Mathematician: 3 is a prime, 5 is a prime, 7 is a prime, and by induction - every odd 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 is a prime,...
Engineer: 3 is a prime, 5 is a prime, 7 is a prime, 9 is a prime, 11 is a prime,...
Programmer: 3's a prime, 5's a prime, 7's a prime, 7's a prime, 7's a prime,...
Salesperson: 3 is a prime, 5 is a prime, 7 is a prime, 9 -- we'll do for you the best we can,...
Computer Software Salesperson: 3 is prime, 5 is prime, 7 is prime, 9 will be prime in the next release,...
Biologist: 3 is a prime, 5 is a prime, 7 is a prime, 9 -- results have not arrived yet,...
Advertiser: 3 is a prime, 5 is a prime, 7 is a prime, 11 is a prime,...
Lawyer: 3 is a prime, 5 is a prime, 7 is a prime, 9 -- there is not enough evidence to prove that it is not a prime,...
Accountant: 3 is prime, 5 is prime, 7 is prime, 9 is prime, deducing 10% tax and 5% other obligations.
Statistician: Let's try several randomly chosen numbers: 17 is a prime, 23 is a prime, 11 is a prime...
Psychologist: 3 is a prime, 5 is a prime, 7 is a prime, 9 is a prime but tries to suppress it,...

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

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.

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 Flood is over and the ark has landed. Noah lets all the animals out and says, "Go forth and multiply."

A few months later, Noah decides to take a stroll and see how the animals are doing. Everywhere he looks he finds baby animals. Everyone is doing fine except for one pair of little 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 of little snakes, everybody is happy. Noah asks, "Want to tell me how the trees helped?"

"Certainly", say the snakes. "We're adders, so we need logs to multiply."

What is the integral of "one over cabin" with respect to "cabin"?
Answer: Natural log cabin + c = houseboat.

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."

Where I come from PI are Round,... Cornbread R Squared!!

What is "pi"?

Mathematician: Pi is the ratio of the circumference of a circle to its diameter.
Engineer: Pi is about 22/7.
Physicist: Pi is 3.14159 plus or minus 0.000005
Computer Programmer: Pi is 3.141592653589 in double precision.
Nutritionist: You one track math-minded fellows, Pie is a healthy and delicious dessert!

Top ln(e^10) reasons why e is better than pi

10) e is easier to spell than pi.
9) pi ~= 3.14 while e ~=2.718281828459045.
8) The character for e can be found on a keyboard, but pi sure can't.
7) Everybody fights for their piece of the pie.
6) ln(pi^1) is a really nasty number, but ln(e^1) = 1.
5) e is used in calculus while pi is used in baby geometry.
4) 'e' is the most commonly picked vowel in Wheel of Fortune.
3) e stands for Euler's Number, pi doesn't stand for squat.
2) You don't need to know Greek to be able to use e.
1) You can't confuse e with a food product.

Top ten reasons why e is inferior to pi

10) e is less challenging to spell than pi.
9) e ~=2.718281828459045, which can be easily memorized to its billionth place, whereas pi needs "skills" to be memorized.
8) The character for e is so cheap that it can be found on a keyboard. But pi is special (it's under "special symbols" in word processor programs.)
7) Pi is the bigger piece of pie.
6) e has an easy limit definition and infinite series. The limit definition of pi and the infinite series are much harder.
5) e you understand what it is even if you start learning it late when you're in pre-calculus. But pi, even after five or six years it's still hard to know what it really is.
4) People mistakenly confuse Euler's Number (e) with Euler's Constant (gamma). There is no confusion with the one and only pi.
3) e is named after a person, but pi stands for itself.
2) Pi is much shorter and easier to say than "Euler's Number".
1) To read pi, you don't have to know that Euler's name is really pronounced Oiler.

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

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

What is the shortest mathematicians joke?
Let epsilon be smaller than zero.

An astronomer, a physicist and a mathematician (it is said) were holidaying in Scotland. Glancing from a train window, they observed a black sheep in the middle of a field.

"How interesting," observed the astronomer, "all scottish sheep are black!"

To which the physicist responded, "No, no! Some Scottish sheep are black!"

