From ProofWiki
Jump to navigation Jump to search


Q: How many mathematicians does it take to change a lightbulb?
A: $0.999999 \ldots$

Banach-Tarski Paradox

Q: Give me an anagram of Banach-Tarski.
A: Banach-Tarski Banach-Tarski.

Educational Standards

Two captains of industry, Arthur and George, were in a restaurant discussing the state of educational standards, particularly in the field of mathematics. Arthur was convinced they were slipping badly, and that your average college student was completely mathematically illiterate. George, on the other hand, was confident that any student would at least know the basics of calculus.

"I bet you a hundred bucks," said Arthur, "that if you were to ask a random college student a basic question in calculus, he wouldn't understand the question, let alone furnish you with an answer."

"I'll think about that," said George. "Not sure whether to take you up on your bet or not, but I reckon you'd be wrong."

Arthur slipped off to the mens' room at that point, and while he was gone, George called over the waitress Jody. (He knew that was her name because it was written on a badge pinned to her uniform. This appears to be a custom in certain chain diners.)

"I'd like you to help settle a wager between me and my colleague," he said. "When he comes back, I'm going to call you over, and ask you a question, to which you are to answer: one third x cubed."

"Wuntur dex cue?"

"One third x cubed."

"One thurrd ex cuebd."

"That's it, one third x cubed."

"One third ... x cubed."

"That's it, perfect. There's a good tip in it for you."

Arthur returned. George said, "Yes, I think I will take you up on it. A hundred bucks says our waitress can answer such a question. Hey, Jody! What's the indefinite integral of x squared with respect to x?"

"One third x cubed," replied Jody, dutifully.

"You see?" said George, pocketing Arthur's hundred.

As Jody turned away, she called back over her shoulder, "Plus a constant."

George ruefully took Arthur's hundred back out of his pocket and dropped it onto the table.

Pythagoras's Theorem

Once upon a time there were three ladies of the First Peoples of America sitting around the campfire.

On a reindeer skin sat a lady who was the mother of a fine young warrior who weighed $140$ pounds.

On a buffalo skin sat a lady who was the mother of a fine young warrior who weighed $160$ pounds.

The third lady, as well she might, was sitting on the skin of a hippopotamus, as she herself weighed a mighty $300$ pounds.

As you can see:

The squaw on the hippopotamus is equal to the sons of the squaws on the other two hides.

Knot Theory

Student A: "What's your favourite area of mathematics?"
Student B: "Knot theory."
Student A: "Me neither."
-- 1994: Colin C. Adams: The Knot Book: Knot Jokes and Pastimes (attributed to Martin Scharlemann)

Circle Geometry

The roundest knight at King Arthur's round table was Sir Cumference.

He acquired his shape from too much pi.

Sufficiently Large

$1+1 = 3$, for sufficiently large values of $1$.

Why? Because $1.4 + 1.4 = 2.8$.

The result follows after rounding to the nearest integer.

Number Bases

Why do mathematicians get Halloween and Christmas confused?

Because $\mathsf{Dec} \ 25$ equals $\mathsf{Oct} \ 31$.

-- 2009: Ian Stewart: Professor Stewart's Hoard of Mathematical Treasures: Halloween $=$ Christmas (but it's a considerably older joke than that.)


There are $10$ sorts of people in the world: those who understand binary and those who don't.


There are $10$ sorts of people in the world: those who understand ternary, those who don't, and those who thought this was going to be the binary joke.



Only dead people understand hexadecimal.

Sorry, I forgot to include you and me.

So that's: only deaf people understand hexadecimal.


There are $10$ sorts of people in the world: those who understand hexadecimal, and F the rest.

Generalised Indexing Policies

People in the world can be categorised as follows:

... from the sublime ...

$1$: Those who start their indexing from $1$
$1$: Those who start their indexing from $0$

... to the ridiculous

$1$: Those who can organise lists properly
$\text B$: Those who organise lists randomly
$\Omega$: Those who pretentiously use Greek letters

... and just plain innumeracy

There are three sorts of people in the world: those who can count, and those who can't.

... and while we're about it ...

There are $2$ types of people in the world. One type can extrapolate from the available data

Average Number of Hands

Most people in the world have more than the average number of hands.


\(\ds \) \(\) \(\ds \frac {\sin x} {\mathrm n}\)
\(\ds \) \(=\) \(\ds \mathrm {si} \ x \frac {\mathrm n} {\mathrm n}\)
\(\ds \) \(=\) \(\ds 6\)

The proof that $\map {\mathrm u} {x \, \mathrm u! \, s}^{-1} = 9$ is left as an exercise for the reader.

Even more Six

\(\ds \dfrac {9 \paren {8 - x} } {\paren {9 - 8} x} + \dfrac {8 - x} {9 - 8} + \dfrac {11 - x} {x - 1}\) \(=\) \(\ds x\)
\(\ds \implies \ \ \) \(\ds x\) \(=\) \(\ds 6\)

What happens when you rotate the above through $180^\circ$?

