets on the same night?
- 14) Taken a math course for a full year?
- 15) Taken two different math courses at the same time?
- 16) Done at least one problem set a week for more than four months?
- 17) Done at least one problem set a night for more than one month (weekends excluded)?
- 18) Done a problem set alone?
- 19) Done a problem set in a group of three or more?
- 20) Done a problem set in a group of 15 or more?
- 21) Was it mixed company?
- 22) Have you ever inadvertently walked in upon people doing a problem set?
- 23) And joined in afterwards?
- 24) Have you ever used food doing a problem set?
- 25) Did you eat it all?
- 26) Have you ever had a domesticated pet or animal walk over you while you were doing a problem set?
- 27) Done a problem set in a public place where you might be discovered?
- 28) Been discovered while doing a problem set?

- Kinky Stuff

- 29) Have you ever applied your math to a hard science?
- 30) Applied your math to a soft science?
- 31) Done an integration by parts?
- 32) Done two integration by parts in a single problem?
- 33) Bounded the domain and range of your function?
- 34) Used the domination test for improper integrals?
- 35) Done Newton's Method?
- 36) Done the Method of Frobenius?
- 37) Used the Sandwich Theorem?
- 38) Used the Mean Value Theorem?
- 39) Used a Gaussian surface?
- 40) Used a foreign object on a math problem (e.g.: calculator)?
- 41) Used a program to improve your mathematical technique (e.g.: MACSYMA)?
- 42) Not used brackets when you should have?
- 43) Integrated a function over its full period?
- 44) Done a calculation in three-dimensional space?
- 45) Done a calculation in n-dimensional space?
- 46) Done a change of basis?
- 47) Done a change of basis specifically in order to magnify your vector?
- 48) Worked through four complete bases in a single night (e.g.: using the Graham-Schmidt method)?
- 49) Inserted a number into an equation?
- 50) Calculated the residue of a pole?
- 51) Scored perfectly on a math test?
- 52) Swallowed everything your professor gave you?
- 53) Used explicit notation in your problem set?
- 54) Purposefully omitted important steps in your problem set?
- 55) Padded your own problem set?
- 56) Been blown away on a test?
- 57) Blown away your professor on a test?
- 58) Have you ever multiplied 23 by 3?
- 59) Have you ever bounded your Bessel function so that the membrane did not shoot to infinity?
- 69) Have you ever understood the following quote:

MATHEMATICS PURITY TEST

Count the number of yes's, subtract from 60, and divide by 0.6.

The Basics

"The relationship between Z^{0} to C_{0}, B_{0},
and H_{0} is an example of a general principle which we have encountered:
the kernel of the adjoint of a linear transformation is both the annihilator
space of the image of the transformation and also the dual space of the
quotient of the space of which the image is a subspace by the image subspace."
(Sternberg & Bamberg's *A "Course" in Mathematics for Students
of Physics*, vol. 2)

A somewhat advanced society has figured how to package basic knowledge in pill form.

A student, needing some learning, goes to the pharmacy and asks what kind of knowledge pills are available. The pharmacist says "Here's a pill for English literature." The student takes the pill and swallows it and has new knowledge about English literature!

"What else do you have?" asks the student.

"Well, I have pills for art history, biology, and world history," replies the pharmacist.

The student asks for these, and swallows them and has new knowledge about those subjects.

Then the student asks, "Do you have a pill for math?"

The pharmacist says "Wait just a moment", and goes back into the storeroom and brings back a whopper of a pill and plunks it on the counter.

"I have to take that huge pill for math?" inquires the student.

The pharmacist replied "Well, you know math always was a little hard to swallow."

"A mathematician is a device for turning coffee into theorems" -- P. Erdos

Three standard Peter Lax jokes (heard in his lectures) :

1. What's the contour integral around Western Europe?

Answer: Zero, because all the Poles are in Eastern Europe!

Addendum: Actually, there ARE some Poles in Western Europe, but they are
removable!

2. An English mathematician (I forgot who) was asked by his very religious
colleague: Do you believe in one God?

Answer: Yes, up to isomorphism!

3. What is a compact city?

Answer: It's a city that can be guarded by finitely many near-sighted policemen!

"Algebraic symbols are used when you do not know what you are talking about."

Heisenberg might have slept here.

Moebius always does it on the same side.

Statisticians probably do it

Algebraists do it in groups.

(Logicians do it) or [not (logicians do it)].

A promising PhD candidate was presenting his thesis at his final examination. He proceeded with a derivation and ended up with something like:

F = -MA

He was embarrassed, his supervising professor was embarrassed, and the rest of the committee was embarrassed. The student coughed nervously and said "I seem to have made a slight error back there somewhere."

One of the mathematicians on the committee replied dryly, "Either that or an odd number of them!"

There was a mad scientist ( a mad *social* scientist ) who kidnapped
three colleagues, an engineer, a physicist, and a mathematician, and locked
each of them in separate cells with plenty of canned food and water but
no can opener.

A month later, returning, the mad scientist went to the engineer's cell and found it long empty. The engineer had constructed a can opener from pocket trash, used aluminium shavings and dried sugar to make an explosive, and escaped.

The physicist had worked out the angle necessary to knock the lids off the tin cans by throwing them against the wall. She was developing a good pitching arm and a new quantum theory.

The mathematician had stacked the unopened cans into a surprising solution to the kissing problem; his desiccated corpse was propped calmly against a wall, and this was inscribed on the floor in blood:

Theorem: If I can't open these cans, I'll die.

Proof: assume the opposite...

Problem: To Catch a Lion in the Sahara Desert.

(Hunting lions in Africa was originally published as "A contribution to the mathematical theory of big game hunting" in the American Mathematical Monthly in 1938 by "H. Petard, of Princeton New Jersey" [actually the late Ralph Boas]. It has been reprinted several times.

1. Mathematical Methods

1.1 The Hilbert (axiomatic) method

We place a locked cage onto a given point in the desert. After that we introduce the following logical system: Axiom 1: The set of lions in the Sahara is not empty. Axiom 2: If there exists a lion in the Sahara, then there exists a lion in the cage. Procedure: If P is a theorem, and if the following is holds: "P implies Q", then Q is a theorem. Theorem 1: There exists a lion in the cage.

1.2 The geometrical inversion method

We place a spherical cage in the desert, enter it and lock it from inside. We then perform an inversion with respect to the cage. Then the lion is inside the cage, and we are outside.

1.3 The projective geometry method

Without loss of generality, we can view the desert as a plane surface. We project the surface onto a line and afterwards the line onto an interior point of the cage. Thereby the lion is mapped onto that same point.

1.4 The Bolzano-Weierstrass method

Divide the desert by a line running from north to south. The lion is then either in the eastern or in the western part. Let's assume it is in the eastern part. Divide this part by a line running from east to west. The lion is either in the northern or in the southern part. Let's assume it is in the northern part. We can continue this process arbitrarily and thereby constructing with each step an increasingly narrow fence around the selected area. The diameter of the chosen partitions converges to zero so that the lion is caged into a fence of arbitrarily small diameter.

1.5 The set theoretical method

We observe that the desert is a separable space. It therefore contains an enumerable dense set of points which constitutes a sequence with the lion as its limit. We silently approach the lion in this sequence, carrying the proper equipment with us.

1.6 The Peano method

In the usual way construct a curve containing every point in the desert. It has been proven [1] that such a curve can be traversed in arbitrarily short time. Now we traverse the curve, carrying a spear, in a time less than what it takes the lion to move a distance equal to its own length.

1.7 A topological method

We observe that the lion possesses the topological gender of a torus. We embed the desert in a four dimensional space. Then it is possible to apply a deformation [2] of such a kind that the lion when returning to the three dimensional space is all tied up in itself. It is then completely helpless.

