fun at math

8/3/2019 fun at math

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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.

Math Jokes

A team of engineers were required to measure the height of a flag pole. They only had ameasuring tape, and were getting quite frustrated trying to keep the tape along the pole. It keptfalling down, etc. A mathematician comes along, finds out their problem, and proceeds toremove the pole from the ground and measure it easily. When he leaves, one engineer says to theother: "Just like a mathematician! We need to know the height, and he gives us the length!"

What is "pi"?Mathematician: Pi is thenumber expressing the relationship between the circumference of acircle and its diameter.Physicist: Pi is 3.1415927plus or minus 0.00000005Engineer: Pi is about 3.

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

Here's a limerick:


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Which, of course, translates to:

Integral t-squared dtfrom 1 to the cube root of 3times the cosine

of three pi over 9equals log of the cube root of 'e'.

And it's correct, too.

Another one:

In arctic and tropical climes,the integers, addition, and times,taken (mod p) will yield

a full finite field,as p ranges over the primes.

The ark lands after The Flood. Noah lets all the animals out. Says, "Go and multiply." Severalmonths pass. Noah decides to check up on the animals. All are doing fine except a pair of snakes."What's the problem?" says Noah. "Cut down some trees and let us live there", say the snakes.Noah follows their advice. Several more weeks pass. Noah checks on the snakes again. Lots oflittle snakes, everybody is happy. Noah asks, "Want to tell me how the trees helped?""Certainly", say the snakes. "We're adders, and we need logs to multiply."

Three men are in a hot-air balloon. Soon, they find themselves lost in a canyon somewhere. Oneof the three men says, "I've got an idea. We can call for help in this canyon and the echo willcarry our voices far."So he leans over the basket and yells out, "Helllloooooo! Where are we?" (They hear the echoseveral 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 menasks, "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."

1. What's the contour integral around Western Europe?Answer: Zero, because all the Poles are in Eastern Europe!

2. An English mathematician was asked by his very religious colleague:Do you believe in one God?Answer: Yes, up to isomorphism!

3. What is a compact city?It's a city that can be guarded by finitely many near-sighted policemen!


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Q: What's purple and commutes?A: An abelian grape.

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

A: Zorn's Lemon.

The great logician Betrand Russell (or was it A.N. Whitehead?) once claimed that he could proveanything if given that 1+1=1. So one day, some smarty-pants asked him, "Ok. Prove that you'rethe Pope." He thought for a while and proclaimed, "I am one. The Pope is one. Therefore, thePope and I are one."

Lemma: All horses are the same color.

Proof (by induction):

Case n=1: In a set with only one horse, it is obvious that all horses in that set are the samecolor.Case n=k: Suppose you have a set of k+1 horses. Pull one of these horses out of the set,so that you have k horses. Suppose that all of these horses are the same color. Now putback the horse that you took out, and pull out a different one. Suppose that all of the khorses now in the set are the same color. Then the set of k+1 horses are all the samecolor. We have k true=> k+1 true; therefore all horses are the same color.

Theorem: All horses have an infinite number of legs.

Proof (by intimidation):

Everyone would agree that all horses have an even number of legs. It is also well-knownthat horses have forelegs in front and two legs in back. 4 + 2 = 6 legs, which is certainlyan odd number of legs for a horse to have! Now the only number that is both even andodd is infinity; therefore all horses have an infinite number of legs.

However, suppose that there is a horse somewhere that does not have an infinite numberof legs. Well, that would be a horse of a different color; and by the Lemma, it doesn'texist.

QED

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, 3is prime, 5 is prime, and by induction, we have that all the odd integers are prime."


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Of course, there are some jeers from some of his friends. The physics student then said, "I'm notsure 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 isprime, 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 notsure 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 gotthe right idea, but you'd end up taking too long doing it. I've just whipped up a program toREALLY go and prove it..." He goes over to his terminal and runs his program. Reading theoutput on the screen he says, "1 is prime, 1 is prime, 1 is prime, 1 is prime...."

A biologist, a statistician and a mathematician 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'sfantastic ! There are white zebra's ! 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."

1 + 1 = 3, for large values of 1

Theorem : All positive integers are equal.

Proof :

Sufficient to show that for any two positive integers, A and B, A = B. Further, it issufficient 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.


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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.

Theorem:

All positive integers are interesting.Proof:Assume the contrary. Then there is a lowest non-interesting positive integer. But, hey, that'spretty interesting! A contradiction.QED

The shortest math joke ever: let epsilon < 0 (*)

Two functions meet in a narrow street. (*)F1: Clear the way!F2: No, I won`t.

F1: Move over, or I will differentiate you!F2: Ok, try it, I am the exp-function!

MathOnLine

"Math Jokes" is featured in the Top Ten Educational Sites on the World-Wide Web

("Learning in Motion's", September 2000 issue), seehttp://www.learn.motion.com

Counting visitors

Mathematical humor

collected by Andrej and Elena Cherkaev

|| Andrej's homepage ||Elena's homepage||
http://www.math.utah.edu/~cherk/mathonline.htmlhttp://www.learn.motion.com/http://www.learn.motion.com/http://v.extreme-dm.com/?login=cherk1http://v.extreme-dm.com/?login=cherk1http://www.math.utah.edu/~cherk/index.htmlhttp://www.math.utah.edu/~cherk/index.htmlhttp://www.math.utah.edu/~elenahttp://www.math.utah.edu/~elenahttp://www.math.utah.edu/~elenahttp://extremetracking.com/open?login=jokemathhttp://extremetracking.com/open?login=jokemathhttp://extremetracking.com/open?login=jokemathhttp://www.math.utah.edu/~elenahttp://www.math.utah.edu/~cherk/index.htmlhttp://v.extreme-dm.com/?login=cherk1http://v.extreme-dm.com/?login=cherk1http://www.learn.motion.com/http://www.math.utah.edu/~cherk/mathonline.html


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The suggested collection of mathematical folklore might be enjoyable for mathematicians and

for students because every joke contains a portion of truth or lie about our profession. The

selected jokes and sayings contain something essential about mathematics, the mathematical

way of thinking, or mathematical pop-culture.

We have slightly edited and systematized selected jokes, and added a few new ones.

We are concerned that publication of sacral lecture jokes may endanger the respect to

math. teachers in freshmen classes. Our excuse for this risky ethnographic research is

that the majority of the jokes already exists on the Internet.

Sometimes, people tend to attribute the jokes either to their beloved teachers (Peter Lax

is so far the champion) or to legendary figures as Norbert Wiener or Paul Erdos;

similarly, physical jokes are attributed to Albert Einstein or Niels Bohr and geometrical

theorems - to Euclid. A number of collected jokes we learned from our professors in

Saint-Petersburg. Generally, attributing the jokes is hopeless. Indeed, the phrasing of the

narrator is as important as the essence of the humor (if this essence does exist at all). To

our mind, a joke goes to "public domain" immediately after being created or modifiedand there should be no authorship in it. Most of the collected sayings and jokes are

repeated in a number of webpages, which makes it difficult to credit a particular Internet

source. Instead, we thank all Internet collectors of math. jokes.

Please email us your comments and new stories:[email protected]!

