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

* *

**Sketches**

A mathematician, a physicist, an engineer went again to the races and laid their money down. Commiserating in the bar after the race, the engineer says, “I don’t understand why I lost all my money. I measured all the horses and calculated their strength and mechanical advantage and figured out how fast they could run…”

The physicist interrupted him: “…but you didn’t take individual variations into account. I did a statistical analysis of their previous performances and bet on the horses with the highest probability of winning…”

“…so if you’re so hot why are you broke?” asked the engineer. But before the argument can grow, the mathematician takes out his pipe and they get a glimpse of his well-fattened wallet. Obviously here was a man who knows something about horses. They both demanded to know his secret.

“Well,” he says, “first I assumed all the horses were identical and spherical…”

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

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A biologist, a physicist and a mathematician were sitting in a street cafe watching the 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, the mathematician concluded.

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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 the answer 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 mathematician, a physicist, and an engineer were traveling through Scotland when 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 in Scotland, and that at least one side of that one sheep is black!”

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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.

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The physicist and the engineer are in a hot-air balloon. Soon, they find themselves lost in a canyon somewhere. They yell out for help: “Helllloooooo! Where are we?”

15 minutes later, they hear an echoing voice: “Helllloooooo! You’re in a hot-air balloon!!”

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 utterly useless.”

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Dean, to the physics department. “Why do I always have to give you guys so much money, for laboratories and expensive equipment and stuff. Why couldn’t you be like the math. department – all they need is money for pencils, paper and waste-paper baskets. Or even better, like the philosophy department. All they need are pencils and paper.”

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A mathematician belives nothing until it is proven

A physicist believes everything until it is proven wrong

A chemist doesn’t care

A biologist doesn’t understand the question.

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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 devil promises to deliver a proof in the four weeks. Half a year later, the devil shows up again – in a rather gloomy mood. “I’m sorry”, he says. “I couldn’t prove the hypothesis either. But” – and his face lightens up – “I think I found a really interesting lemma…”

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**Excuses for not doing homeworks:**

**Top ten excuses for not doing math homework:**

- I accidentally divided by zero and my paper burst into flames.
- Isaac Newton’s birthday.
- 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 is the square root of negative one.
- I could have sworn I put the homework inside a Klein bottle, but this morning I couldn’t find it.

**Humor**

*“Roses are red,
Violets are blue,
Greens’ functions are boring
And so are Fourier transforms.”*

**How to prove it. **

1)Proof by vigorous handwaving:

Works well in a classroom or seminar setting.

2)Proof by forward reference:Reference is usually to a forthcoming paper of the author, which is often not as forthcoming as at first.

3)Proof by funding:How could three different government agencies be wrong?

4)Proof by example:The author gives only the case n = 2 and suggests that it contains most of the ideas of the general proof.

5)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”.

6)Proof by picture:A more convincing form of proof by example. Combines well with proof by omission.

7)Proof by intimidation:”Trivial.”

8)Proof by adverb:”As is quite clear, the elementary aforementioned statement is obviously valid.”

9)Proof by seduction:”Convince yourself that this is true! ”

10)Proof by cumbersome notation:Best done with access to at least four alphabets and special symbols.

11)Proof by exhaustion:An issue or two of a journal devoted to your proof is useful.

12)Proof by obfuscation:A long plotless sequence of true and/or meaningless syntactically related statements.

13)Proof by wishful citation:The author cites the negation, converse, or generalization of a theorem from the literature to support his claims.

14)Proof by eminent authority:”I saw Karp in the elevator and he said it was probably NP- complete.”

15)Proof by personal communication:”Eight-dimensional colored cycle stripping is NP-complete [Karp, personal communication].”

16)Proof by reduction to the wrong problem:”To see that infinite-dimensional colored cycle stripping is decidable, we reduce it to the halting problem.”

17)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.

18)Proof by importance:A large body of useful consequences all follow from the proposition in question.

19)Proof by accumulated evidence:Long and diligent search has not revealed a counterexample.

20)Proof by cosmology:The negation of the proposition is unimaginable or meaningless. Popular for proofs of the existence of God.

21)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.

22)Proof by metaproof:A method is given to construct the desired proof. The correctness of the method is proved by any of these techniques.

23)Proof by vehement assertion:It is useful to have some kind of authority relation to the audience.

24)Proof by ghost reference:Nothing even remotely resembling the cited theorem appears in the reference given.

25)Proof by semantic shift:Some of the standard but inconvenient definitions are changed for the statement of the result.

26)Proof by appeal to intuition:Cloud-shaped drawings frequently help here.

**Theorems**

*Salary Theorem*

The 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 of **Work **done.

**Jokes**

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

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 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 does the zero say to the the eight?

A: Nice belt!

One day, Jesus said to his disciples: “The Kingdom of Heaven is like 3x squared plus 8x minus 9.” St. Thomas looked very confused and asked St. Peter: “What does the teacher mean?” St.Peter replied: “Don’t worry – it’s just another one of his parabolas.”

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.

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?

Q: How does one insult a mathematician?

A: You say: “Your brain is smaller than any >0!”

Trigonometry for farmers: swine and coswine…

**i to π: Be rational.
π to i: Get real.**

**Math insults**

“Let’s just say…he’s just a few vertices short of a polygon.”

“You might as well take topology; you wouldn’t know a donut from a coffee mug.”

“The intersection of her brain and reality, is the null set.”

“Geez, his social life is about as exciting as derivatives of e^x.”

“Are you kidding? The guy couldn’t find his a**hole with a Lorenz Attractor.”

“He probably thinks googol is a search engine.”

**Limericks**

A mathematician confided

That the M”obius band is one-sided

And you’ll get quite a laugh

If you cut one in half

‘Cause it stays in one piece when divided.

A mathematician named Klein

Thought the M”obius band was divine

Said he: If you glue

The edges of two

You’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 contraction

Reduced his rapier to a disk.

‘Tis a favorite project of mine

A new value of pi to assign.

I would fix it at 3

For it’s simpler, you see,

Than 3 point 1 4 1 5 9

If inside a circle a line

Hits the center and goes spine to spine

And the line’s length is “d”

the circumference will be

d times 3.14159

Pi goes on and on and on …

And e is just as cursed.

I wonder: Which is larger

When their digits are reversed?

A challenge for many long ages

Had 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 1

Over x, you will find

Here’s the value defined:

2.718281…

Integral z-squared dz

from 1 to the cube root of 3

times the cosine

of three pi over 9

equals log of the cube root of ‘e’.

*And it’s correct, too.*

A burleycque dancer, a pip

Named Virginia, could peel in a zip;

But she read science fiction

and died of constriction

Attempting 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,

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 yield

a full finite field,

as p ranges over the primes.

A graduate student from Trinity

Computed the cube of infinity;

But it gave him the fidgets

To 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 profound

Is 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.

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 seen.