1.8 The Cauchy method

We examine a lion-valued function f(z). Let \zeta be the cage. Consider the integral

1 [ f(z) ------ I -------- dz 2 pi i ] z - zeta C

where C represents the boundary of the desert. Its value is f(zeta), i.e. there is a lion in the cage [3].

1.9 The Wiener-Tauber method

We obtain a tame lion, L_{0}, from the class L(-oo,oo), whose
Fourier transform vanishes nowhere. We put this lion somewhere in the desert.
L_{0} then converges toward our cage. According to the general
Wiener-Tauner theorem [4] every other lion L will converge toward the same
cage. (Alternatively we can approximate L arbitrarily close by translating
L_{0} through the desert [5].)

2 Theoretical Physics Methods

2.1 The Dirac method

We assert that wild lions can ipso facto not be observed in the Sahara desert. Therefore, if there are any lions at all in the desert, they are tame. We leave catching a tame lion as an exercise to the reader.

2.2 The Schroedinger method

At every instant there is a non-zero probability of the lion being in the cage. Sit and wait.

2.3 The Quantum Measurement Method

We assume that the sex of the lion is *ab initio* indeterminate.
The wave function for the lion is hence a superposition of the gender eigenstate
for a lion and that for a lioness. We lay these eigenstates out flat on
the ground and orthogonal to each other. Since the (male) lion has a distinctive
mane, the measurement of sex can safely be made from a distance, using
binoculars. The lion then collapses into one of the eigenstates, which
is rolled up and placed inside the cage.

2.4 The nuclear physics method

Insert a tame lion into the cage and apply a Majorana exchange operator [6] on it and a wild lion.

As a variant let us assume that we would like to catch (for argument's sake) a male lion. We insert a tame female lion into the cage and apply the Heisenberg exchange operator [7], exchanging spins.

2.5 A relativistic method

All over the desert we distribute lion bait containing large amounts of the companion star of Sirius. After enough of the bait has been eaten we send a beam of light through the desert. This will curl around the lion so it gets all confused and can be approached without danger.

3 Experimental Physics Methods

3.1 The thermodynamics method

We construct a semi-permeable membrane which lets everything but lions pass through. This we drag across the desert.

3.2 The atomic fission method

We irradiate the desert with slow neutrons. The lion becomes radioactive and starts to disintegrate. Once the disintegration process is progressed far enough the lion will be unable to resist.

3.3 The magneto-optical method

We plant a large, lens shaped field with cat mint (nepeta cataria) such that its axis is parallel to the direction of the horizontal component of the earth's magnetic field. We put the cage in one of the field's foci . Throughout the desert we distribute large amounts of magnetised spinach (spinacia oleracea) which has, as everybody knows, a high iron content. The spinach is eaten by vegetarian desert inhabitants which in turn are eaten by the lions. Afterwards the lions are oriented parallel to the earth's magnetic field and the resulting lion beam is focused on the cage by the cat mint lens.

[1] After Hilbert, cf. E. W. Hobson, "The Theory of Functions of a Real Variable and the Theory of Fourier's Series" (1927), vol. 1, pp 456-457

[2] H. Seifert and W. Threlfall, "Lehrbuch der Topologie" (1934), pp 2-3

[3] According to the Picard theorem (W. F. Osgood, Lehrbuch der Funktionentheorie, vol 1 (1928), p 178) it is possible to catch every lion except for at most one.

[4] N. Wiener, "The Fourier Integral and Certain of its Applications" (1933), pp 73-74

[5] N. Wiener, ibid., p 89

[6] cf. e.g. H. A. Bethe and R. F. Bacher, "Reviews of Modern Physics", 8 (1936), pp 82-229, esp. pp 106-107

[7] ibid.

4 Contributions from Computer Science.

4.1 The search method

We assume that the lion is most likely to be found in the direction to the north of the point where we are standing. Therefore the REAL problem we have is that of speed, since we are only using a PC to solve the problem.

4.2 The parallel search method.

By using parallelism we will be able to search in the direction to the north much faster than earlier.

4.3 The Monte-Carlo method.

We pick a random number indexing the space we search. By excluding neighbouring points in the search, we can drastically reduce the number of points we need to consider. The lion will according to probability appear sooner or later.

4.4 The practical approach.

We see a rabbit very close to us. Since it is already dead, it is particularly easy to catch. We therefore catch it and call it a lion.

4.5 The common language approach.

If only everyone used ADA/Common Lisp/Prolog, this problem would be trivial to solve.

4.6 The standard approach.

We know what a Lion is from ISO 4711/X.123. Since CCITT have specified a Lion to be a particular option of a cat we will have to wait for a harmonised standard to appear. $20,000,000 have been funded for initial investigations into this standard development.

4.7 Linear search.

Stand in the top left hand corner of the Sahara Desert. Take one step east. Repeat until you have found the lion, or you reach the right hand edge. If you reach the right hand edge, take one step southwards, and proceed towards the left hand edge. When you finally reach the lion, put it the cage. If the lion should happen to eat you before you manage to get it in the cage, press the reset button, and try again.

4.8 The Dijkstra approach:

The way the problem reached me was: catch a wild lion in the Sahara Desert. Another way of stating the problem is:

Axiom 1: Sahara elem deserts

Axiom 2: Lion elem Sahara

Axiom 3: NOT(Lion elem cage)

We observe the following invariant:

P1: C(L) v not(C(L))

where C(L) means: the value of "L" is in the cage.

Establishing C initially is trivially accomplished with the statement

;cage := {}

Note 0: This is easily implemented by opening the door to the cage and shaking out any lions that happen to be there initially. (End of note 0.)

The obvious program structure is then:

;cage:={} ;do NOT (C(L)) -> ;"approach lion under invariance of P1" ;if P(L) -> ;"insert lion in cage" [] not P(L) -> ;skip ;fi ;od

where P(L) means: the value of L is within arm's reach.

Note 1: Axiom 2 ensures that the loop terminates. (End of note 1.)

Exercise 0: Refine the step "Approach lion under invariance of P1". (End of exercise 0.)

Note 2: The program is robust in the sense that it will lead to abortion if the value of L is "lioness". (End of note 2.)

Remark 0: This may be a new sense of the word "robust" for you. (End of remark 0.)

Note 3: From observation we can see that the above program leads to the desired goal. It goes without saying that we therefore do not have to run it. (End of note 3.) (End of approach.)

For other articles, see also:

A Random Walk in Science - R.L. Weber and E. Mendoza

More Random Walks In Science - R.L. Weber and E. Mendoza

In Mathematical Circles (2 volumes) - Howard Eves

Mathematical Circles Revisited - Howard Eves

Mathematical Circles Squared - Howard Eves

Fantasia Mathematica - Clifton Fadiman

The Mathematical Magpi - Clifton Fadiman

Seven Years of Manifold - Jaworski

The Best of the Journal of Irreproducible Results - George H. Scheer

Mathematics Made Difficult - Linderholm

A Stress-Analysis of a Strapless Evening Gown - Robert Baker

The Worm-Runners Digest

Knuth's April 1984 CACM article on The Space Complexity of Songs

Stolfi and ?? SIGACT article on Pessimal Algorithms and Simplexity Analysis

Not a joke, but a humorous ditty I heard from some guys in an engineering fraternity (to the best of my recollection):

I'll do it phonetically:

ee to the ex dee ex,

ee to the why dee why,

sine x, cosine x, natural log of y,

derivative on the left derivative on the right

integrate, integrate,

fight! fight! fight!

The Programmers' Cheer --

Shift to the left, shift to the right! Pop up, push down, byte, byte, byte!