Andrej and Elena

Contents

1. Definitions

2. A mathematician and ..

3. Math education

4. Seminar semantics, etc.

5. Theorems

6. Playground

7. Puns

8. Anecdotes

9. Limericks

10. Links

To the top

1. Definitions

Let's start with general definitions.
mailto:[email protected]:[email protected]:[email protected]://www.math.utah.edu/~cherk/mathjokes.html#topic1http://www.math.utah.edu/~cherk/mathjokes.html#topic3http://www.math.utah.edu/~cherk/mathjokes.html#topic4http://www.math.utah.edu/~cherk/mathjokes.html#topic4http://www.math.utah.edu/~cherk/mathjokes.html#topic2http://www.math.utah.edu/~cherk/mathjokes.html#topic5http://www.math.utah.edu/~cherk/mathjokes.html#topic6http://www.math.utah.edu/~cherk/mathjokes.html#topic7http://www.math.utah.edu/~cherk/mathjokes.html#topic8http://www.math.utah.edu/~cherk/mathjokes.html#topic9http://www.math.utah.edu/~cherk/mathjokes.html#topic10http://www.math.utah.edu/~cherk/mathjokes.html#topic0http://www.math.utah.edu/~cherk/mathjokes.html#topic0http://www.math.utah.edu/~cherk/mathjokes.html#topic0http://www.math.utah.edu/~cherk/mathjokes.html#topic10http://www.math.utah.edu/~cherk/mathjokes.html#topic9http://www.math.utah.edu/~cherk/mathjokes.html#topic8http://www.math.utah.edu/~cherk/mathjokes.html#topic7http://www.math.utah.edu/~cherk/mathjokes.html#topic6http://www.math.utah.edu/~cherk/mathjokes.html#topic5http://www.math.utah.edu/~cherk/mathjokes.html#topic2http://www.math.utah.edu/~cherk/mathjokes.html#topic4http://www.math.utah.edu/~cherk/mathjokes.html#topic3http://www.math.utah.edu/~cherk/mathjokes.html#topic1mailto:[email protected]


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Mathematics is made of 50 percent formulas, 50 percent proofs, and 50 percentimagination.

"A mathematician is a device for turning coffee into theorems" (P. Erdos)Addendum: American coffee is good for lemmas.

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

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

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

Mathematics is the art of giving the same name to different things. -- J. H.Poincare

What is a rigorous definition of rigor?

There is no logical foundation of mathematics, and Gdel has proved it!

I do not think -- therefore I am not.

Here is the illustration of this principle:One evening Rene Descartes went to relax at a local tavern. The tenderapproached and said, "Ah, good evening Monsieur Descartes! Shall I serve youthe usual drink?". Descartes replied, "I think not.", and promptly vanished.


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A topologist is a person who doesn't know the difference between a coffee cupand a doughnut.

A mathematician is a blind man in a dark room looking for a black cat which isn'tthere. (Charles R Darwin)

A statistician is someone who is good with numbers but lacks the personality tobe an accountant.

Classification of mathematical problems as linear and nonlinear is likeclassification of the Universe as bananas and non-bananas.

A law of conservation of difficulties: there is no easy way to prove a deep result.

A tragedy of mathematics is a beautiful conjecture ruined by an ugly fact.

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

Philosophy is a game with objectives and no rules.Mathematics is a game with rules and no objectives.

Math is like love; a simple idea, but it can get complicated.

The actual quote from the Webster dictionary:trillion n


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syn SCAD, gob(s), heap, jillion, load(s), million, oodles, quantities, thousand,wad(s)

Mathematics is like checkers in being suitable for the young, not too difficult,amusing, and without peril to the state. (Plato)

The difference between an introvert and extrovert mathematicians is: An introvertmathematician looks at his shoes while talking to you. An extrovertmathematician looks at your shoes.

A bit of theology.

Math is the language God used to write the universe.

Asked if he believes in one God, a mathematician answered:" Yes, up to isomorphism."

God is real, unless proclaimed integer.

Medicine makes people ill, mathematics make them sad and theology makes themsinful. (Martin Luther)

The good Christian should beware of mathematicians and all those who makeempty prophecies. The danger already exists that mathematicians have made acovenant with the devil to darken the spirit and confine man in the bonds of Hell.(St. Augustine)


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He who can properly define and divide is to be considered a god. (Plato)

"God geometrizes" says Plato.

and here is the analytical continuation of this saying:

Biologists think they are biochemists,

Biochemists think they are Physical Chemists,

Physical Chemists think they are Physicists,

Physicists think they are Gods,

And God thinks he is a Mathematician.

Physicists defer only to mathematicians, mathematicians defer only to God.

To the top

2. A mathematician and ...The following sketches show our dedication to abstract thinking in the most unusual

situations and strong belief in the universality of mathematical methods. Mathematicians

are always impatient and intelligent.

A mathematician and a Wall street broker went to races. The broker suggested tobet $10,000 on a horse. The mathematician was sceptical, saying that he wantedfirst to understand the rules, to look on horses, etc. The broker whispered that heknew a secret algorithm for the success, but he could not convince themathematician."You are too theoretical," he said and bet on a horse. Surely, that horse came firstbringing him a lot of money. Triumphantly, he exclaimed:"I told you, I knew the secret!""What is your secret?" the mathematician asked."It is rather easy. I have two kids, three and five year old. I sum up their ages andI bet on number nine.""But, three and five is eight," the mathematician protested."I told you, you are too theoretical!" the broker replied, "Haven't I just shownexperimentally, that my calculation is correct! 3+5=9!"
http://www.math.utah.edu/~cherk/mathjokes.html#topic0http://www.math.utah.edu/~cherk/mathjokes.html#topic0http://www.math.utah.edu/~cherk/mathjokes.html#topic0


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A mathematician, a physicist, an engineer went again to the races and laid theirmoney down. Commiserating in the bar after the race, the engineer says, "I don'tunderstand why I lost all my money. I measured all the horses and calculated theirstrength and mechanical advantage and figured out how fast they could run..."

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

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

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

An engineer, a physicist and a mathematician are staying in a hotel.The engineer wakes up and smells smoke. He goes out into the hallway and sees afire, so he fills a trash can from his room with water and douses the fire. He goesback to bed.Later, the physicist wakes up and smells smoke. He opens his door and sees a firein the hallway. He walks down the hall to a fire hose and after calculating theflame velocity, distance, water pressure, trajectory, etc. extinguishes the fire withthe minimum amount of water and energy needed.Later, the mathematician wakes up and smells smoke. He goes to the hall, sees the

fire and then the fire hose. He thinks for a moment and then exclaims, "Ah, asolution exists!" and then goes back to bed.

A physicist and a mathematician are sitting in a faculty lounge. Suddenly, thecoffee machine catches on fire. The physicist grabs a bucket and leap towards thesink, filled the bucket with water and puts out the fire. Second day, the same twosit in the same lounge. Again, the coffee machine catches on fire. This time, themathematician stands up, got a bucket, hands the bucket to the physicist, thusreducing the problem to a previously solved one.

Another version:

A mathematician and an engineer are on desert island. They find two palm trees with

one coconut each. The engineer climbs up one tree, gets the coconut, eats. The

mathematician climbs up the other tree, gets the coconut, climbs the other tree and

puts it there. "Now we've reduced it to a problem we know how to solve."


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A biologist, a physicist and a mathematician were sitting in a street cafe watchingthe crowd. Across the street they saw a man and a woman entering a building.Ten minutes they reappeared together with a third person.

- They have multiplied, said the biologist.- Oh no, an error in measurement, the physicist sighed.- If exactly one person enters the building now, it will be empty again, themathematician concluded.

Several scientists were all posed the following question: "What is 2 * 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, then announces: "I don't know what theanswer is, but I can tell you, an answer exists!".Philosopher smiles: "But what do you mean by 2 * 2 ?"Logician replies: "Please define 2 * 2 more precisely."The sociologist: "I don't know, but is was nice talking about it".Behavioral Ecologist: "A polygamous mating system".Medical Student : "4" All others looking astonished : "How did you know ??"Medical Student : :I memorized it."

A physicist, a mathematician, and a mystic were asked to name the greatestinvention of all time. The physicist chose the fire, which gave humanity the powerover matter. The mathematician chose the alphabet, which gave humanity powerover symbols. The mystic chose the thermos bottle."Why a thermos bottle?" the others asked."Because the thermos keeps hot liquids hot in winter and cold liquids cold insummer.""Yes -- so what?""Think about it." said the mystic reverently. That little bottle -- how does it*know*?"