The mathematician gazed heavenward in supplication, and then intoned, "In Scotland there exists at least one field, containing at least one sheep, at least one side of which is black."

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

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

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

An engineer, a chemist and a mathematician are staying in three adjoining cabins at an old motel. First the engineer's coffee maker catches fire. He smells the smoke, wakes up, unplugs the coffee maker, throws it out the window, and goes back to sleep.

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

The mathematician, of course, has been watching all this out the window. So later, when he finds that his pipe ashes have set the bedsheet on fire, he is not in the least taken aback. He says: "Aha! A solution exists!" and goes back to sleep.

A mathematician, a biologist and a physicist are sitting in a street cafe watching people going in and coming out of the house on the other side of the street.

First they see two people going into the house. Time passes. After a while they notice three persons coming out of the house.

The physicist: "The measurement wasn't accurate."
The biologists: "They have reproduced".
The mathematician: "If now exactly one person enters the house then it will be empty again."

One day a mathematician decides that he is sick of math. So, he walks down to the fire department and announces that he wants to become a fireman.
The fire chief says, "Well, you look like a good guy. I'd be glad to hire you, but first I have to give you a little test."

The firechief takes the mathematcian to the alley behind the fire department which contains a dumpster, a spicket, and a hose. The chief then says, "OK, you're walking in the alley and you see the dumpster here is on fire. What do you do?"
The mathematician replies, "Well, I hook up the hose to the spicket, turn the water on, and put out the fire."

The chief says, "That's great... perfect. Now I have to ask you just one more question. What do you do if you're walking down the alley and you see the dumpster is not on fire?"
The mathematician puzzles over the question for awhile and he finally says, "I light the dumpster on fire."
The chief yells, "What? That's horrible! Why would you light the dumpster on fire?"
The mathematician replies, "Well, that way I reduce the problem to one I've already solved."

A mathematician and an engineer attend a lecture by a physicist. The topic concerns Kulza-Klein theories involving physical processes that occur in spaces with dimensions of 9, 12 and even higher. The mathematician is sitting, clearly enjoying the lecture, while the engineer is frowning and looking generally confused and puzzled. By the end the engineer has a terrible headache. At the end, the mathematician comments about the wonderful lecture.

The engineer says "How do you understand this stuff?"
Mathematician: "I just visualize the process."
Engineer: "How can you visualize something that occurs in 9-dimensional space?"
Mathematician: "Easy, first visualize it in N-dimensional space, then let N go to 9."

A mathematician is in Africa trying to capture a lion. When he spots one he proceeds to build a fence around himself and says, "I define this to be outside!"

Aleph-null bottles of beer on the wall,
Aleph-null bottles of beer,
You take one down, and pass it around,
Aleph-null bottles of beer on the wall.

A mathematician wandered home at 3 AM. His wife became very upset, telling him, "You're late! You said you'd be home by 11:45!" The mathematician replied, "I'm right on time. I said I'd be home by a quarter of twelve."

Two 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!"

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

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

Why did the chicken cross the Möbius strip?
To get to the same side.

There was once a very smart horse. Anything that was shown it, it mastered easily, until one day, its teachers tried to teach it about rectangular coordinates and it couldn't understand them. All the horse's acquaintances and friends tried to figure out what was the matter and couldn't. Then a new guy looked at the problem and said,
"Of course he can't do it. Why, you're putting Descartes before the horse!"

HOW TO PROVE IT

proof by example:

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

proof by intimidation:

"Trivial."

proof by vigorous handwaving:

Works well in a classroom or seminar setting.

proof by cumbersome notation:

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

proof by exhaustion:

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

proof by omission:

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

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 funding:

How could three different government agencies be wrong?

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.

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 picture:

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

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 forward reference:

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

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.

A quiet little man was brought before a judge. The judge looked down at the man and then at the charges and then down at the little man in amazement. "Can you tell me in your own words what happened?" he asked the man.

"I'm a mathematical logician dealing in the nature of proof."

"Yes, go on," said the astounded judge.

"Well, I was at the library and I found the books I wanted and went to take them out. They told me my library card had expired and I had to get a new one. So I went to the registration office and got in another line. And filled out my forms for another card. And got back in line for my card."