Other cheers:

E to the x dx dy

radical transcendental pi

secant cosine tangent sine

3.14159

2.71828

come on folks let's integrate!!

E to the i dx dy

E to y dy

cosine secant log of pi

disintegrate em RPI !!!

square root, tangent hyperbolic sine,

3.14159

e to the x, dy, dx,

sliderule, slipstick,

TECH TECH TECH!

e to the u, du/dx

e to the x dx

cosine, secant, tangent, sine,

3.14159

integral, radical, u dv,

slipstick, slide rule, MIT!

E to the X D-Y, D-X

E to the X D-X.

Cosine, Secant, Tangent, Sine

3.14159

E-I, Radical, Pi

Fight'em, Fight'em, WPI!

Go Worcester Polytechnic Institute!!!!!!

Words in {} should be interpreted as Greek letters:

Q: I M A {pi}{rho}Maniac. R U_{0} 1,2?
(U_{o} <- read as "U-not" )

A: Y_{o}

("I
am a pyromaniac. Are you not one, too?" "Why not?")

F U \{can\} \{read\} Ths U \{Mst\} \{use\} TeX

("If
you can read this, you must use TeX")

Three men are in a hot-air balloon. Soon, they find themselves lost in a canyon somewhere. One of the three men says, "I've got an idea. We can call for help in this canyon and the echo will carry our voices far."

So he leans over the basket and yells out, "Helllloooooo! Where are we?" (They hear the echo several times.)

15 minutes later, they hear this echoing voice: "Helllloooooo! You're lost!!"

One of the men says, "That must have been a mathematician."

Puzzled, one of the other men asks, "Why do you say that?"

The reply: "For three reasons. (1) he took a long time to answer, (2) he was absolutely correct, and (3) his answer was absolutely useless."

Actually, I prefer the IBM version of this joke...

A small, 14-seat plane is circling for a landing in Atlanta. It's totally fogged in, zero visibility, and suddenly there's a small electrical fire in the cockpit which disables all of the instruments and the radio. The pilot continues circling, totally lost, when suddenly he finds himself flying next to a tall office building.

He rolls down the window (this particular airplane happens to have roll-down windows) and yells to a person inside the building, "Where are we?"

The person responds "In an airplane!"

The pilot then banks sharply to the right, circles twice, and makes a perfect landing at Atlanta International.

As the passengers emerge, shaken but unhurt, one of them says to the pilot, "I'm certainly glad you were able to land safely, but I don't understand how the response you got was any use."

"Simple," responded the pilot. "I got an answer that was completely accurate and totally irrelevant to my problem, so I knew it had to be the IBM building."

(I'm not sure if the following one is a true story or not) The great logician Bertrand Russell (or was it A.N. Whitehead?) once claimed that he could prove anything if given that 1+1=1. So one day, some smarty-pants asked him, "Ok. Prove that you're the Pope." He thought for a while and proclaimed, "I am one. The Pope is one. Therefore, the Pope and I are one."

[NOTE: The following is from merritt@Gendev.slc.paramax.com (Merritt). The story about 1+1=1 causing ridiculous consequences was, I believe, originally the product of a conversation at the Trinity High Table. It is recorded in Sir Harold Jeffreys' Scientific Inference, in a note to chapter one. Jeffreys remarks that the fact that everything followed from a single contradiction had been noticed by Aristotle (I doubt this way of putting it is quite correct, but that is beside the point). He goes on to say that McTaggart denied the consequence: "if 2+2=5, how can you prove that I am the pope?" Hardy is supposed to have replied: "if 2+2=5, 4=5; subtract 3; then 1=2; but McTaggart and the pope are two; therefore McTaggart and the pope are one." When I consider this story, I am astonished at how much more brilliant some people are than I (quite independent of the fallacies in the argument).

Since McTaggart, Hardy, Whitehead, and Russell (the last two of whom were credited with a variant of Hardy's argument in your post) were all fellows of Trinity and Jeffreys (their exact contemporary) was a fellow of St. Johns, I suspect that (whatever the truth of Jeffreys' story) it is very unlikely that Whitehead or Russell had anything to do with it. The extraordinary point to me about the story is that Hardy was able to snap this argument out between mouthfuls, so to speak, and he was not even a logician at all. This is probably why it came in some people's minds to be attributed to one or other of the famous Trinity logicians.

THE STORY OF BABEL:

In the beginning there was only one kind of Mathematician, created by the Great Mathematical Spirit form the Book: the Topologist. And they grew to large numbers and prospered.

One day they looked up in the heavens and desired to reach up as far as the eye could see. So they set out in building a Mathematical edifice that was to reach up as far as "up" went. Further and further up they went ... until one night the edifice collapsed under the weight of paradox.

The following morning saw only rubble where there once was a huge structure reaching to the heavens. One by one, the Mathematicians climbed out from under the rubble. It was a miracle that nobody was killed; but when they began to speak to one another, SURPRISE of all surprises! they could not understand each other. They all spoke different languages. They all fought amongst themselves and each went about their own way. To this day the Topologists remain the original Mathematicians.

- adapted from an American Indian legend of the Mound Of Babel

Methods of Mathematical Proof

This is from __A Random Walk in Science__ (by Joel E. Cohen?):

To illustrate the various methods of proof we give an example of a logical system.

THE PEJORATIVE CALCULUS

Lemma 1. All horses are the same colour. (Proof by induction)

Proof.

It is obvious that one horse is the same colour. Let us assume the proposition P(k) that k horses are the same colour and use this to imply that k+1 horses are the same colour. Given the set of k+1 horses, we remove one horse; then the remaining k horses are the same colour, by hypothesis. We remove another horse and replace the first; the k horses, by hypothesis, are again the same colour. We repeat this until by exhaustion the k+1 sets of k horses have been shown to be the same colour. It follows that since every horse is the same colour as every other horse, P(k) entails P(k+1). But since we have shown P(1) to be true, P is true for all succeeding values of k, that is, all horses are the same colour.

Theorem 1. Every horse has an infinite number of legs. (Proof by intimidation.)

Proof.

Horses have an even number of legs. Behind they have two legs and in front they have fore legs. This makes six legs, which is certainly an odd number of legs for a horse. But the only number that is both odd and even is infinity. Therefore horses have an infinite number of legs. Now to show that this is general, suppose that somewhere there is a horse with a finite number of legs. But that is a horse of another colour, and by the lemma that does not exist.

Corollary 1. Everything is the same colour.

Proof.

The proof of lemma 1 does not depend at all on the nature of the object under consideration. The predicate of the antecedent of the universally-quantified conditional 'For all x, if x is a horse, then x is the same colour,' namely 'is a horse' may be generalised to 'is anything' without affecting the validity of the proof; hence, 'for all x, if x is anything, x is the same colour.'

Corollary 2. Everything is white.

Proof.

If a sentential formula in x is logically true, then any particular substitution instance of it is a true sentence. In particular then: 'for all x, if x is an elephant, then x is the same colour' is true. Now it is manifestly axiomatic that white elephants exist (for proof by blatant assertion consult Mark Twain 'The Stolen White Elephant'). Therefore all elephants are white. By corollary 1 everything is white.

Theorem 2. Alexander the Great did not exist and he had an infinite number of limbs.

Proof.

We prove this theorem in two parts. First we note the obvious fact that historians always tell the truth (for historians always take a stand, and therefore they cannot lie). Hence we have the historically true sentence, 'If Alexander the Great existed, then he rode a black horse Bucephalus.' But we know by corollary 2 everything is white; hence Alexander could not have ridden a black horse. Since the consequent of the conditional is false, in order for the whole statement to be true the antecedent must be false. Hence Alexander the Great did not exist. We have also the historically true statement that Alexander was warned by an oracle that he would meet death if he crossed a certain river. He had two legs; and 'forewarned is four-armed.' This gives him six limbs, an even number, which is certainly an odd number of limbs for a man. Now the only number which is even and odd is infinity; hence Alexander had an infinite number of limbs. We have thus proved that Alexander the Great did not exist and that he had an infinite number of limbs.