At least this time we are together with the physicist! :

An chemist, a physicist, and a mathematician are stranded on an island when acan of food rolls ashore. The chemist and the physicist comes up with many


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ingenious ways to open the can. Then suddenly the mathematician gets a brightidea: "Assume we have a can opener ..."

A mathematician is asked to design a table. He first designs a table with no legs.Then he designs a table with infinitely many legs. He spend the rest of his lifegeneralizing the results for the table with N legs (where N is not necessarily anatural number).

Several scientists were all posed the following question: "What is pi ?"The engineer said: "It is approximately 3 and 1/7"The physicist said: "It is 3.14159"The mathematician thought a bit, and replied "It is equal to pi".

(A nutritionist: "Pie is a healthy and delicious dessert!" )

An engineer, a physicist and a mathematician were asked to hammer a nail into awall.The engineer went to build a Universal Automatic Nailer -- a device able tohammer every possible nail into every possible wall.The physicist conducted series of experiments on strength of hammers, nails, andwalls and developed a revolutionary technology of ultra-sonic nail hammering at

super-low temperature.The mathematician generalized the problem to a N dimensional problem ofpenetration of a knotted one dimensional nail into a N-1 dimensional hyper-wall.Several fundamental theorems are proved. Of course, the problem is too rich tosuggest a possibility of a simple solution, even the existence of a solution is farfrom obvious.

A mathematician, a physicist, and an engineer were traveling through Scotlandwhen 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 inScotland, and that at least one side of that one sheep is black!"


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A mathematician, scientist, and engineer are each asked: "Suppose we define ahorse's tail to be a leg. How many legs does a horse have?" The mathematiciananswers "5"; the scientist "1"; and the engineer says "But you can't do that!

A mathematician, a physicist, and an engineer are all given identical rubber ballsand told to find the volume. They are given anything they want to measure it, andhave all the time they need. The mathematician pulls out a measuring tape andrecords the circumference. He then divides by two times pi to get the radius,cubes that, multiplies by pi again, and then multiplies by four-thirds and therebycalculates the volume. The physicist gets a bucket of water, places 1.00000gallons of water in the bucket, drops in the ball, and measures the displacement tosix significant figures. And the engineer? He writes down the serial number of theball, and looks it up.

A Mathematician (M) and an Engineer (E) attend a lecture by a Physicist. Thetopic concerns Kulza-Klein theories involving physical processes that occur inspaces with dimensions of 9, 12 and even higher. The M is sitting, clearlyenjoying the lecture, while the E is frowning and looking generally confused andpuzzled. By the end the E has a terrible headache. At the end, the M commentsabout the wonderful lecture.E: "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"

A team of engineers were required to measure the height of a flag pole. They onlyhad a measuring tape, and were getting quite frustrated trying to keep the tapealong the pole. It kept falling down, etc. A mathematician comes along, finds outtheir problem, and proceeds to remove the pole from the ground and measure iteasily. 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 mathematician and a physicist agree to a psychological experiment. The(hungry) mathematician is put in a chair in a large empty room and his favoritemeal, perfectly prepared, is placed at the other end of the room. The psychologistexplains, "You are to remain in your chair. Every minute, I will move your chairto a position halfway between its current location and the meal." The


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mathematician looks at the psychologist in disgust. "What? I'm not going to gothrough this. You know I'll never reach the food!" And he gets up and storms out.The psychologist ushers the physicist in. He explains the situation, and thephysicist's eyes light up and he starts drooling. The psychologist is a bit confused."Don't you realize that you'll never reach the food?" T he physicist smiles and

replies: "Of course! But I'll get close enough for all practical purposes!"

One day a farmer called up an engineer, a physicist, and a mathematician andasked 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 mostefficient design.The physicist made a long, straight line and proclaimed "We can assume thelength is infinite..." and pointed out that fencing off half of the Earth was certainlya more efficient way to do it.

The Mathematician just laughed at them. He built a tiny fence around himself andsaid "I declare myself to be on the outside."

The physicist and the engineer are in a hot-air balloon. Soon, they find themselveslost in a canyon somewhere. They yell out for help: "Helllloooooo! Where arewe?"15 minutes later, they hear an echoing voice: "Helllloooooo! You're in a hot-airballoon!!"The physicist says, "That must have been a mathematician."

The engineer asks, "Why do you say that?"The physicist replied: "The answer was absolutely correct, and it was utterlyuseless."

Several scientists were asked to prove that all odd integers higher than 2 areprime.

Mathematician: 3 is a prime, 5 is a prime, 7 is a prime, and by induction - everyodd integer higher than 2 is a prime.

Physicist: 3 is a prime, 5 is a prime, 7 is a prime, 9 is an experimental error, 11 isa prime. Just to be sure, try several randomly chosen numbers: 17 is a prime, 23 isa prime...Engineer: 3 is a prime, 5 is a prime, 7 is a prime, 9 is an approximation to a prime,11 is a prime,...Programmer (reading the output on the screen): 3 is a prime, 3 is a prime, 3 a isprime, 3 is a prime....Biologist: 3 is a prime, 5 is a prime, 7 is a prime, 9 -- results have not arrived


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yet,...Psychologist: 3 is a prime, 5 is a prime, 7 is a prime, 9 is a prime but tries tosuppress it,...Chemist (or Dan Quayle): What's a prime?Politician: "Some numbers are prime.. but the goal is to create a kinder, gentler

society where all numbers are prime... "Programmer: "Wait a minute, I think I have an algorithm from Knuth on findingprime numbers... just a little bit longer, I've found the last bug... no, that's not it...ya know, I think there may be a compiler bug here - oh, did you want IEEE-998.0334 rounding or not? - was that in the spec? - hold on, I've almost got it - Iwas up all night working on this program, ya know... now if management wouldjust get me that new workstation that just came out, I'd be done by now... etc., etc...."

(Two is the oddest prime of all, because it's the only one that's even!)

Dean, to the physics department. "Why do I always have to give you guys somuch money, for laboratories and expensive equipment and stuff. Why couldn'tyou be like the math. department - all they need is money for pencils, paper andwaste-paper baskets. Or even better, like the philosophy department. All theyneed are pencils and paper."

A mathematician, an engineer, and a chemist were walking down the road when

they saw a pile of cans of beer. Unfortunately, they were the old-fashioned cansthat do not have the tab at the top. One of them proposed that they split up andfind can openers. The chemist went to his lab and concocted a magical chemicalthat dissolves the can top in an instant and evaporates the next instant so that thebeer inside is not affected. The engineer went to his workshop and created a newHyperOpener that can open 25 cans per second.

They went back to the pile with their inventions and found the mathematicianfinishing the last can of beer. "How did you manage that?" they asked inastonishment. The mathematician answered, "Oh, well, I assumed they were openand went from there."

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 realizes the situationand starts laughing. A few minutes later the physicist understands too and


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chuckles to himself happily as he now has enough experimental evidence topublish a paper.

This leaves the mathematician somewhat perplexed, as he had observed rightaway that he was the subject of an anecdote, and deduced quite rapidly the

presence of humor from similar anecdotes, but considers this anecdote to be tootrivial a corollary to be significant, let alone funny.

New York (CNN). At John F. Kennedy International Airport today, a high schoolmathematics teacher was arrested trying to board a flight while in possession of acompass, a protractor and a graphical calculator. According to law enforcementofficials, he is believed to have ties to the Al-Gebra network. He will be chargedwith carrying weapons of math instruction. It was later discovered that he taughtthe students to solve their problem with the help of radicals!

A mathematician organizes a lottery in which the prize is an infinite amount ofmoney. When the winning ticket is drawn, and the jubilant winner comes to claimhis prize, the mathematician explains the mode of payment: "1 dollar now, 1/2dollar next week, 1/3 dollar the week after that..."

