There was an Indian Chief, and he had three squaws, and kept them in three teepees. When he would come home late from hunting, he would not know which teepee contained which squaw, being dark and all. He went hunting one day, and killed a hippopotamus, a bear, and a buffalo. He put the a hide from each animal into a different teepee, so that when he came home late, he could feel inside the teepee and he would know which squaw was inside.

Well after about a year, all three squaws had children. The squaw on the bear had a baby boy, the squaw on the buffalo hide had a baby girl. But the squaw on the hippopotamus had a girl and a boy. So what is the moral of the story?

***********************

The squaw on the hippopotamus is equal to the sum of the squaws on the other two hides.

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 rectanguar coordinates and it couldn't understand them. All the horse's aquaintences 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!"

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

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

### 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 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.

A Physicist and a mathematician setting in a faculty lounge. Suddenly, the coffee machine catches on fire. The physicist grabs a bucket and leap towards the sink, filled the bucket with water and puts out the fire. Second day, the same two sit in the same lounge. Again, the coffee machine catches on fire. This time, the mathematician stands up, got a bucket, hand the bucket to the physicist, thus reduce the problem to a previousely solved one.

An engineer, a mathematician, and a physicist are staying in three adjoiningcabins 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.

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 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.

A mathematician, a physicist and an engineer are given an identical problem: Prove that all odd numbers greater than 2 are prime numbers. They proceed:

Mathematician: 3 is a prime, 5 is a prime, 7 is a prime, 9 is not a prime - counterexample - 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, ...

A Mathemetician (M) and an Engineer (E) attend a lecture by a Physicist. The topic concerns Kulza-Klein theories involving physical processes that occur in spaces with dimensions of 9, 12 and even higher. The M is sitting, clearly enjoying the lecture, while the E is frowning and looking generally confused and puzzled. By the end the E has a terrible headache. At the end, the M comments about the wonderful lecture. The E says, "How do you understand this stuff?"

M: "I just visualize the process."

E: "How can you POSSIBLY visualize something that occurs in 9-dimensional space?"

M: "Easy, first visualize it in N-dimensional space, then let N go to 9."

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^x."

Why did the cat fall off the roof?

Because he lost his mu. (mew=sound cats make, mu=coeff of friction)

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

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.

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 realize that you'll never reach her?" The physicist smiles and replied, "Of course! But I'll get close enough for all practical purposes!"

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.

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."

Q:What did the acorn say when it grew up?

A:Geometry

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

A. He works it out with a pencil.

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

Moebius always does it on the same side.

Heisenberg might have slept here.

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 seperate 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 aluminum 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 dessicated 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...

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."

(I'm not sure if the following one is a true story or not)

The great logician Betrand 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."

What is "pi"?

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

Physicist: Pi is 3.1415927plus or minus 0.000000005

Ya' hear about the geometer who went to the beach to catch the rays and became a tangent ?

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

A biologist, a statistician, a mathematician and a computer scientist are on a photo-safari in africa. They drive out on the savannah in their jeep, stop and scout the horizon with their binoculars.

The biologist: "Look! There's a herd of zebras! And there, in the middle: A white zebra! It's fantastic! There are white zebras! We'll be famous!"

The statistician: "It's not significant. We only know there's one white zebra."

The mathematician: "Actually, we only know there exists a zebra, which is white on one side."

The computer scientist: "Oh, no! A special case!"

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

1 + 1 = 3, for large values of 1

Lumberjacks make good musicians because of their natural logarithms.

Pie are not square. Pie are round. Cornbread are square.

A physics joke:

"Energy equals milk chocolate square"

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

The lawyer says: "For sure 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 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 can do some mathematics."

Von Neumann and Nobert Weiner 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."

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...

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."

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 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, ..."

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!"

Two male mathematiciens 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 mathematicien 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 cuebd'? Yes, that's right, he says. So she agrees, and goes off mumbling to herself, `one thir dex cuebd...'.

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'!

The Method of Inversive Geometry: We place a spherical cage in the desert, enter it, and lock it. We perform an inversion with respect to the cage. The lion is then in the interior of the cage, and we are outside.

The Set Theoretic Method: We observe that the desert is a separable space. It therefore contains an enumerable dense set of points, from which can be extracted a sequence having the lion as limit. We then approach the lion stealthily along this sequence, bearing with us suitable equipment.

A Topological Method: We observe that a lion has at least the connectivity of the torus. We transport the desert into four-space. It is then possible to carry out such a deformation that the lion can be returned to three-space in a knotted condition. He is then helpless.

The Dirac Method: We observe that wild lions are, ipso facto, not observable in the Sahara Desert. Consequently, if there are any lions in the Sahara, they are tame. The capture of a tame lion may be left as an exercise for the reader.

The Thermodynamical Method: We construct a semi-permeable membrane, permeable to everything except lions, and sweep it across the desert.

The Schrodinger Method: At any given moment there is a positive probability that there is a lion in the cage. Sit down and wait.

## MATHEMATICS PURITY TEST

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

### The Basics

1. Have you ever been excited about math?
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?
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

1. Have you ever applied your math to a hard science?
2. Applied your math to a soft science?
3. Done an integration by parts?
4. Done two integration by parts in a single problem?
5. Bounded the domain and range of your function?
6. Used the domination test for improper integrals?
7. Done Newton's Method?
8. Done the Method of Frobenius?
9. Used the Sandwich Theorem?
10. Used the Mean Value Theorem?
11. Used a Gaussian surface?
12. Used a foreign object on a math problem (eg: calculator)?
13. Used a program to improve your mathematical technique (eg: MACSYMA)?
14. Not used brackets when you should have?
15. Integrated a function over its full period?
16. Done a calculation in three-dimensional space?
17. Done a calculation in n-dimensional space?
18. Done a change of bases?
19. Done a change of bases specifically in order to magnify your vector?
20. Worked through four complete bases in a single night (eg: using the Graham-Schmidt method)?
21. Inserted a number into an equation?
22. Calculated the residue of a pole?
23. Scored perfectly on a math test?
24. Swallowed everything your professor gave you?
25. Used explicit notation in your problem set?
26. Puposefully omitted important steps in your problem set?
28. Been blown away on a test?
29. Blown away your professor on a test?
30. Have you ever multiplied 23 by 3?
31. Have you ever bounded your Bessel function so that the membrane did not shoot to infinity?
32. Have you ever understood the following quote: "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." (Shlomo & Bamberg's _A "Course" in Mathematics for Students of Physics_)

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

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

-- from a button I bought at Nancy Lebowitz's table at Boskone

There are three kinds of mathematicians: those who can count and those who cannot.