Not precisely pure-math, but ...

Fuller's Law of Cosmic Irreversibility:

1 pot T --> 1 pot P but 1 pot P -/-> 1 pot T

A tribe of Native Americans generally referred to their woman by the animal hide with which they made their blanket. Thus, one woman might be known as Squaw of Buffalo Hide, while another might be known as Squaw of Deer Hide. This tribe had a particularly large and strong woman, with a very unique (for North America anyway) animal hide for her blanket. This woman was known as Squaw of Hippopotamus hide, and she was as large and powerful as the animal from which her blanket was made.

Year after year, this woman entered the tribal wrestling tournament, and easily defeated all challengers; male or female. As the men of the tribe admired her strength and power, this made many of the other woman of the tribe extremely jealous. One year, two of the squaws petitioned the Chief to allow them to enter their sons together as a wrestling tandem in order to wrestle Squaw of the Hippopotamus hide as a team. In this way, they hoped to see that she would no longer be champion wrestler of the tribe.

As the luck of the draw would have it, the two sons who were wrestling as a tandem met the squaw in the final and championship round of the wrestling contest. As the match began, it became clear that the squaw had finally met an opponent that was her equal. The two sons wrestled and struggled vigorously and were clearly on an equal footing with the powerful squaw. Their match lasted for hours without a clear victor. Finally the chief intervened and declared that, in the interests of the health and safety of the wrestlers, the match was to be terminated and that he would declare a winner.

The chief retired to his teepee and contemplated the great struggle he had witnessed, and found it extremely difficult to decide a winner. While the two young men had clearly outmatched the squaw, he found it difficult to force the squaw to relinquish her tribal championship. After all, it had taken two young men to finally provide her with a decent match. Finally, after much deliberation, the chief came out from his teepee, and announced his decision. He said...

"The Squaw of the Hippopotamus hide is equal to the sons of the squaws of the other two hides"

A topologist is a man who doesn't know the difference between a coffee cup and a doughnut.

A statistician can have his head in an oven and his feet in ice, and he will say that on the average he feels fine.

A guy decided to go to the brain transplant clinic to refresh his supply of brains. The secretary informed him that they had three kinds of brains available at that time. Doctors' brains were going for $20 per ounce and lawyers' brains were getting $30 per ounce. And then there were mathematicians' brains which were currently fetching $1000 per ounce.

"A 1000 dollars an ounce!" he cried. "Why are they so expensive?"

"It takes more mathematicians to get an ounce of brains," she explained.

A topologist walks into a bar and orders a drink. The bartender, being a number theorist, says, "I'm sorry, but we don't serve topologists here."

The disgruntled topologist walks outside, but then gets an idea and performs Dahn surgery upon herself. She walks into the bar, and the bartender, who does not recognise her since she is now a different manifold, serves her a drink. However, the bartender thinks she looks familiar, or at least locally similar, and asks, "Aren't you that topologist that just came in here?"

To which she responds, "No, I'm a frayed knot."

There are three kinds of people in the world; those who can count and those who can't.

And the related:

There are two groups of people in the world; those who believe that the world can be divided into two groups of people, and those who don't.

And then:

There are two groups of people in the world: Those who can be categorised into one of two groups of people, and those who can't.

The world is divided into two classes: people who say "The world is divided into two classes", and people who say The world is divided into two classes: people who say: "The world is divided into two classes", and people who say: The world is divided into two classes: people who say ...

What follows is a "quiz" a student of mine once showed me (which she'd gotten from a previous teacher, etc....). It's multiple choice, and if you sort the letters (with upper and lower case disjoint) questions and answers will come out next to each other. Enjoy...

S. What the acorn said when he grew up

N. bisects

u. A dead parrot

g. centre

F. What you should do when it rains

R. hypotenuse

m. A geometer who has been to the beach

H. coincide

h. The set of cards is missing

y. polygon

A. The boy has a speech defect

t. secant

K. How they schedule gym class

p. tangent

b. What he did when his mother-in-law wanted to go home

D. ellipse

O. The tall kettle boiling on the stove

W. geometry

r. Why the girl doesn't run a 4-minute mile

j. decagon

___ 1. That which Noah built.

___ 2. An article for serving ice cream.

___ 3. What a bloodhound does in chasing a woman.

___ 4. An expression to represent the loss of a parrot.

___ 5. An appropriate title for a knight named Koal.

___ 6. A sunburned man.

___ 7. A tall coffee pot perking.

___ 8. What one does when it rains.

___ 9. A dog sitting in a refrigerator.

___ 10. What a boy does on the lake when his motor won't run.

___ 11. What you call a person who writes for an inn.

___ 12. What the captain said when the boat was bombed.

___ 13. What a little acorn says when he grows up.

___ 14. What one does to trees that are in the way.

___ 15. What you do if you have yarn and needles.

___ 16. Can George Washington turn into a country?

A. hypotenuse

I. circle

B. polygon

J. axiom

C. inscribe

K. cone

D. geometry

L. coincide

E. unit

M. cosecant

F. centre

N. tangent

G. decagon

O. hero

H. arc

P. perpendicular

A team of engineers were required to measure the height of a flag pole. They only had a measuring tape, and were getting quite frustrated trying to keep the tape along the pole. It kept falling down, etc.

A mathematician comes along, finds out their problem, and proceeds to remove the pole from the ground and measure it easily.

When he leaves, one engineer says to the other: "Just like a mathematician! We need to know the height, and he gives us the length!"

A man camped in a national park, and noticed Mr. Snake and Mrs. Snake slithering by. "Where are all the little snakes?" he asked. Mr. Snake replied, "We are adders, so we cannot multiply."

The following year, the man returned to the same camping spot. This time there were a whole batch of little snakes. "I thought you said you could not multiply," he said to Mr. Snake. "Well, the park ranger came by and built a log table, so now we can multiply by adding!"

Einstein dies and goes to heaven only to be informed that his room is not yet ready. "I hope you will not mind waiting in a dormitory. We are very sorry, but it's the best we can do and you will have to share the room with others." he is told by the doorman (say his name is Pete). Einstein says that this is no problem at all and that there is no need to make such a great fuss. So Pete leads him to the dorm. They enter and Albert is introduced to all of the present inhabitants. "See, Here is your first room mate. He has an IQ of 180!" "Why that's wonderful!" Says Albert. "We can discuss mathematics!" "And here is your second room mate. His IQ is 150!" "Why that's wonderful!" Says Albert. "We can discuss physics!" "And here is your third room mate. His IQ is 100!" "That Wonderful! We can discuss the latest plays at the theater!" Just then another man moves out to capture Albert's hand and shake it. "I'm your last room mate and I'm sorry, but my IQ is only 80." Albert smiles back at him and says, "So, where do you think interest rates are headed?"

97.3% of all statistics are made up.

Did you hear the one about the statistician?

Probably....

There was once a very smart horse. Anything that was shown it, it mastered easily, until one day, its teachers tried to teach it about rectangular co-ordinates and it couldn't understand them. All the horse's acquaintances and friends tried to figure out what was the matter and couldn't. Then a new guy (what the heck, a computer engineer) looked at the problem and said,

"Of course he can't do it. Why, you're putting Descartes before the horse!"