A Mathematician was put in a room. The room contains a table and three metal

spheres about the size of a softball. He was told to do whatever he wants with theballs and the table in one hour. After an hour, the balls are arranges in a triangle atthe center of the table. The same test is given to a Physicist. After an hour, theballs are stacked one on top of the other in the center of the table. Finally, anEngineer was tested. After an hour, one of the balls is broken, one is missing, andhe's carrying the third out in his lunchbox.

A mathematician decides he wants to learn more about practical problems. Hesees 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 wellknown ..."

When a statistician passes the airport security check, they discover a bomb in hisbag. He explains. "Statistics shows that the probability of a bomb being on an


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airplane is 1/1000. However, the chance that there are two bombs at one plane is1/1000000. So, I am much safer..."

What is the difference between a Psychotic, a Neurotic and a mathematician? APsychotic believes that 2+2=5. A Neurotic knows that 2+2=4, but it kills him. Amathematician simply changes the base.

Q: What will a logician choose: a half of an egg or eternal bliss in the afterlife? A:A half of an egg! Because nothing is better than eternal bliss in the afterlife, and ahalf of an egg is better than nothing.

A physicist has been conducting experiments and has worked out a set ofequations which seem to explain his data. He asks a mathematician to check them.A week later, the mathematician calls "I'm sorry, but your equations are completenonsense." "But these equations accurately predict results of experiments. Areyou sure they are completely wrong? "To be precise, they are not always acomplete nonsense. But the only case in which they are true is the trivial onewhere the field is Archimedean..."

A mathematician belives nothing until it is provenA physicist believes everything until it is proven wrongA chemist doesn't carebiologist doesn't understand the question.

An engineer and a topologist were locked in the rooms for a day with a can offood but without an opener. At the end of the day, the engineer is sitting on thefloor of his room and eating from the open can: He threw it against the walls until

it cracked open. In the mathematician's room, the can is still closed but themathematician has disappeared. There are strange noises coming from inside thecan... When it is opened and the mathematician crawls out. "Damn! I got a signwrong..."


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A mathematician has spent ten years trying to prove the Riemann hypothesis.Finally, he decides to sell his soul to the devil in exchange for a proof. The devilpromises to deliver a proof in the four weeks. Half a year later, the devil shows upagain - in a rather gloomy mood. "I'm sorry", he says. "I couldn't prove thehypothesis either. But" - and his face lightens up - "I think I found a really

interesting lemma..."

To mathematicians, solutions mean finding the answers. But to chemists,solutions are things that are still all mixed up.

To the top

3. Math. education

These sketches demonstrate how desperately we want to push the math into the public

education, and the struggle and passion of math. students.

The Evolution of Math Teaching

o 1960s: A peasant sells a bag of potatoes for $10. His costs amount to 4/5 of his sellingprice. What is his profit?

o 1970s: A farmer sells a bag of potatoes for $10. His costs amount to 4/5 of his sellingprice, that is, $8. What is his profit?

o 1970s (new math): A farmer exchanges a set P of potatoes with set M of money. Thecardinality of the set M is equal to 10, and each element of M is worth $1. Draw ten big

dots representing the elements of M. The set C of production costs is composed of two

big dots less than the set M. Represent C as a subset of M and give the answer to the

question: What is the cardinality of the set of profits?

o 1980s: A farmer sells a bag of potatoes for $10. His production costs are $8, and hisprofit is $2. Underline the word "potatoes" and discuss with your classmates.

o 1990s: A farmer sells a bag of potatoes for $10. His or her production costs are 0.80 ofhis or her revenue. On your calculator, graph revenue vs. costs. Run the POTATO

program to determine the profit. Discuss the result with students in your group. Write a

brief essay that analyzes this example in the real world of economics.


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(Anon: adapted from The American Mathematical Monthly, Vol. 101, No. 5, May1994 (Reprinted by STan Kelly-Bootle in Unix Review, Oct 94)

Top ten excuses for not doing homework:

o I accidentally divided by zero and my paper burst into flames.o Isaac Newton's birthday.o I could only get arbitrarily close to my textbook. I couldn't actually reach it.o I have the proof, but there isn't room to write it in this margin.o I was watching the World Series and got tied up trying to prove that it converged.o I have a solar powered calculator and it was cloudy.o I locked the paper in my trunk but a four-dimensional dog got in and ate it.o I couldn't figure out whether i am the square of negative one or i is the square root of

negative one.

o I took time out to snack on a doughnut and a cup of coffee.o I spent the rest of the night trying to figure which one to dunk.o I could have sworn I put the homework inside a Klein bottle, but this morning I couldn't

find it.

Warning! It is against the rule to use these excuses in my classes! A. Ch.

A professor's enthusiasm for teaching precalculus varies inversely with thelikelihood of his having to do it.

A student comes to the department with a shiny new cup, the sort of which youget when having won something. He explained:I won it in the MD Math Contest. They asked what 7 + 7 is. I said 12 and got 3rdplace!

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 onedisagrees, and claims that most people can cope with a reasonable amount ofmath.

The first mathematician goes off to the washroom, and in his absence the secondcalls over the waitress. He tells her that in a few minutes, after his friend hasreturned, he will call her over and ask her a question. All she has to do is answerone third x cubed.


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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 offmumbling to herself, "one thir dex cuebd...".

The first guy returns and the second proposes a bet to prove his point, that mostpeople do know something about basic math. He says he will ask the blondewaitress an integral, and the first laughingly agrees. The second man calls overthe waitress and asks "what is the integral of x squared?".The waitress says "one third x cubed" and while walking away, turns back andsays over her shoulder "plus a constant!"

Frankly, this story is sad. Indeed, the blonde waitress solves the problem correctly, better than

the poser. But he is a mathematician, and she cleans tables. Funny, isn't it?

A mathematician, native Texan, once was asked in his class: "What ismathematics good for?" He replied: "This question makes me sick. Like whenyou show somebody the Grand Canyon for the first time, and he asks you `What'sis good for?' What would you do? Why, you would kick the guy off the cliff".

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 ofknowledge pills are available. The pharmacist says "Here's a pill for Englishliterature." The student takes the pill and swallows it and has new knowledgeabout English literature!"What else do you have?" asks the student."Well, I have pills for art history, biology, and world history," replies thepharmacist.The student asks for these, and swallows them and has new knowledge aboutthose 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 andbrings 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 toswallow."


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Golden rule for math teachers: You must tell the truth, and nothing but the truth,but not the whole truth.

A math professor is one who talks in someone else's sleep.

Q:What do you get when you add 2 apples to 3 apples?A:Answer: A senior high school math problem.

Teacher: Now suppose the number of sheep is x...Student: Yes sir, but what happens if the number of sheep is not x?

Mathematician U. was a great friend of his five-year old grandson. Theydiscussed everything including math and U. was very proud of the boys mathtalents. The child went to kindergarten; In two weeks the he ask U.to help withthe difficult math problem: "There are four airplanes flying, then two moreairplanes join them. How many airplanes are flying now? U. was verydisappointed by the simplicity of the problem. "What confuses you?" he asked.The child says: " I know, of course, that 4 + 2 =6, but I cannot figure out what theairplanes have do with this!"

A lecturer tells some students to learn the phone-book by heart.The mathematicians are baffled: `By heart? You kidding?'The mathematicians are baffled: `By heart? You kidding?'The physics-students ask: `Why?'The engineers sigh: `Do we have to?'The chemistry-students ask: `Till next Monday?'The accounting-students (scribbling): `Till tomorrow?'The laws-students answer: `We already have.'

The medicine-students ask: `Should we start on the Yellow Pages?'

Quotes from math students and lecturers


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"This is a one line proof...if we start sufficiently far to the left."

"The problems for the exam will be similar to the discussed in the class.

Of course, the numbers will be different. But not all of them. Pi will stillbe 3.14159... "

"Roses are red,Violets are blue,Greens' functions are boringAnd so are Fourier transforms."

"Sex and drugs? They're nothing compared with a good proof!"

