Several students were given 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:
My geometry teacher was sometimes acute, and sometimes obtuse, but always, he was right.
Q: What's the title of this picture?
.. .. ____ .. ..
\\===/======\\==
|| | | ||
|| |____| ||
|| ( ) ||
|| \____/ ||
|| ||
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|| ||
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|| (\ ||
|| ) ) ||
|| //||\\ ||
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 -----
3->4 \/ 3 = 2
and:
lim -----
8->9 \/ 8 = 3
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: Dan Quayle and the letter "e" made the 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 )
/
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: "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 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 realized 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 plans 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.
An assemblage of the most gifted minds in the world were all posed the following question:
"What is 2 * 2 ?"
The engineer whips out his slide rule 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 * 2 ?"
Logician: "Please define 2 * 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 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.
lim sin(x)
n->oo ------ = 6
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 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'!
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!"
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 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 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...
Mathematician's Cheers:
E to the x dx,
E to the y dy,
sine x, cosine x,
natural log of y,
derivative on the left
derivative on the right
integrate, integrate,
fight! fight! fight!
E to the x dx dy
radical transcendental pi
secant cosine tangent sine
3.14159
2.71828
come on folks let's integerate!!
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! (Worcester Polytechnic Institute)
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."
IBM version of the previous 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."
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 [email protected] (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 from 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, SUPRISE 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":
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 generalized 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 Irreversability:
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 refreshen 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 recognize 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 categorized 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 ...
Math Quiz: Match the correct answers to the statements.
___ 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
B. polygon
C. inscribe
D. geometry
E. unit
F. center
G. decagone
H. arc
I. circle
J. axiom
K. cone
L. coincide
M. cosecant
N. tangent
O. hero
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!"
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