**TOP TEN EXCUSES FOR NOT DOING THE MATH HOMEWORK **

1. I accidentally divided by zero and my paper burst into flames.

2. Isaac Newton's birthday.

3. I could only get arbitrarily close to my textbook. I couldn't actually reach it.

4. I have the proof, but there isn't room to write it in this margin.

5. I was watching the World Series and got tied up trying to prove that it converged.

6. I have a solar powered calculator and it was cloudy.

7. I locked the paper in my trunk but a four-dimensional dog got in and ate it

. 8. I couldn't figure out whether i am the square of negative one or i is the square root of negative one.

9. I took time out to snack on a doughnut and a cup of coffee. I spent the rest of the night trying to figure which one to dunk.

10. I could have sworn I put the homework inside a Klein bottle, but this morning I couldn't find it.

The guy gets on a bus and starts threatening everybody: "I'll integrate you! I'll differentiate you!!!" So everybody gets scared and runs away. Only one person stays. The guy comes up to him and says: "Aren't you scared, I'll integrate you, I'll differentiate you!!!" And the other guy says; "No, I am not scared, I am e to the x."

A mathematician went insane and believed that he was the differentiation operator. His friends had him placed in a mental hospital until he got better. All day he would go around frightening the other patients by staring at them and saying "I differentiate you!"

One day he met a new patient; and true to form he stared at him and said "I differentiate you!", but for once, his victim's expression didn't change. Surprised, the mathematician marshalled his energies, stared fiercely at the new patient and said loudly "I differentiate you!", but still the other man had no reaction. Finally, in frustration, the mathematician screamed out "I DIFFERENTIATE YOU!" -- at which point the new patient calmly looked up and said, "You can differentiate me all you like: I'm e to the x."

/ | 1 | ----- = log cabin | cabin /

Oops, you forgot your constant of integration.

/ | 1 | ----- = log cabin + C | cabin /

And, as we all know,

log cabin + C = houseboat

If

8 lim - = oo x->0 x

then what does

5 lim - = ??? x->0 x

answer: (write 5 on it's side)

Why did the cat fall off the roof?

Because he lost his mu.

Ralph: Dad, will you do my math for me tonight?

Dad: No, son, it wouldn't be right.

Ralph: Well, you could try.

Mrs. Johnson the elementary school math teacher was having children do problems on the blackboard that day.

``Who would like to do the first problem, addition?''

No one raised their hand. She called on Tommy, and with some help he finally got it right.

``Who would like to do the second problem, subtraction?''

Students hid their faces. She called on Mark, who got the problem but there was some suspicion his girlfriend Lisa whispered it to him.

``Who would like to do the third problem, division?''

Now a low collective groan could be heard as everyone looked at nothing in particular. The teacher called on Suzy, who got it right (she has been known to hold back sometimes in front of her friends).

``Who would like to do the last problem, multiplication?''

Tim's hand shot up, surprising everyone in the room. Mrs. Johnson finally gained her composure in the stunned silence. ``Why the enthusiasm, Tim?''

``God said to go fourth and multiply!''

**Definitions of Terms Commonly Used in Higher Math **

The following is a guide to the weary student of mathematics who is often confronted with terms which are commonly used but rarely defined. In the search for proper definitions for these terms we found no authoritative, nor even recognised, source. Thus, we followed the advice of mathematicians handed down from time immortal: "Wing It."

**CLEARLY:** I don't want to write down all the "in- between"
steps.

**TRIVIAL:** If I have to show you how to do this, you're in the wrong
class.

**OBVIOUSLY: **I hope you weren't sleeping when we discussed this earlier,
because I refuse to repeat it.

**RECALL:** I shouldn't have to tell you this, but for those of you
who erase your memory tapes after every test...

**WLOG** (Without Loss Of Generality): I'm not about to do all the possible
cases, so I'll do one and let you figure out the rest.

**IT CAN EASILY BE SHOWN:** Even you, in your finite wisdom, should
be able to prove this without me holding your hand.

**CHECK or CHECK FOR YOURSELF: **This is the boring part of the proof,
so you can do it on your own time.

**SKETCH OF A PROOF:** I couldn't verify all the details, so I'll break
it down into the parts I couldn't prove.

**HINT: **The hardest of several possible ways to do a proof.

**BRUTE FORCE **(AND IGNORANCE): Four special cases, three counting
arguments, two long inductions, "and a partridge in a pair tree."

**SOFT PROOF:** One third less filling (of the page) than your regular
proof, but it requires two extra years of course work just to understand
the terms.

**ELEGANT PROOF:** Requires no previous knowledge of the subject matter
and is less than ten lines long.

**SIMILARLY:** At least one line of the proof of this case is the same
as before.

**CANONICAL FORM:** 4 out of 5 mathematicians surveyed recommended this
as the final form for their students who choose to finish.

**TFAE** (The Following Are Equivalent): If I say this it means that,
and if I say that it means the other thing, and if I say the other thing...

**BY A PREVIOUS THEOREM:** I don't remember how it goes (come to think
of it I'm not really sure we did this at all), but if I stated it right
(or at all), then the rest of this follows.

**TWO LINE PROOF:** I'll leave out everything but the conclusion, you
can't question 'em if you can't see 'em.

**BRIEFLY:** I'm running out of time, so I'll just write and talk faster.

**LET'S TALK IT THROUGH:** I don't want to write it on the board lest
I make a mistake.

**PROCEED FORMALLY: **Manipulate symbols by the rules without any hint
of their true meaning (popular in pure math courses).

**QUANTIFY: **I can't find anything wrong with your proof except that
it won't work if x is a moon of Jupiter (Popular in applied math courses).

**PROOF OMITTED:** Trust me, It's true.

In the bayous of Louisiana, there is a small river called the Dirac. Many wealthy people have their mansions near its mouth. One of the social leaders decided to have a grand ball. Being a cousin of the Governor, she arranged for a detachment of the state militia to serve as guards and traffic directors for the big doings. A captain was sent over with a small company; naturally he asked if there was enough room for him and his unit. The social leader replied, "But of course, Captain! It is well known that the Dirac delta function has unit area."

Albert Einstein, who fancied himself as a violinist, was rehearsing a Haydn string quartet. When he failed for the fourth time to get his entry in the second movement, the cellist looked up and said, "The problem with you, Albert, is that you simply can't count."

Some famous mathematician was to give a keynote speech at a conference. Asked for an advance summary, he said he would present a proof of Fermat's Last Theorem -- but they should keep it under their hats. When he arrived, though, he spoke on a much more prosaic topic. Afterwards the conference organisers asked why he said he'd talk about the theorem and then didn't. He replied this was his standard practice, just in case he was killed on the way to the conference.

When I was a Math/Chem grad student at Princeton in 1973-74, there was a story going around about a grad student. This guy was always late. One day he stumbled into class late, saw seven problems written on the board, and wrote them down. As the week went on he began to panic: the math department at Princeton is fiercely competitive, and here he was unable to do most of a simple homework assignment! When the next class rolled around he only had solved two of the problems, although he had a pretty good idea of how to solve a third but not enough time to complete it.

When he dejectedly flung his partial assignment on the prof's desk, the prof asked him "What's that?" "The homework." "What homework?" Eventually it came out that what the prof had written on the board were the seven most important unsolved problems in the field.

This is largely an academic legend, at least according to Jan Harold
Brunvand, the author of a series of books on so-called Urban Legends. He
talks about it in his latest book __Curses! Broiled Again!__ in the
chapter entitled "*The Unsolvable Math Problem."* It is,
however, based in some fact. The Stanford mathematician, George B. Danzig,
apparently managed to solve two statistics problems previously unsolved
under similar circumstances.

The following problem can be solved either the easy way or the hard way.

Two trains 200 miles apart are moving toward each other; each one is going at a speed of 50 miles per hour. A fly starting on the front of one of them flies back and forth between them at a rate of 75 miles per hour. It does this until the trains collide and crush the fly to death. What is the total distance the fly has flown?

