Using calculus to show why teachers are underpaid:

Postulate 1: Knowledge is Power

Postulate 2: Time is Money

From Physics, we know that: Power = Work / Time

If Knowledge is Power and Time = Money, then by substitution, we get:

Knowledge = Work / Money

Solving for Money: Money = Work / Knowledge

Thus Money approaches infinity as Knowledge approaches zero, regardless of the work done.

What this means is "The less you know, the more you make."

Two mathematicians were having dinner. One was complaining, "The average person is a mathematical idiot. People cannot do arithmetic properly, cannot balance a check book, cannot figure tips, cannot do percents,..." The other mathematician disagreed, "You're exaggerating. People know all the math they need to know."

Later in the dinner, the complainer went to the men's room. The other mathematician beckoned to the waitress and said, "The next time you come past our table, I am going to stop you and ask you a question. No matter what I say, I want you to answer by saying 'x-squared."

When the other mathematician returned, his companion said, "I am tired of your complaining. I am going to stop the next person who comes by our table and ask him or her an elementary calculus question, and I bet the person can solve it." Soon the waitress came by and he asked, "Excuse me, Miss, but can you tell me what the integral of 2x with respect to x is?" The waitress replied, "x-squared." The mathematician said, "See!" His friend said, "Oh I guess you're right." And the waitress said, "Plus a constant."


Understanding Engineers ...
  • "Normal people ... believe that if it ain't broke, don't fix it.
  • Engineers believe that if it ain't broke, it doesn't have enough features yet."
    ----- Scott Adams, The Dilbert Principle


Understanding Engineers ...
  • To the optimist, the glass is half full.
  • To the pessimist, the glass is half empty.
  • To the engineer, the glass is twice as big as it needs to be.


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 Biologist's conclusion: "They have reproduced".
  • The Mathematician: "If now exactly 1 person enters the house then it will be empty again."


In some foreign country a priest, a lawyer and an engineer are about to be guillotined.   The priest puts his head on the block, they pull the rope and nothing happens -- he declares that he's been saved by divine intervention -- so he's let go.   The lawyer is put on the block, and again the rope doesn't release the blade, he claims he can't be executed twice for the same crime so he is set free too.   They grab the engineer and shove his head into the guillotine, he looks up at the release mechanism and says, "Wait a minute, I see your problem..."

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

  • The lawyer says: "For sure a mistress is better. If you have a wife and want a divorce, it causes all sorts of legal problems.
  • The doctor says: "It's better to have a wife because the sense of security lowers your stress and is good for your health.
  • The mathematician says: " You're both wrong. It's best to have both so that when the wife thinks you're with the mistress and the mistress thinks you're with your wife --- you can do some mathematics.


YOU MIGHT BE AN ENGINEER IF...

  • If you enjoy pain.
  • If you know vector calculus but you can't remember how to do long division.
  • If you chuckle whenever anyone says "centrifugal force."
  • If you've actually used every single function on your graphing calculator.
  • If it is sunny and 70 degrees outside, and you are working on a computer.
  • If you frequently whistle the theme song to "MacGyver."
  • If you know how to integrate a chicken and can take the derivative of water.
  • If you think in "math."
  • If you've calculated that the World Series actually diverges.
  • If you hesitate to look at something because you don't want to break down its wave function.
  • If you have a pet named after a scientist.
  • If you laugh at jokes about mathematicians.
  • If you can translate English into Binary.
  • If you can't remember what's behind the door in the engineering building which says "Exit."
  • If you have to bring a jacket with you, in the middle of summer, because there's a wind-chill factor in the lab.
  • If you are completely addicted to caffeine.
  • If you avoid doing anything because you don't want to contribute to the eventual heat-death of the universe.
  • If you consider ANY non-engineering course "easy."
  • If when your professor asks you where your homework is, you claim to have accidentally determined its momentum so precisely, that according to Heisenberg it could be anywhere in the universe.
  • If the "fun" center of your brain has deteriorated from lack of use.
  • If you'll assume that a "horse" is a "sphere" in order to make the math easier.
  • If you understood more than five of these indicators.
  • If you make a hard copy of this list, and post it on your door (or your home page!)


A pastor, a doctor and an engineer were waiting one morning for a particularly slow group of golfers.
The engineer fumed, "What's with these guys? We must have been waiting for 15 minutes!"
The doctor chimed in, "I don't know, but I've never seen such ineptitude!"
The pastor said, "Hey, here comes the greenskeeper. Let's have a word with him."

"Hi George. Say, what's with that group ahead of us? They're rather slow, aren't they?"
The greenskeeper replied, "Oh, yes, that's a group of blind firefighters. They lost their sight saving our clubhouse from a fire last year, so we always let them play for free anytime."