Yeah, I used to think it was just recreational... then I started doin' it during theweek... you know, simple stuff: differentiation, kinematics. Then I got intointegration by parts... I started doin' it every night: path integrals, holomorphicfunctions. Now I'm on diophantine equations and sinking deeper into transfiniteanalysis. Don't let them tell you it's just recreational.

Fortunately, I can quit any time I want.

"He was restless during the days and couldn't sleep at night - always trying tosolve his problem. When he had finally done it, he wasn't happy: he calls himselfa complete idiot and throws all his notes into the garbage. Then he said, he reallyenjoyed it."

"Do you love your math more than me?""Of course not, dear - I love you much more.""Then prove it!""OK... LetR be the set of all lovable objects..."


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A graduate student of mathematics who used to come to the University on footevery day arrives one day on a fancy new bicycle. "Where did you get the bikefrom?" his friends asked. "It's a `thank you' present", he explains, "from thatfreshman girl I've been tutoring. Yesterday she called me and told that she hadpassed her math final and wanted to drop by to thank me in person. She arrived at

my place on her bicycle. When I had let her in, she took all her clothes off, smiledat me, and said: `You can get from me whatever you desire!'" One of his friendsremarks: "You made a really smart choice when you took the bicycle." "Yeah",another friend adds, "just imagine how silly you would have looked in a girl'sclothes - and they wouldn't have fit you anyway!"

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4. Seminar semantics, etc.Next passages contain little professional secrets. They reflect the conflict between the

dreams of classical clear presentations, the complexity of modern math problems, and the

survival tactics of the authors.

A lecturer:"Now we'll prove the theorem. In fact I'll prove it all by myself."

How to prove it. Guide for lecturers.

Proof by vigorous handwaving:

Works well in a classroom or seminar setting.

Proof by forward reference:

Reference is usually to a forthcoming paper of the author, which is often not as forthcoming as

at first.

Proof by funding:


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How could three different government agencies be wrong?

Proof by example:

The author gives only the case n = 2 and suggests that it contains most of the ideas of thegeneral proof.

Proof by omission:

"The reader may easily supply the details" or "The other 253 cases are analogous"

Proof by deferral:

"We'll prove this later in the course".

Proof by picture:

A more convincing form of proof by example. Combines well with proof by omission.

Proof by intimidation:

"Trivial."

Proof by adverb:

"As is quite clear, the elementary aforementioned statement is obviously valid."

Proof by seduction:

"Convince yourself that this is true! "

Proof by cumbersome notation:

Best done with access to at least four alphabets and special symbols.

Proof by exhaustion:


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An issue or two of a journal devoted to your proof is useful.

Proof by obfuscation:

A long plotless sequence of true and/or meaningless syntactically related statements.

Proof by wishful citation:

The author cites the negation, converse, or generalization of a theorem from the literature to

support his claims.

Proof by eminent authority:

"I saw Karp in the elevator and he said it was probably NP- complete."

Proof by personal communication:

"Eight-dimensional colored cycle stripping is NP-complete [Karp, personal communication]."

Proof by reduction to the wrong problem:

"To see that infinite-dimensional colored cycle stripping is decidable, we reduce it to the halting

problem."

Proof by reference to inaccessible literature:

The author cites a simple corollary of a theorem to be found in a privately circulated memoir of

the Slovenian Philological Society, 1883.

Proof by importance:

A large body of useful consequences all follow from the proposition in question.

Proof by accumulated evidence:

Long and diligent search has not revealed a counterexample.


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Proof by cosmology:

The negation of the proposition is unimaginable or meaningless. Popular for proofs of the

existence of God.

Proof by mutual reference:

In reference A, Theorem 5 is said to follow from Theorem 3 in reference B, which is shown to

follow from Corollary 6.2 in reference C, which is an easy consequence of Theorem 5 in

reference A.

Proof by metaproof:

A method is given to construct the desired proof. The correctness of the method is proved by

any of these techniques.

Proof by vehement assertion:

It is useful to have some kind of authority relation to the audience.

Proof by ghost reference:

Nothing even remotely resembling the cited theorem appears in the reference given.

Proof by semantic shift:

Some of the standard but inconvenient definitions are changed for the statement of the result.

Proof by appeal to intuition:

Cloud-shaped drawings frequently help here.

Dictionary of Definitions of Terms Commonly Used in Math. lectures.

The following is a guide to terms which are commonly used but rarely defined. In thesearch for proper definitions for these terms we found no authoritative, nor even


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recognized, source. Thus, we followed the advice of mathematicians handed down fromtime 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.


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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 THROUGH IT:

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.

Traditional - contemporary math dictionary.


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WHAT'S OUT AND WHAT'S IN FOR MATHEMATICAL TERMS

by

Michael Stueben (November 7, 1994)

Today it is considered an egregious faux pas to speak or write in the

crude antedated terms of our grandfathers. To assist the isolated

student and the less sophisticated teacher, I have prepared the

following list of currently fashionable mathematical terms in

academia. I pass this list on to the general public as a matter of

charity and in the hope that it will lead to more refined elucidation

from young scholars.

thinking: hypothesizing.

proof by contradiction or indirect proof: reductio ad absurdum.

mistake: non sequitur.

starting place: handle.

with corresponding changes: mutatis mutandis.

counterexample: pathological exception.consequently: ipso facto.

swallowing results: digesting proofs.

therefore: ergo.

has an easy-to-understand, but hard-to-find solution: obvious.

has two easy-to-understand, but hard-to-find solutions: trivial.

truth: tautology.

empty: vacuous.

drill problems: plug-and-chug work.

criteria: rubric.

example: substantive

instantiation.

similar structure: homomorphic.

very similar structure: isomorphic.

same area: isometric.

arithmetic: number theory.

count: enumerate.

one: unity.

generally/specifically: globally/locally.

constant: invariant.

bonus result: corollary.

distance: metric measure.

several: a plurality.

function/argument: operator/operand.

separation/joining: bifurcation/confluence.

fourth power or quartic: biquadratic.

random: stochastic.

unique condition: a singularity.uniqueness: unicity.

tends to zero: vanishes.

tip-top point: apex.

half-closed: half-open.

concave: non-convex.

rectangular prisms: parallelepipeds.

perpendicular (adj.): orthogonal.

perpendicular (n.): normal.

Euclid: Descartes.


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Fermat: Wiles.

path: trajectory.

shift: rectilinear

translation.

similar: homologous.

very similar: congruent.

whopper-jawed: skew or oblique.

change direction: perturb.

join: concatenate.

approximate to two or more places: accurate.

high school geometry or plane geometry: geometry of the

Euclidean plane

under the Pythagorean metric.

clever scheme: algorithm.

initialize to zero: zeroize.

* : splat.

{ : squiggle.

decimal: denary.

alphabetical order: lexical order.

a divide-and-conquer method: an algorithm of

logarithmicorder.

student ID numbers: witty passwords.

numerology and number sophistry: descriptive statistics

Special thanks to Peter Braxton who got me started

writing this stuff and who contributed five of

the items above.

Professional secrets.

The highest moments in the life of a mathematician are the first few moments after one

has proved the result, but before one finds the mistake.

Golden rule of deriving: never trust any result that was proved after 11 PM.

The professional quality of a mathematician is inversely proportional to the

importance it attaches to space and equipment.

Relations between pure and applied mathematicians are based on trust andunderstanding. Namely, pure mathematicians do not trust applied mathematicians,and applied mathematicians do not understand pure mathematicians.


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How dare of you to think that I am an analyst!

Some mathematicians become so tense these days that they that they do not go tosleep during seminars.