The fly actually hits each train an infinite number of times before it gets crushed, and one could solve the problem the hard way with pencil and paper by summing an infinite series of distances. The easy way is as follows: Since the trains are 200 miles apart and each train is going 50 miles an hour, it takes 2 hours for the trains to collide. Therefore the fly was flying for two hours. Since the fly was flying at a rate of 75 miles per hour, the fly must have flown 150 miles. That's all there is to it.

When this problem was posed to John von Neumann, he immediately replied, "150 miles."

"It is very strange," said the poser, "but nearly everyone tries to sum the infinite series."

"What do you mean, strange?" asked Von Neumann. "That's how I did it!"

Mathematicians are like Frenchmen: whatever you say to them, they translate it into their own language, and forthwith it means something entirely different. -- Johann Wolfgang von Goethe

"The reason that every major university maintains a department of mathematics is that it is cheaper to do this than to institutionalise all those people."

Three mathematicians and a physicist walk into a bar. You'd think the second one would have ducked. (Ha, that quack's me up!)

What do you call a young eigensheep?

A lamb, duh!!!

"The world is everywhere dense with idiots." - LFS

One day a farmer called up an engineer, a physicist, and a mathematician and asked them to fence of the largest possible area with the least amount of fence. The engineer made the fence in a circle and proclaimed that he had the most efficient design. The physicist made a long, straight line and proclaimed 'We can assume the length is infinite...' and pointed out that fencing off half of the Earth was certainly a more efficient way to do it. The Mathematician just laughed at them. He built a tiny fence around himself and said 'I declare myself to be on the outside.'

An engineer, a mathematician, and a computer programmer are driving down the road when the car they are in gets a flat tire. The engineer says that they should buy a new car. The mathematician says they should sell the old tire and buy a new one. The computer programmer says they should drive the car around the block and see if the tire fixes itself.

A math/computer science convention was being held. On the train to the convention, a bunch of math majors and a bunch of computer science majors were on the train. Each of the math majors had his/her train ticket. The group of computer science majors had only ONE ticket for all of them. The math majors started laughing and snickering.

Then, one of the CS majors said "here comes the conductor" and then all of the CS majors went into the bathroom. The math majors were puzzled. The conductor came aboard and said "tickets please" and got tickets from all the math majors. He then went to the bathroom and knocked on the door and said "ticket please" and the CS majors stuck the ticket under the door. The conductor took it and then the CS majors came out of the bathroom a few minutes later. The math majors felt really stupid.

So, on the way back from the convention, the group of math majors had one ticket for the group. They started snickering at the CS majors, for the whole group had no tickets amongst them. Then, the CS major lookout said "Conductor coming!". All the CS majors went to the bathroom. All the math majors went to another bathroom. Then, before the conductor came on board, one of the CS majors left the bathroom, knocked on the other bathroom, and said "ticket please."

The following is supposedly a true story about Russell. It isn't really a math joke since it makes fun of the British hierarchy, but it's funny anyway....

Around the time when Cold War started, Bertrand Russell was giving a lecture on politics in England. Being a leftist in a conservative women's club, he was not received well at all: the ladies came up to him and started attacking him with whatever they could get their hands on. The guard, being an English gentleman, did not want to be rough to the ladies and yet needed to save Russell from them. He said, "But he is a great mathematician!" The ladies ignored him. The guard said again, "But he is a great philosopher!" The ladies ignore him again. In desperation, finally, he said, "But his brother is an earl!" Bert was saved.

Another "true" story, kinda like the aforementioned urban legend:

Enrico Fermi, while studying in college, was bored by his math classes. He walked up to the professor and said, "My classes are too easy!" The professor looked at him, and said, "Well, I'm sure you'll find this interesting." Then the professor copied 9 problems from a book to a paper and gave the paper to Fermi. A month later, the professor ran into Fermi, "So how are you doing with the problems I gave you?" "Oh, they are very hard. I only managed to solve 6 of them." The professor was visibly shocked, "What!? But those are unsolved problems!"

An engineer, a physicist, and a mathematician find themselves in an anecdote, indeed an anecdote quite similar to many that you have no doubt already heard. After some observations and rough calculations, the engineer realises the situation and starts laughing. A few minutes later the physicist understands, too, and chuckles to himself happily as he now has enough experimental evidence to publish a paper. This leaves the mathematician somewhat perplexed, as he had observed right away that he was the subject of an anecdote, and deduced quite rapidly the presence of humour from similar anecdotes, but considers this anecdote to be too trivial a corollary to be significant, let alone funny.

"A person who can, within a year, solve x^{2} - 92y^{2}
= 1 is a mathematician." -- Brahmagupta

Math and Alcohol don't mix, so...

PLEASE DON'T DRINK AND DERIVE

Then there's every parent's scream when their child walks into the room dazed and staggering:

OH NO...YOU'VE BEEN TAKING DERIVATIVES!!

MADD = Mathematicians Against Drunk Deriving

Here's a limerick - looks better on paper.

3_ \/3 / | 2 3_ | z dz X cos(3 pi) = ln (\/e ) | 9 / 1

Which, of course, translates to:

Integral z-squared dz

from 1 to the cube root of 3

times the cosine

of three pi over 9

equals log of the cube root of 'e'.

And it's correct, too.

This poem was written by John Saxon (an author of math textbooks).

((12 + 144 + 20 + (3 * 4^{(1/2)})) / 7) + (5 * 11) = 9^{2}
+ 0

Or for those who have trouble with the poem:

A Dozen, a Gross and a Score,

plus three times the square root of four,

divided by seven, plus five times eleven,

equals nine squared and not a bit more.

'Tis a favourite project of mine

A new value of pi to assign.

I would fix it at 3

For it's simpler, you see,

Than 3 point 1 4 1 5 9.

("The Lure of the Limerick" by W.S. Baring-Gould, p.5. Attributed to Harvey L. Carter).

If inside a circle a line

Hits the centre and goes spine to spine

And the line's length is "d"

the circumference will be

d times 3.14159

If (1+x) (real close to 1)

Is raised to the power of 1

Over x, you will find

Here's the value defined:

2.718281...

An engineer thinks that his equations are an approximation to reality. A physicist thinks reality is an approximation to his equations. A mathematician doesn't care.

Why is the number 10 afraid of seven?

-- because seven ate nine.

We use epsilons and deltas in mathematics because mathematicians tend to make errors.

What's big, grey, and proves the uncountability of the reals?

Cantor's Diagonal Elephant!

How can you tell that Harvard was laid out by a mathematician?

The div school [divinity school] is right next to the grad school...

The Stanford Linear Accelerator Centre was known as SLAC, until the big earthquake, when it became known as SPLAC.

SPLAC? Stanford Piecewise Linear Accelerator.

Q: How many topologists does it take to change a light bulb?

A: It really doesn't matter, since they'd rather knot.

A mathematician decides he wants to learn more about practical problems. He sees a seminar with a nice title: "The Theory of Gears." So he goes. The speaker stands up and begins, "The theory of gears with a real number of teeth is well known ..."

A group of scientists were doing an investigation into problem-solving techniques, and constructed an experiment involving a physicist, an engineer, and a mathematician.

The experimental apparatus consisted of a water spigot and two identical pails, one of which was fastened to the ground ten feet from the spigot.

Each of the subjects was given the second pail, empty, and told to fill the pail on the ground.

The physicist was the first subject: he carried his pail to the spigot, filled it there, carried it full of water to the pail on the ground, and poured the water into it. Standing back, he declared, "There: I have solved the problem."

The engineer and the mathematician each approached the problem similarly. Upon finishing, the engineer noted that the solution was exact, since the volumes of the pails were equal. The mathematician merely noted that he had proven that a solution exists.