The group was silent for a moment. The pastor said, "That's so sad. I think I will say a special prayer for them tonight."
The doctor said, "Good idea. And I'm going to contact my ophthalmologist buddy and see if there's anything he can do for them."
The engineer said, "Why can't these guys play at night?"


Some engineers are trying to measure the height of a flagpole.   They only have a measuring tape and they haven't been able to slide the tape up the pole.   A mathematician walks by and asks what they are doing, and they explain.

"The solution is easy," he says.   He pulls the pole out of the ground, lays it down, and measures it.

After he leaves, one of the engineers says, "That is so typical!   We tell a mathematician that we need to know the height and he gives us the length!"

Two statisticians were flying on a plane.   An hour into the flight, the pilot announces that they have lost an engine, but that they shouldn't worry because there are still three left.   However, instead of three hours, the trip will now take four hours.

A little later, the pilot announces that a second engine has failed, but there are still two left, only now it will now take six hours to get to their destination.

A little while later, the pilot announces that a third engine has gone out.   "Don't worry," he announces, because the plane can still fly safely with just one engine.   However, the trip will now take twelve hours.

At this point, one statistician turns to the other and says, "I sure hope we don't lose that last engine or we'll be up forever!"

Six engineers and six mathematicians are attending a conference and are traveling by train.

One by one, each of the engineers goes up to the ticket counter and buys a ticket to the conference. But only one of the mathematicians does. The engineers look puzzled and one of the mathematicians says, "Optimization."

The twelve get on the same car and one mathematician stands at each end of the car. Now the engineers are really puzzled. After a while, the mathematician at one end, yells, "Conductor!" On that cue, all the mathematicians pile into the rest room and lock the door.

The conductor enters the car and announces, "Tickets, please. Tickets!" He passes the engineers and punches each of their tickets. At the end of the car, he notices the restroom is occupied and knocks on the door, "Ticket, please."

The ticket slides out from under the door, he punches it and slides it back, then leaves the car and continues to the next car.

The engineers look at each other and decide how clever the mathematicians have been, and then wink at each other.

They all attend the conference and have a good time. Upon arriving at the train station, one engineer buys a ticket and they giggle at each other. The mathematicians do not buy any. This time again, the engineers look puzzled, and the same mathematician says, "Optimization."

This time all the mathematicians sit down and the engineers have the lookouts.   One engineer, peers down a couple of cars and shouts, "Conductor!"   Immediately all the engineers pile into the rest room, while the mathematicians just sit there.   Once the engineers are in the rest room, one of the mathematicians knocks on the door and says, "Ticket, please."   The ticket slides out under the door, the mathematician grabs it and along with the other mathematicians, runs to the other rest room and they lock themselves in.

-- contributed by Keith Mealy (and the next one, too)


Three statisticians went rabbit hunting one day.   While walking along, they scared a rabbit out of the brush and send him running.   The first statistician shot and there was a puff of dust 1 yard behind the rabbit.   The second shot next and there was a puff of dust one yard in front of the rabbit.   The third one yelled, "We got it!!"

A math professor and a minister reach the Pearly Gates, and St. Peter shows them around Heaven.

They walk for awhile and stop in front of a gorgeous mansion, adorned with fountains and ponds in th front yeard.   St. Peter turns to the math professor and says, "This is your house, where you will be spending eternity."

St. Peter tells the minister to follow him, and beyond the mansion, they pass a medium sized house, then a smaller home, and then a mobile home.   Finally, they reach a tree house that appears to have been built from scrap lumber.   St. Peter points at the tree house and says to the minister, "This is where you will be spending eternity."

The minister can't believe his eyes.   "The math professor gets a mansion," he says, "and all I get is a tree house?"

"We base the size of your home on how many people you got to pray during your years on Earth.   And a whole lot more people prayed in his math class than ever prayed in your church!"

A scientist has two large jars before him, one containing many fleas, the other empty. He gently removes a flea from the flea jar, places it on the table before the empty jar, steps back, and commands "Jump," whereupon the flea jumps into the empty jar.   Methodically he gently removes each flea, places it on the table, says "Jump," and the flea jumps into the originally empty jar.

When he has transferred all the fleas in this way, he removes one from the now full jar, carefully pulls off its back legs, and places it on the table before the original jar.   He commands "Jump," but the flea does not move.   He takes another flea from the jar, carefully pulls off its back legs, and places it on the table.   Again he commands "Jump," but the flea does not move.   Methodically, he goes through this same procedure with the remaining fleas, and gets the same results.

The scientist records in his notebook, "A flea, when its back legs are pulled off, cannot hear."