If I have seen farther than others, it is because I was standing on the shoulders ofgiants.-- Isaac Newton

In the sciences, we are now uniquely privileged to sit side by side with the giants

on whose shoulders we stand.-- Gerald Holton

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

Mathematicians stand on each other's shoulders.-- Gauss

Mathematicians stand on each other's shoulders while computer scientists stand

on each other's toes.-- Richard Hamming

It has been said that physicists stand on one another's shoulders. If this is the case,then programmers stand on one another's toes, and software engineers dig eachother's graves.-- Unknown

These days, even the most pure and abstract mathematics is in danger to be

applied.

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


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To the top

5. Theorems

Here, the powerful mathematical methods are successively applied to the "real life problems".

Interesting Theorem:All positive integers are interesting.Proof:Assume the contrary. Then there is a lowest non-interesting positive integer. But,hey, that's pretty interesting! A contradiction.

Boring Theorem:All positive integers are boring.Proof:Assume the contrary. Then there is a lowest non-boring positive integer. Whocares!

Discovery.Mathematicians have announced the existence of a new whole number which lies

between 27 and 28. "We don't know why it's there or what it does," saysCambridge mathematician, Dr. Hilliard Haliard, "we only know that it doesn'tbehave properly when put into equations, and that it is divisible by six, thoughonly once."

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

Theorem:

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


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is divided into two classes",

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

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

There are 10 kinds of people in the world, those who understand binary math, andthose who don't.

There really are only two types of people in the world, those that DON'T

DO MATH, and those that take care of them.

"The world is everywhere dense with idiots."

Cat Theorem:A cat has nine tails.Proof:

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

Salary TheoremThe less you know, the more you make.Proof:

Postulate 1: Knowledge is Power.

Postulate 2: Time is Money.As every engineer knows: Power = Work / Time

And since Knowledge = Power and Time = Money

It is therefore true that Knowledge = Work / Money .

Solving for Money, we get:

Money = Work / Knowledge

Thus, as Knowledge approaches zero, Money approaches infinity, regardless of the

amount ofWork done.


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Q: How do you tell that you are in the hands of the Mathematical Mafia?A: They make you an offer that you can't understand.

The cherry theorem(a puzzle that reminds some of calculus theorems)Q: What is a small, red, round thing that has a cherry pit inside?A: A cherry.

Notes on the horse colors problem

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

Proof. It is obvious that one horse is the same color. Let us assume the propositionP(k) that k horses are the same color and use this to imply that k+1 horses are thesame color. Given the set ofk+1 horses, we remove one horse; then the remainingk horses are the same color, by hypothesis. We remove another horse and replacethe first; the k horses, by hypothesis, are again the same color. We repeat thisuntil by exhaustion the k+1 sets ofk horses have been shown to be the samecolor. It follows that since every horse is the same color as every other horse, P(k)entails P(k+1). But since we have shown P(1) to be true, P is true for allsucceeding values ofk, that is, all horses are the same color.

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 infront they have fore legs. This makes six legs, which is certainly an odd numberof 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 isgeneral, suppose that somewhere there is a horse with a finite number of legs. Butthat is a horse of another color, and by the lemma that does not exist.

Corollary 1. Everything is the same color.

Proof. The proof of lemma 1 does not depend at all on the nature of the objectunder consideration. The predicate of the antecedent of the universally-quantifiedconditional 'For all x, if x is a horse, then x is the same color,' namely 'is a horse'may be generalized to 'is anything' without affecting the validity of the proof;hence, 'for all x, ifx is anything, x is the same color.'

Corollary 2. Everything is white.


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Proof. If a sentential formula in x is logically true, then any particular substitutioninstance of it is a true sentence. In particular then: 'for all x, ifx is an elephant,then x is the same color' is true. Now it is manifestly axiomatic that whiteelephants exist (for proof by blatant assertion consult Mark Twain 'The StolenWhite 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 oflimbs.

Proof. We prove this theorem in two parts. First we note the obvious fact thathistorians always tell the truth (for historians always take a stand, and thereforethey cannot lie). Hence we have the historically true sentence, 'If Alexander theGreat existed, then he rode a black horse Bucephalus.' But we know by corollary2 everything is white; hence Alexander could not have ridden a black horse. Sincethe 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 anoracle 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 iscertainly an odd number of limbs for a man. Now the only number which is evenand odd is infinity; hence Alexander had an infinite number of limbs. We havethus proved that Alexander the Great did not exist and that he had an infinitenumber of limbs.

The mathematical theory of big game hunting(Aug-Sept. AMM, 446-447, 1938):

According to statistics, there are 42 million alligator eggs laid every year. Of those, onlyabout half get hatched. Of those that hatch, three fourths of them get eaten by predators inthe first 36 days. And of the rest, only 5 percent get to be a year old for one reason oranother. Isn't statistics wonderful? If it weren't for statistics, we'd be eaten by alligators!

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http://abel.math.umu.se/~frankw/lion.htmlhttp://abel.math.umu.se/~frankw/lion.htmlhttp://www.math.utah.edu/~cherk/mathjokes.html#topic0http://www.math.utah.edu/~cherk/mathjokes.html#topic0http://www.math.utah.edu/~cherk/mathjokes.html#topic0http://abel.math.umu.se/~frankw/lion.html


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6. Playground

Let's play with math objects!

An insane mathematician gets on a bus and starts threatening everybody: "I'llintegrate you! I'll differentiate you!!!" Everybody gets scared and runs away.Only one lady stays. The guy comes up to her and says: "Aren't you scared, I'llintegrate you, I'll differentiate you!!!" The lady calmly answers: "No, I am notscared, I am e^x ."

More advanced and more New York style story:

A constant function and e^x are walking on Broadway. Then suddenly theconstant function sees a differential operator approaching and runs away. So e^xfollows him and asks why the hurry. "Well, you see, there's this differential

operator coming this way, and when we meet, he'll differentiate me and nothingwill be left of me...!" "Ah," says e^x, "he won't bother ME, I'm e to the x!" and hewalks on. Of course he meets the differential operator after a short distance.e^x: "Hi, I'm e^x"diff.op.: "Hi, I'm d/dy"

"The number you have dialed is imaginary. Please rotate your phone 90 degreesand try again."

The shortest math joke: let epsilon be < 0

Funny formulas

The limit as 3 goes to 4 of3^2 is 16.(For native LaTex speakers: $$\lim_{3 \rightarrow 4} 3^2 = 16$$)

1 + 1 =3, for sufficiently large one's.

The combination of the Einstein and Pythagoras discoveries:E= m c^2= m ( a^2 + b^2)

2 and 2 is 22


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The limit as n goes to infinity ofsin (x) /n is 6.Proof: cancel the n in the numerator and denominator.

As x goes to zero, the limit of8 /x is 00 (infinity), then the limit (as x goes tozero) ofZ /x is N

Examples of inverse problems:

Q: To what question is the answer "9W."A: "Dr. Wiener, do you spell your name with a V?"

Q: To what question is the answer "Dr. Livingstone, I presume."A: "What is your full name, Dr. Presume?"

Q: how many times can you subtract 7 from 83, and what is left afterwards?

A: I can subtract it as many times as I want, and it leaves 76 every time.

A Neanderthal child rode to school with a boy from Hamilton. When his motherfound out she said, "What did I tell you? If you commute with a Hamiltonianyou'll never evolve!"

Pope has settled the continuum hypothesis!He has declared that cardinals above 80 have no powers.

In modern mathematics, algebra has become so important that numbers will soononly have symbolic meaning.

A circle is a round straight line with a hole in the middle.

In the topologic hell the beer is packed in Klein's bottles.


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He thinks he's really smooth, but he's only C^1.

Moebius strip no-wear belt drive! (Please see other side for warranty details.)

Q: Why couldn't the moebius strip enroll at the school?A: They required an orientation.

Q: What is the world's longest song?A: "Aleph-nought Bottles of Beer on the Wall."

Q: Why do Computer Scientists get Halloween and Christmas mixed up?A: Because Oct. 31 = Dec. 25.

Q: Why did the chicken cross the Moebius strip?A: To get to the other ... er, um ...