Now, the experimenters altered the parameters of the task a bit: the pail on the ground was still empty, but the subjects were presented with a pail that was already half-filled with water.

The physicist immediately carried his pail over to the one on the ground,
emptied the water into it, went back to the spigot, **filled** the pail,
and finally emptied the entire contents into the pail on the ground, overflowing
it and spilling some of the water. Upon finishing, he commented that the
problem should have been better stated.

The engineer, in turn, thought for some time before going into action. He then took his half-filled pail to the spigot, filled it to the brim, and filled the pail on the ground from it. Again he noted that the problem had an exact solution, which of course he had found.

The mathematician thought for a long time before stirring. At last he stood up, emptied his pail onto the ground, and declared, "The problem has been reduced to one already solved."

Professor Dirac, a famous Applied Mathematician-Physicist, had a horse shoe over his desk. One day a student asked if he really believed that a horse shoe brought luck. Professor Dirac replied, "I understand that it brings you luck if you believe in it or not."

First of all let me make it clear that I have nothing against contravariant functors. Some of my best friends are cohomology theories! But now you aren't supposed to call them contravariant anymore. It's Algebraically Correct to call them 'differently arrowed'!!

In the same way that transcendental numbers are polynomially challenged?

Manifolds are personifolds (humanifolds).

Neighbourhoods are neighbour victims of society.

It's the Asian Remainder Theorem.

It isn't politically correct to use "singularity" - the function is "convergently challenged" there.

Why did the computer scientist die in the shower? Because he read the instructions on the shampoo bottle, "Lather, rinse, repeat."

Why did the calculus student have so much trouble making Kool-Aid?

Because he couldn't figure out how to get a quart of water into the little
package.

Q: Why do computer scientists confuse Christmas and Halloween?

A: Because Oct 31 = Dec 25

Here are some phrases used to remember SIN, COS, and TAN.

(SIN = Opposite/Hypotenuse, COS = Adjacent/H, TAN = O/A).

1. SOHCAHTOA (sock-a-toe-a)

2. The Cat Sat On An Orange And Howled Hard

3. Some Old Hulks Carry A Huge Tub Of Ale

4. Silly Old Hitler Caused Awful Headaches To Our Airmen

5. Some Old Hag Cracked All Her Teeth On Asparagus

6. Some Old Hairy Camels Are Hairier Than Others Are

7. Silly Old Harry Caught A Herring Trawling Off America

8. SOPHY, CADHY, TOAD

2 monograms 1 diagram

8 nickels 2 paradigms

2 wharves 1 paradox

10E5 bicycles 2 megacycles

1 unit of suspense in an Agatha Christie novel 1 whod unit

Three Laws of Thermodynamics (paraphrased):

First Law: You can't get anything without working for it.

Second Law: The most you can accomplish by work is to break even.

Third Law: You can't break even.

Q: What goes "Pieces of seven! Pieces of seven!"?

A: A parroty error!!

Q: What did the circle say to the tangent line?

A: "Stop touching me!"

A mathematician is a person who says that, when 3 people are supposed to be in a room but 5 came out, 2 have to go in so the room gets empty...

- Pocket calculator
- Commodore Pet / Apple II / TRS 80 / Commodore 64 / Timex Sinclair (Choose any of the above)
- IBM PC
- Apple Macintosh
- Fastest workstation of the time (HP, DEC, IBM, SGI: your choice)
- Minicomputer (HP, DEC, IBM, SGI: your choice)
- Mainframe (IBM, Cray, DEC: your choice)
- And then you reach the pinnacle of modern computing facilities:

The upgrade path to the most powerful and satisfying computer:

**G R A D U A T E S T U D E
N T S **

- Multi-processing, with as many processes as you have students. You
can easily add more power by promising more desperate undergrads that they
can indeed escape college through your guidance. Special student units
can even handle several tasks
**on their own**! - Full voice recognition interface. Never touch a keyboard or mouse again.
Just mumble commands and they
**will**be understood (or else!). - No hardware upgrades and no installation required. Every student comes complete with all hardware necessary. Never again fry a chip or $10,000 board by improper installation! Just sit that snivelling student at a desk, give it writing utensils (making sure to point out which is the dangerous end) and off it goes.
- Low maintenance. Remember when that hard disk crashed in your Beta
9900, causing all of your work to go the great bit bucket in the sky? This
won't happen with grad. students. All that is required is that you give
them a good
**whack!**upside the head when they are acting up, and they will run good as new. - Abuse module. Imagine yelling expletives at your computer. Doesn't work too well, because your machine just sits there and ignores you. Through the grad student abuse module you can put the fear of god in them, and get results to boot!
- Built-in lifetime. Remember that awful feeling two years after you bought your GigaPlutz mainframe when the new faculty member on the block sneered at you because his FeelyWup workstation could compute rings around your dinosaur? This doesn't happen with grad. students. When they start wearing and losing productivity, simply give them the PhD and boot them out onto the street to fend for themselves. Out of sight, out of mind!
- Cheap fuel: students run on Coca Cola (or the high-octane equivalent -- Jolt Cola) and typically consume hot spicy Chinese dishes, cheap taco substitutes, or completely synthetic macaroni replacements. It is entirely unnecessary to plug the student into the wall socket (although this does get them going a little faster from time to time).
- Expansion options. If your grad. students don't seem to be performing too well, consider adding a handy system manager or software engineer upgrade. These guys are guaranteed to require even less than a student, and typically establish permanent residence in the computer room. You'll never know they are around! (Which you certainly can't say for an AXZ3000-69 150gigahertz space-heater sitting on your desk with its ten noisy fans....) [Note however that the engineering department still hasn't worked out some of the idiosyncratic bugs in these expansion options, such as incessant muttering at nobody in particular, occasionally screaming at your grad. students, and posting ridiculous messages on world-wide bulletin boards.]

Yes, you just sit back and do all of your computing through lowly graduate students. Imagine the advantages:

So forget your Babbage Engines and abacuses (abaci?) and PortaBooks and DEK 666-3D's and all that other silicon garbage. The wave of the future is in wetware, so invest in graduate students today! You'll never go back!

If I have seen farther than others, it is because I was standing on the shoulder of giants. -- Isaac Newton

If I have not seen as far as others, it is because giants were standing on my shoulders. -- Hal Abelson

In computer science, we stand on each other's feet. -- Brian K. Reid

He thinks he's really smooth, but he's only C^{1}. He's always
going off on a tangent.

A mathematician and a physicist agree to a psychological experiment. The mathematician is put in a chair in a large empty room and a beautiful naked woman is placed on a bed at the other end of the room. The psychologist explains, "You are to remain in your chair. Every five minutes, I will move your chair to a position halfway between its current location and the woman on the bed." The mathematician looks at the psychologist in disgust. "What? I'm not going to go through this. You know I'll never reach the bed!" And he gets up and storms out. The psychologist makes a note on his clipboard and ushers the physicist in. He explains the situation, and the physicist's eyes light up and he starts drooling. The psychologist is a bit confused. "Don't you realise that you'll never reach her?" The physicist smiles and replied, "Of course! But I'll get close enough for all practical purposes!"

Dean, to the physics department. "Why do I always have to give you guys so much money, for laboratories and expensive equipment and stuff. Why couldn't you be like the math department - all they need is money for pencils, paper and waste-paper baskets. Or even better, like the philosophy department. All they need are pencils and paper."

An engineer, physicist, and mathematician are all challenged with a problem: to fry an egg when there is a fire in the house. The engineer just grabs a huge bucket of water, runs over to the fire, and puts it out. The physicist thinks for a long while, and then measures a precise amount of water into a container. He takes it over to the fire, pours it on, and with the last drop the fire goes out. The mathematician pores over pencil and paper. After a few minutes he goes "Aha! A solution exists!" and goes back to frying the egg.