Biologists think they're biochemists.
Biochemists think they're chemists.
Chemists think the're physical chemists.
Physical Chemists think they're physicists.
Physicists think they're God.
God thinks he is a mathematician.


A somewhat advanced society has figured how to package basic knowledge in pill form.
A student, needing some learning, goes to the pharmacy and asks what kind of knowledge pills are available.
The pharmacist says "Here's a pill for English literature."
The student takes the pill and swallows it and has new knowledge about English literature!
"What else do you have?" asks the student.
"Well, I have pills for art history, biology, and world history," replies the pharmacist.
The student asks for these, and swallows them and has new knowledge about those subjects.
Then the student asks, "Do you have a pill for math?"
The pharmacist says "Wait just a moment", and goes back into the storeroom and brings back a whopper of a pill and plunks it on the counter.
"I have to take that huge pill for math?" inquires the student.
The pharmacist replied "Well, you know math always was a little hard to swallow."

A mathematician asked a fortune teller, "Tell me, are the proofs to unsolved theorems found in heaven?"

"I have good news and I have some bad news," she replies.

"What's the good news?"

"Not only are all of the proofs revealed in heaven, but they are the most elegant proofs possible!"

"That's awesome!   What's the bad news?"

"By this time tomorrow, You'll have an elegant proof of the Riemann Hypothesis."

A mathematician is invited to speak at a math conference.   His talk is entitled, "Proof of the Riemann Hypothesis."

When the conference takes place, he speaks about an entirely different topic.

A colleague comes up to him afterwards and says, "Did you find an error in your proof?"

He replies, "No, I never had one."

"So, why did you make this announcement?"

"That's my standard precaution -- in case I die on the way to the conference."

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

A man in a hot air balloon realized he was lost.   He reduced altitude and spotted a woman below.   He descended a bit more and shouted,” Excuse me, can you help?   I promised a friend I would meet him an hour ago, but I don't know where I am."

The woman below replied, "You are in a hot air balloon hovering approximately 30 feet above the ground.   You are between 40 and 41 degrees north latitude and between 59 and 60 degrees west longitude."

"You must be an engineer," said the balloonist.

"I am," replied the woman. "How did you know?"

"Well," answered the balloonist, "everything you told me is technically correct, but it was completely useless, and the fact is I am still lost.   Frankly, you've not been much help so far."

The woman below responded, "You must be in management."

"I am," replied the balloonist, "but how did you know?"

"Well," said the woman, "you don't know where you are or where you are going.   You have risen to where you are, due to a large quantity of hot air.   You made a promise which you have no idea how to keep, and you expect people beneath you to solve your problems.   The fact is you are in exactly the same position you were in before we met, but now, somehow, it's my fault!"

Q: What do a mathematician and a physicist [or engineer, or musician, or whatever the profession of the person addressed] have in common?
A: They are both stupid, with the exception of the mathematician.

SUBJ: Career Choices

The graduate with a physics degree asks, "Why does it work?"
The graduate with an engineering degree asks, "How does it work?"
The graduate with an accounting degree asks, "How much will it cost?"
The graduate with a liberal arts degree asks, "Do you want fries with that?"

Equations and the Real World
  • Engineers think that equations approximate the real world.
  • Scientists think that the real world approximates equations.
  • Mathematicians are unable to make the connection...


A physicist and mathematician participate as subjects in an experiment.
The experimenters give them both the same resources, a match, a bunsen burner, a sink, and a bowl.
They tell them the goal is to produce boiling water.
The subjects do the same thing.
They both fill the bowl with water, light the burner, and place the bowl on the burner.
Accordingly, the water boils.
Next, the experimenters say they are going to vary the experiment slightly.
This time they supply the same resources, but at the start the bowl is already filled with water.
Now the physicist lights the burners and places the bowl on it as before.
The mathematician, however, empties the bowl down the sink and says that she has reduced the problem to one that has already been solved.
(submitted by Roxanne Eckenrode who heard it from Dr. Lisa Koch)

Three recent graduates -- a pure mathematician, an applied mathematician, and a statistican -- are being interviewed for a job.   All three are asked the same question, "What is one-third plus two-thirds?"

The pure mathematician says, "one."

The applied mathematician takes out his pocket calculator, punches in the numbers, and declares, "0.9999999."

The statistician askd, "What would you like it to be?"

The chef instructs his apprentice, "Take two-thirds water, one-third broth, one-third milk, ..."

The apprentice interrupts, "But that's already four-thids!"

"So, get a bigger pot!"

A physicist, a mathematician, and a logician were riding on a train through Montana.   They see a large flock of sheep in a field near the track.