"And?" said the judge.

"And he asked 'Can you prove you are from New York City?' ...So I stabbed him."

The book Dynamic Programming by Richard Bellman is an important, pioneering work in which a group of problems is collected together at the end of some chapters under the heading "Exercises and Research Problems," with extremely trivial questions appearing in the midst of deep, unsolved problems. It is rumored that someone once asked Dr. Bellman how to tell the exercises apart from the research problems, and he replied: "If you can solve it, it is an exercise; otherwise it's a research problem."

A mathematician is a machine for turning coffee into theorems.

A conjecture both deep and profound
Is whether a circle is round.
In a paper of Erdös
Written in Kurdish
A counterexample is found.

Approximately ten excuses for not doing homework:

• I accidentally divided by zero and my paper burst into flames.
• I could only get arbitrarily close to my textbook. I couldn't actually reach it.
• I have the proof, but there isn't room to write it in this margin.
• I was watching the World Series and got tied up trying to prove that it converged.
• I have a solar powered calculator and it was cloudy.
• I locked the paper in my trunk but a four-dimensional dog got in and ate it.
• I couldn't figure out whether I am the square of negative one or I am the square root of negative one.
• I took time out to snack on a doughnut and a cup of coffee, and then I spent the rest of the night trying to figure which one to dunk.
• I could have sworn I put the homework inside a Klein bottle, but this morning I couldn't find it.

The Dictionary: what mathematics professors say and what they mean by 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.
It can easily be shown: No more than four hours are needed to prove it.
Check for yourself: This is the boring part of the proof, so you can do it on your own time.
Hint: The hardest of several possible ways to do a proof.
Brute force: Four special cases, three counting arguments and two long inductions.
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.
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.
Proceed formally: Manipulate symbols by the rules without any hint of their true meaning.
Proof omitted: Trust me, It's true.

Mathematics Revisited

Life is complex. It has real and imaginary components.

What keeps a square from moving? Square roots, of course.

The law of the excluded middle either rules or does not rule.

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

To a mathematician, real life is a special case.

I heard that parallel lines actually do meet, but they are very discrete.

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

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

How mathematicians do it...

Combinatorists do it as many ways as they can.
Combinatorists do it discretely.
(Logicians do it) or [not (logicians do it)].
Logicians do it by symbolic manipulation.
Algebraists do it in groups.
Algebraists do it in a ring.
Algebraists do it in a field.
Analysts do it continuously.
Real analysts do it almost everywhere.
Pure mathematicians do it rigorously.
Topologists do it openly.
Topologists do it on rubber sheets.
Dynamicists do it chaotically.
Mathematicians do it forever if they can do one and can do one more.

Cantor did it diagonally.
Fermat tried to do it in the margin, but couldn't fit it in.
Galois did it the night before.
Möbius 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.

• you are fascinated by the equation e^(i pi)+1=0 .
  
• you know by heart the first fifty digits of pi.
  
• you have tried to prove Fermat's Last Theorem.
  
• you know ten ways to prove Pythagoras' Theorem.
  
• your telephone number is the sum of two prime numbers.
  
• you have calculated that the World Series actually diverges.
  
• you are sure that differential equations are a very useful tool.
  
• you comment to your wife that her straight hair is nice and parallel.
  
• when you say to a car dealer "I'll take the red car or the blue one" you must add "but not both of them."
  
  

How many mathematicians does it take to change a light bulb?
None. It's left to the reader as an exercise.
None. The answer is intuitively obvious.
One. He gives it to four programmers, thereby simplifying the problem to a previous question.

How many numerical analysts does it take to change a light bulb?
3.9967 (after six iterations).

How many mathematical logicians does it take to change a light bulb?
None. They can't do it, but they can easily prove that it can be done.

How many classical geometers does it take to change a light bulb?
None. You can't do it with a straight edge and a compass.

How many analysts does it take to change a light bulb?
Three. One to prove existence, one to prove uniqueness and one to derive a nonconstructive algorithm to do it.

How many number theorists does it take to change a light bulb?
I don't know the exact number, but I am sure it must be some rather elegant prime.