Sequel: This time they are asked simply to fry an egg (no fire). The engineer just does it, kludging along; the physicist calculates carefully and produces a carefully cooked egg; and the mathematician lights a fire in the corner, and says "I have reduced it to the previous problem."

A physicist and a mathematician are sitting in a faculty lounge. Suddenly, the coffee machine catches on fire. The physicist grabs a bucket and leaps towards the sink, fills the bucket with water and puts out the fire. The second day, the same two sit in the same lounge. Again, the coffee machine catches on fire. This time, the mathematician stands up, gets a bucket, hands the bucket to the physicist, thus reducing the problem to a previously solved one.

An engineer, a mathematician, and a physicist are staying in three adjoining cabins at a decrepit old motel.

First the engineer's coffee maker catches fire on the bathroom vanity. He smells the smoke, wakes up, unplugs it, throws it out the window, and goes back to sleep.

Later that night the physicist smells smoke too. He wakes up and sees that a cigarette butt has set the trash can on fire. He says to himself, "Hmm. How does one put out a fire? One can reduce the temperature of the fuel below the flash point, isolate the burning material from oxygen, or both. This could be accomplished by applying water." So he picks up the trash can, puts it in the shower stall, turns on the water, and, when the fire is out, goes back to sleep.

The mathematician, of course, has been watching all this out the window. So later, when he finds that his pipe ashes have set the bedsheet on fire, he is not in the least taken aback. He immediately sees that the problem reduces to one that has already been solved and goes back to sleep.

A mathematician and a physicist were asked the following question:

Suppose you walked by a burning house and saw a hydrant and a hose not connected to the hydrant. What would you do?

P: I would attach the hose to the hydrant, turn on the water, and put out the fire.

M: I would attach the hose to the hydrant, turn on the water, and put out the fire.

Then they were asked this question:

Suppose you walked by a house and saw a hose connected to a hydrant. What would you do?

P: I would keep walking, as there is no problem to solve.

M: I would disconnect the hose from the hydrant and set the house on fire, reducing the problem to a previously solved form.

There were two men trying to decide what to do for a living. They went to see a counsellor, and he decided that they had good problem solving skills.

He tried a test to narrow the area of speciality. He put each man in a room with a stove, a table, and a pot of water on the table. He said "Boil the water". Both men moved the pot from the table to the stove and turned on the burner to boil the water. Next, he put them into a room with a stove, a table, and a pot of water on the floor. Again, he said "Boil the water". The first man put the pot on the stove and turned on the burner. The counsellor told him to be an Engineer, because he could solve each problem individually. The second man moved the pot from the floor to the table, and then moved the pot from the table to the stove and turned on the burner. The counsellor told him to be a mathematician because he reduced the problem to a previously solved problem.

So a mathematician, an engineer, and a physicist are out hunting together. They spy a deer(*) in the woods.

The physicist calculates the velocity of the deer and the effect of gravity on the bullet, aims his rifle and fires. Alas, he misses; the bullet passes three feet behind the deer. The deer bolts some yards, but comes to a halt, still within sight of the trio.

"Shame you missed," comments the engineer, "but of course with an ordinary gun, one would expect that." He then levels his special deer-hunting gun, which he rigged together from an ordinary rifle, a sextant, a compass, a barometer, and a bunch of flashing lights which don't do anything but impress onlookers, and fires. Alas, his bullet passes three feet in front of the deer, who by this time wises up and vanishes for good.

"Well," says the physicist, "your contraption didn't get it either."

"What do you mean?" pipes up the mathematician. "Between the two of you, that was a perfect shot!"

(*) How they knew it was a deer:

The physicist observed that it behaved in a deer-like manner, so it
must be a deer.

The mathematician asked the physicist what it was, thereby reducing it
to a previously solved problem.

The engineer was in the woods to hunt deer, therefore it was a deer.

A computer scientist, mathematician, a physicist, and an engineer were travelling through Scotland when they saw a black sheep through the window of the train.

"Aha," says the engineer, "I see that Scottish sheep are black."

"Hmm," says the physicist, "You mean that some Scottish sheep are black."

"No," says the mathematician, "All we know is that there is at least one sheep in Scotland, and that at least one side of that one sheep is black!"

"Oh, no!" shouts the computer scientist, "A special case!"

A Mathematician and an Engineer attend a lecture by a Physicist. The topic concerns Kulza-Klein theories involving physical processes that occur in spaces with dimensions of 11, 12 and even higher. The Mathematician is sitting, clearly enjoying the lecture, while the Engineer is frowning and looking generally confused and puzzled. By the end the Engineer has a terrible headache. At the end, the Mathematician comments about the wonderful lecture. The Engineer says "How do you understand this stuff?"

Mathematician: "I just visualise the process."

Engineer: "How can you POSSIBLY visualise something that occurs in 11-dimensional space?"

Mathematician: "Easy, first visualise it in N-dimensional space, then let N go to 11."

What is "Pi"?

Mathematician: Pi is the number expressing the relationship between the circumference of a circle and its diameter.

Physicist: Pi is 3.1415927 plus or minus 0.00000005

Engineer: Pi is about 3.

When considering the behaviour of a howitzer:

A mathematician will be able to calculate where the shell will land.

A physicist will be able to explain how the shell gets there.

An engineer will stand there and try to catch it.

An engineer, a physicist and a mathematician find themselves in an anecdote, indeed an anecdote quite similar to many that you have no doubt already heard. After some observations and rough calculations the engineer realises the situation and starts laughing. A few minutes later the physicist understands too and chuckles to himself happily as he now has enough experimental evidence to publish a paper.

This leaves the mathematician somewhat perplexed, as he had observed right away that he was the subject of an anecdote, and deduced quite rapidly the presence of humour from similar anecdotes, but considers this anecdote to be too trivial a corollary to be significant, let alone funny.

Q: What's purple and commutes?

A: An abelian grape.

Q: Why did the mathematician name his dog "Cauchy"?

A: Because he left a residue at every pole.

Q: Why is it that the more accuracy you demand from an interpolation
function, the more expensive it becomes to compute?

A: That's the Law of Spline Demand.

Q: How many mathematicians does it take to screw in a lightbulb?

A: One, who gives it to six Californians, thereby reducing it to an earlier
riddle.

PS: The answer to that riddle is usually "Six Californians don't screw
in a lightbulb they screw in a hottub."

Q: What do a mathematician and a physicist [or engineer, or musician,
or whatever the profession of the person addressed] have in common?

A: They are both stupid, with the exception of the mathematician.

Q: What do you call a teapot of boiling water on top of mount Everest?

A: A high-pot-in-use

Q: What do you call a broken record?

A: A Decca-gone

Q: What do you get when you cross 50 female pigs and 50 male deer?

A: One hundred sows-and-bucks

Q: Why did the chicken cross the Moebius strip?

A: To get to the other ... er, um ...

Q: What is the world's longest song?

A: "Aleph-nought Bottles of Beer on the Wall."

Q: What does a mathematician do when he's constipated?

A: He works it out with a pencil.

Q: What's yellow and equivalent to the Axiom of Choice.

A: Zorn's Lemon.

Q: What do you get if you cross an elephant with a zebra.

A: Elephant zebra sin theta.

Q: What do you get if you cross an elephant with a mountain climber.

A: You can't do that. A mountain climber is a scalar.

Q: What do you get when you cross an elephant with a banana?

A: Elephant banana sine theta in a direction mutually perpendicular to
the two as determined by the right hand rule.

Q: To what question is the answer "9W."

A: "Dr. Wiener, do you spell your name with a V?"

**If you have reached this part,
you have more stamina than brains!**