Q: Why did the mathematician name his dog "Cauchy"?A: Because he left a residue at every pole.

Q: What do you get when you cross an elephant and a banana?A: | elephant | * | banana | * sin(theta)

Q: What do you get if you cross a mosquito with a mountain climber.A: You can't cross a vector with a scalar.

Q: What is a compact city?A: It's a city that can be guarded by finitely many near-sighted policemen.


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Two mathematicians are studying a convergent series. The first one says: "Do yourealize that the series converges even when all the terms are made positive?" Thesecond one asks: "Are you sure?" "Absolutely!"

Q: What does the zero say to the the eight?A: Nice belt!

Life is complex: it has both real and imaginary components.

Math problems? Call 1-800-[(10x)(13i)2]-[sin(xy)/2.362x].

"Divide fourteen sugar cubes into three cups of coffee so that each cup has an oddnumber of sugar cubes in it." "That's easy: one, one, and twelve." "But twelve isn'todd!" "Twelve is an odd number of cubes to put in a cup of coffee..."

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

Q: Did you hear the one about the statistician?A: Probably....

The light bulb problem

Q: How many mathematicians does it take to screw in a light bulb?A1: None. It's left to the reader as an exercise.A2: None. A mathematician can't screw in a light bulb, but he can easily prove thework can be done.A3: One. He gives it to four programmers, thereby reducing the problem to thealready solved (ask a programmer, how)


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A4: The answer is intuitively obviousA5: Just one, once you've managed to present the problem in terms he/she isfamiliar with.A6: In earlier work, Wiener [1] has shown that one mathematician can change alight bulb.

Ifk mathematicians can change a light bulb, and if one more simply watchesthem do it, then k+1 mathematicians will have changed the light bulb.Therefore, by induction, for all n in the positive integers, n mathematicians canchange a light bulb.Bibliography:[1] Weiner, Matthew P,...

How many mathematical logicians does it take to replace a lightbulb??None: They can't do it, but they can prove that it can be done.

How many numerical analysts does it take to replace a lightbulb??

3.9967: (after six iterations).

How many classical geometers does it take to replace a lightbulb??None: You can't do it with a straight edge and a compass.

How many constructivist mathematicians does it take to replace a lightbulb??None: They do not believe in infinitesimal rotations.

How many simulationists does it take to replace a lightbulb??Infinity: Each one builds a fully validated model, but the light actually never goeson.

How many topologists does it take to screw in a lightbulb??Just one. But what will you do with the doughnut?

How many analysts does it take to screw in a lightbulb??Three: One to prove existence, one to prove uniqueness and one to derive anonconstructive algorithm to do it.

How many Bourbakists does it take to replace a lightbulb: ?Changing a lightbulb is a special case of a more general theorem concerning themaintain and repair of an electrical system. To establish upper and lower bounds

for the number of personnel required, we must determine whether the sufficientconditions of Lemma 2.1 (Availability of personnel) and those of Corollary 2.3.55(Motivation of personnel) apply. Iff these conditions are met, we derive the resultby an application of the theorems in Section 3.1123. The resulting upper bound is,of course, a result in an abstract measure space, in the weak-* topology.


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How many professors does it take to replace a lightbulb??One: With eight research students, two programmers, three post-docs and asecretary to help him.

How many university lecturers does it take to replace a lightbulb??

Four: One to do it and three to co-author the paper.

How many graduate students does it take to replace a lightbulb??Only one: But it takes nine years.

How many math department administrators does it take to replace a lightbulb?None: What was wrong with the old one then???

How we do it ...

Aerodynamicists do it in drag.

Algebraists do it by symbolic manipulation.

Algebraists do it in a ring, in fields, in groups.

Analysts do it continuously and smoothly.

Applied mathematicians do it by computer simulation.

Banach spacers do it completely.

Bayesians do it with improper priors.

Catastrophe theorists do it falling off part of a sheet.

Combinatorists do it as many ways as they can.

Complex analysts do it between the sheets

Computer scientists do it depth-first.

Cosmologists do it in the first three minutes.

Decision theorists do it optimally.

Functional analysts do it with compact support.

Galois theorists do it in a field.


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Game theorists do it by dominance or saddle points.

Geometers do it with involutions.

Geometers do it symmetrically.

Graph theorists do it in four colors.

Hilbert spacers do it orthogonally.

Large cardinals do it inaccessibly.

Linear programmers do it with nearest neighbors.

Logicians do it by choice, consistently and completely.

Logicians do it incompletely or inconsistently.

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

Number theorists do it perfectly and rationally.

Mathematical physicists understand the theory of how to do it, but have difficultyobtaining practical results.

Pure mathematicians do it rigorously.

Quantum physicists can either know how fast they do it, or where they do it, butnot both.

Real analysts do it almost everywhere

Ring theorists do it non-commutatively.

Set theorists do it with cardinals.

Statisticians probably do it.

Topologists do it openly, in multiply connected domains

Variationists do it locally and globally.

Cantor did it diagonally.


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Fermat tried to do it in the margin, but couldn't fit it in.

Galois did it the night before.

Mbius always does it on the same side.

Markov does it in chains.

Newton did it standing on the shoulders of giants.

Turing did it but couldn't decide if he'd finished.

A SLICE OF PI

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

3.141592653589791640628620899

23172535940

881097566

5432664

09171

036

5

To the top

7. Puns

These jokes are sometimes stupid, but still funny.

Math and Alcohol don't mix, so... PLEASE DON'T DRINK AND DERIVE

Motto of the society: Mathematicians Against Drunk Deriving

Q: What's the contour integral around Western Europe?

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

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

removable!


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One day, Jesus said to his disciples: "The Kingdom of Heaven is like 3x squaredplus 8x minus 9." St. Thomas looked very confused and asked St. Peter: "Whatdoes the teacher mean?" St.Peter replied: "Don't worry - it's just another one of his

parabolas."

Q: What is the area of a circle?

A: pi R^2?

R: Pie are not square. Pie are round. Cornbread are square.

Q:What is a proof?

A: One-half percent of alcohol.

Q:What is a dilemma?A: A lemma that proves two results.

Q: What's nonorientable and lives in the sea?A: Moebius Dick.

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

Q: What's purple and commutes?A: An abelian grape.

Q: What's yellow, linear, normed and complete?A: A Bananach space.


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Q: What's a polar bear?A: A rectangular bear after a coordinate transform.

Some say the pope is the greatest cardinal.But others insist this cannot be so, as every pope has a successor.

Q: How many light bulbs does it take to change a light bulb?A: One, if it knows its own Goedel number.

Q: What does the little mermaid wear?

A: An Algebra

Was General Calculus a Roman war hero?

"What's your favorite thing about mathematics?" "Knot theory." "Yeah, meneither."

Noah's Ark lands after The Flood and Noah releases all the animals, saying, "Goforth and multiply." Several months pass and Noah decides to check up on theanimals. All are doing fine except a pair of snakes. "What's the problem?" asksNoah. "Cut down some trees and let us live there," say the snakes. Noah followstheir advice. Several more weeks pass and Noah checks up on the snakes again.He sees lots of little snakes; everybody is happy. Noah says, "So tell me how thetrees helped." "Certainly," reply the snakes. "We're adders, and we need logs tomultiply."

Q: Why didn't Newton discover group theory?A: Because he wasn't Abel.


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In Alaska, where it gets very cold, pi is only 3.00. As you know, everythingshrinks in the cold. They call it Eskimo pi.

How do you prove in three steps that a sheet of paper is a lazy dog?1. A sheet of paper is an ink-lined plane.2. An inclined plane is a slope up.3. A slow pup is a lazy dog.

A geometer went to the beach to catch the rays and became a TanGent.

Life is complex. It has real and imaginary components.

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

To the top

8. Anecdotes

Next several stories are attributed to real mathematicians. For most of them, it was impossible

to check the truthfulness of the story. Therefore the names are often removed.