The physicist looks out and says, "Appears all the sheep in Montana are white."

The mathematician interjects, "I beg your pardon sir... but the most you can conclude from that observation is that at least some of the sheep in Montana are white."

To which the logician replies, "I beg your pardon sir, but the most you can conclude from that observation is that at least some of the sheep in Montana are white on at least one side."
(Submitted by Dan Heim)

How can you tell if a mathematician is an extrovert?
        Answer: When he talks to you, he looks at your shoes.

What is the difference between an economist and a confused old man with Alzhemer's?
        Answer: The economist has a calculator.

A cannibal is buying brains for dinner.   In the butcher's shop, he is told that mathematician brain costs $1 a pound, engineer brain costs $2 a pound, and politican brain cost $10 a pound.

The cannibal is bewildered.   He asks the butcher, "why does politicain brain cost ten times as much as mathematician brain?   Is the quality that much better?

The butcher replies, "No, but it takes a lot more politicians to make a pound."

A mechanical engineer, an electrical engineer, and a computer engineer are riding in a car when it breaks down.   They pull off to the side of the road.

"Pop the hood," said the mechanical engineer.   "I'm sure it's a problem with the gears, so I'll go take a look."

"No," says the electrical engineer.   "I'm sure it's a problem with the wires.   Pop the hood, and I'll go take a look."

"I've got a better idea," says the computer engineer.   "Why don't we just get out, get back in, and try to start it again?"

A young businesswoman once said, "My life is just basic arithmetic.   I try to add to my income, subtract from my weight, divide my time, and keep from multiplying."

A statistics professor was completing what he thought was a very inspiring lecture on the importance of significance testing in today's world.   A young nursing student raised her hand and asked, "But sir, why do nurses have to take statistics?"

The professor thought for a moment and then said, "Because statistics saves lives!"

The nursing student was surprised but persisted in getting a better answer.   "But sir, please tell us how statistics saves lives."

"Well," the professor said angrily, "Statistics keeps idiots out of the nursing profession!"

James Bonk was a Duke chemistry professor and was perhaps most notorious for the flat tire story, which went something like this: Four of his students, who had performed well on all their tests and quizzes and had solid A's, decided to go to Virginia to party the weekend before the final exam.   They made it back Monday just before the exam, but weren't ready to take it.   So they found Bonk, told him they had gotten a flat tire and asked to take the test later.   He said okay.

The day to take the make up exam came.   He put the students in separate rooms and gave them their exam.   The first problem was pretty easy and worth 5 points.   The next question -- worth 95 points -- was more challenging.   It simply asked, which tire?

That story is rumored to have happened sometime in the sixties, but no one knows the exact date.   But it did add to the legendary status that Bonk accumulated over his years at Duke.

Two scientists walk into a bar.
The first one says, "I'll have some H2O.
The second one says, "I'll have some H2O, too.
The second scientist dies.

(H2O2 is Hydrogen Peroxide)

Jean-Paul Sartre is sitting at a French cafe, revising his draft of Being and Nothingness.   He says to the waitress, "I'd like a cup of coffee please, with no cream."   The waitress replies, "I'm sorry, Monsieur, we are out of cream.   How about with no milk?"

A mathematician, a physicist and an engineer were each given the following problem to solve.

A school dance floor included a straight line down the middle dividing the floor in two equal halves.   Boys were lined up against one wall and girls against the opposite wall, each facing the center line.   They were instructed to advance in stages towards the center line every ten seconds, where the distance from the person to the center line at each stage is equal to one-half the distance at the past stage.

i.e.: If the starting distance from the wall to center line was D, the progressive series of distances at t = 0, 10 seconds, 20 seconds...10n seconds to the center line is (D, D/2, D/4, D/8, .....D/2n)

The question is, when will they meet at the middle?

The mathematician said that they would never meet.

The physicist said they would meet when time equals infinity.

The engineer said that in one minute they would be close enough for all practical purposes.

A mathematician, a physicist, and an engineer are all given identical rubber balls and told to find the volume.   They are given anything they want to measure it, and have all the time they need.

The mathematician pulls out a measuring tape and records 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 thereby calculates the volume.

The physicist gets a bucket of water, places 1.00000 gallons of water in the bucket, drops in the ball, and measures the displacement to six significant figures.

And the engineer? He writes down the serial number of the ball, and looks it up.

A well-known story repates how Queen Victoria was so utterly charmed by Lewis Carroll's Alice's Adventures in Wonderland that she demanded:
Send me the next book Mr. Carroll produces --
The next book duly arrived; it was entitled An Elementary Treatise on Determinants.   Queen Victoria was not amused.