In 1915, Emma Noether arrived in Gttingen but was denied the private-docentstatus. The argument was that a woman cannot attend the University senate (thefaculty meetings). Hilbert's reaction was: "Gentlemen! There is nothing wrong tohave a woman in the senate. Senate is not a bath."


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After Laplace completed his masterpiece Mecanique Celeste (Mechanics of theHeavens) he presented a copy to his friend Napoleon. Napoleon, who also was amathematician, after going through the book called in Laplace and said to him:"You have written a book about Mechanics of the Heavens without mentioningGod?" Laplace replied: "Sire, I had no need of that hypothesis".

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 aspeed of 50 miles per hour. A fly starting on the front of one of them flies backand forth between them at a rate of 75 miles per hour. It does this until the trainscollide 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 summingan infinite series of distances. The easy way is as follows: Since the trains are 200miles apart and each train is going 50 miles an hour, it takes 2 hours for the trainsto collide. Therefore the fly was flying for two hours. Since the fly was flying at arate of 75 miles per hour, the fly must have flown 150 miles. That's all there is toit.

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 infiniteseries."

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

Another von Neumann quote : Young man, in mathematics you don't understandthings, you just get used to them.

The mathematician S. had to move to a new place. His wife didn't trust him verymuch, so when they stood down on the street with all their things, she asked him

to watch their ten trunks, while she get a taxi. Some minutes later she returned.Said the husband:"I thought you said there were ten trunks, but I've only counted to nine."The wife said: "No, they're TEN!""But I have counted them: 0, 1, 2, ..."


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N. 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 tosolve problems. One time one of his students tried to get more helpful informationby asking if there was another way to solve the problem. N. looked blank for amoment, thought, and then answered, "Yes".

In his lecture, ** formulated a theorem and said: "The proof is obvious". Then hethought for a minute, left the lecture room, returned after 15 minutes and happilyconcluded: "Indeed, it is obvious!"

A famous mathematician was to give a keynote speech at a conference. Asked foran 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 amuch more prosaic topic. Afterwards the conference organizers asked why he saidhe'd talk about the theorem and then didn't. He replied this was his standardpractice, just in case he was killed on the way to the conference.

A mathematician about his late colleague:" He made a lot of mistakes, but he made them in a good direction. I tried to copythis, but I found out that it is very difficult to make good mistakes. "

This story is attributed to Professor Lev Loytiansky, the stage is in Soviet Union

in thirties or forties.

L. organized the seminar in hydrodynamics in his University. Among the regularattendees there were two men in the uniform, obviously military engineers. Theynever discussed the problems they were working on. But one day they ask L. tohelp with a math. problem. They explained that the solution of a certain equationoscillated and asked how they should change the coefficients to make itmonotonic. L. looked on the equation and said: "Make the wings longer!"

Students asked ** to exclude a part of the course from the final exam. ** agreed.Encouraged by the easy success, the students asked to skip another part of thecourse, and ** agreed again, and then again. However, in the end of the term hedid include all this material in the exam. The class loudly complained:


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"Dr **, you promised us to skip this stuff!"** answered: "Yes, I did. But I lied!"

Ernst Eduard Kummer (1810-1893), a German algebraist, was sometimes slow atcalculations.. Whenever he had occasion to do simple arithmetic in class, hewould get his students to help him. Once he had to find 7 x 9. "Seven times nine,"he began, "Seven times nine is er -- ah --- ah -- seven times nine is. . . ." "Sixty-one," a student suggested. Kummer wrote 61 on the board. "Sir," said anotherstudent, "it should be sixty-nine." "Come, come, gentlemen, it can't be both,"Kummer exclaimed. "It must be one or the other."

This anecdote is attributed to Landau (the Russian physicist Lev not the Gttingen

mathematician Edmund).

Landau's group was discussing a bright new theory, and one of junior colleaguesof Landau bragged that he had independently discovered the theory a couple ofyears ago, but did not bother to publish his finding.

"I would not repeat this claim if I were you," Landau replied: "There is nothingwrong if one has not founda solution to a particular problem. However, if one has found it but does not

publish it, he shows a poor judgment and inability to understand what importantis in modern physics".

A famous mathematician was to give a keynote speech at a conference. Asked foran 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 amuch more prosaic topic. Afterwards the conference organizers asked why he saidhe'd talk about the theorem and then didn't. He replied this was his standardpractice, just in case he was killed on the way to the conference.

To the top


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9. Limericks

Limericks are always limericks. (The obscene math limericks were mercilessly excluded)

A mathematician confidedThat the M"obius band is one-sidedAnd you'll get quite a laughIf you cut one in half'Cause it stays in one piece when divided.

A mathematician named KleinThought the M"obius band was divineSaid he: If you glue

The edges of twoYou'll get a weird bottles like mine.

There was a young fellow named Fisk,A swordsman, exceedingly brisk.So fast was his action,The Lorentz contractionReduced his rapier to a disk.

'Tis a favorite project of mineA new value of pi to assign.I would fix it at 3For it's simpler, you see,Than 3 point 1 4 1 5 9

If inside a circle a lineHits the center and goes spine to spineAnd the line's length is "d"the circumference will bed times 3.14159


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Pi goes on and on and on ...And e is just as cursed.I wonder: Which is largerWhen their digits are reversed?

A challenge for many long agesHad baffled the savants and sages.Yet at last came the light:Seems old Fermat was right--To the margin add 200 pages.

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

Is raised to the power of 1Over x, you will findHere's the value defined:2.718281...

Integral z-squared dzfrom 1 to the cube root of 3times the cosineof three pi over 9

equals log of the cube root of 'e'.

And it's correct, too.

A burleycque dancer, a pipNamed Virginia, could peel in a zip;But she read science fictionand died of constrictionAttempting a Moebius strip.

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

A Dozen, a Gross and a Score,plus three times the square root of four,


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divided by seven,plus five times eleven,equals nine squared and not a bit more.

In arctic and tropical climes,the integers, addition, and times,taken (mod p) will yielda full finite field,as p ranges over the primes.

A graduate student from TrinityComputed the cube of infinity;

But it gave him the fidgetsTo write down all those digits,So he dropped math and took up divinity.

Chebychev said it and I'll say it again:There's always a prime between n and 2n!

A conjecture both deep and profoundIs whether the circle is round;In a paper by Erdo"s,written in Kurdish,A counterexample is found.

(Note: Erdo"s is pronounced "Air - dish")

There once was a number named pi

Who frequently liked to get high.All he did every day

Was sit in his room and play

With his imaginary friend named i.

There once was a number named e

Who took way too much LSD.


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She thought she was great.

But that fact we must debate;

We know she wasn't greater than 3.

There once was a log named Lynn

Whose life was devoted to sin.

She came from a tree

Whose base was shaped like an e.

She's the most natural log I've

1. Ian earns 420 a week after a 5% rise. What was his pay before?Ian had a 5% rise, so 420 is 105% of his original pay.To find 1% of his original earnings, divide 420 by 105.

Multiply this by 100 to find his old pay:

1% of his original earnings = 420/105 = 4Original earnings = 4 100 = 400

2.AnIyonix PCis sold for 1200 at a reduction of 20% on itsrecommended retail price. What was the computer's original price?

1200 is 80% of the original price, so 1% of the original cost would be1200/80 = 15

So the original price would be 15 100 = 1500

3. Kenny has 3200 in a savings account. After a year, the bank payshim interest increasing his balance to 3360. What percentage ratewas applied to the account?

The interest earned was 3360-3200 = 160.

As a percentage of the original amount this is 160/3200100 = 5%

4. On my sister's 15th birthday, she was 159 cm in height, having grown6% since the year before. How tall was she the previous year?

159 cm is 106% of her old height, so 1% of her previous height is

159/106 = 1.5Her previous height was therefore 1.5 100 = 150 cm.

seen.
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