\(\ds 9\) \(=\) \(\ds x\) \(\ds \impliedby\)
\(\ds x\) \(=\) \(\ds \frac {1 - x} {x - 11} + \frac{8 - 6} {x - 8} + \frac {x \paren {8 - 6} } {\paren {x - 8} 6}\)

All Odd Numbers Are Prime

Proof by inductive argument:

$1$, that's prime (well not technically, but that's just mathematical double-talk).
$3$, that's prime.
$5$, that's prime.
$7$, that's prime.
$9$, that's prime (although when I measured it, it looked like it might not be - experimental error, ignore that one)
$11$, that's prime.
$13$, that's prime.

We can extrapolate from there.

Black Friday customer proof:

$1$, that's prime, it's obvious it is, no argument there. I said, no argument there.
$3$, that's prime.
$5$, that's prime.
$7$, that's prime.
$9$, that's prime YES IT IS -- DON'T ARGUE! YOU ARE STUPID!
$11$, that's prime.
$13$, that's prime.

Any more slackwit stupid people out there want to argue wit' me?


Hear about the constipated mathematician?

He worked out logs with a pencil.


Is a wisdom tooth a radicand?

Axiom of Intuition

The Axiom of Choice is obviously true; the Well Ordering Principle is obviously false; and who can tell about Zorn's Lemma?
-- Jerry Bona

Log Cabin

\(\ds \int \frac 1 {\text{cabin} } \rd \, \text{cabin}\) \(=\) \(\ds \ln \text{cabin} + C\)
\(\ds \) \(=\) \(\ds \text{houseboat}\)
-- Can apparently be found in Gravity's Rainbow by Thomas Pynchon


Q: How many Bourbakists does it take to change a lightbulb?
A: Changing a lightbulb is a special case of a more general theorem concerning the maintenance and repair of an electrical system. To establish upper and lower bounds for the number of personnel required, we must determine whether the sufficient conditions of Lemma $2.1$ (Availability of personnel) and those of Corollary $2.3.55$ (Motivation of personnel) apply. If these conditions are met, we derive the result by an application of the theorems in Section $3.11.23$. The resulting upper bound is, clearly, a result in an abstract measure space, in the weak-$*$ topology.


Q: How many lightbulbs does it take to change a lightbulb?
A: One, if it knows its own Gödel number.
-- 2005: P. Renteln and A. DundesFoolproof: A Sampling of Mathematical Folk Humor (Notices of the AMS Vol. 52, no. 1)

Q: How many mathematicians does it take to change a lightbulb?
A: I don't know, but a solution exists.

Q: How many physicists does it take to change a lightbulb?
A: One, but he'll need a mathematician to help him.

Principia Mathematica

Lyrics: Colin Fine
Music: Burt Bacharach

What do you get if you take a set
Add an associative operation
Give it an identity, make everything invertible?
A-a-ah, a-a-a-a-a-a-ah, it's a group
A-a-a-a-ah, it's a group.
What do you get if you take a group
Add an associative operation
Make it distributive over the first one?
A-a-ah, a-a-a-a-a-a-ah, it's a ring
A-a-a-a-ah, it's a ring.
Don't tell me it's too hard for you
Cos I can prove it so I know it's true
Out of a handful of simple axioms
I can build mathematics to satisfaction
What do you get if you take a ring
Make the multiply commutative
Give a reciprocal for each non-zero element?
A-a-ah, a-a-a-a-a-a-ah, it's a field
A-a-a-a-ah, it's a field.
(And not a skew field either!)
What do you get if you take a field
And you take a group with a scalar multiply
Make it associative with the field multiply
A-a-ah, a-a-a-a-a-a-ah, it's a vector space
A-a-a-a-ah, it's a vector space.
You can go on like this all day
Building structures in this kind of way
You end up feeling pretty cocksure
When you get into categories with meta-structure!
What do you get with some proofs and rules
Some axioms to give you a formal system?
You try to prove that it's consistent,
A-a-ah, a-a-a-a-a-a-ah ...??
Godel's Theorem!

In prime mover's defence, he remembers meeting Colin Fine at one or two SF conventions in the 1980's. He recently found this poem, a copy of which he got hold of in approximately 1987, lurking near the bottom of a pile of old magazines.

Mathematical Double-talk

[Then he] proved that an automorphic resonance field has a semi-infinite number of irresolute prime ideals.
-- Colin Fine again, as it appears in Pyramids by Terry Pratchett. The above line was the result of a specific request for an example of plausible-sounding mathematical double-talk.

Medical Conditions

Ring epimorphism? I had one of them once. The doctor had to give me suppositories.
-- Mrs. Prime.mover.

Imaginary numbers

After eating too much food, the mathematician announced: "$\sqrt {\paren {-1 / 64} }$."

-- Kit Yates, via Twitter

A constant argument

$i$: "Be rational."
$\pi$: "Get real!"


Three logicians walk into a pub.

The barmaid asks: "Are you all having beer?"

The first logician replies: "I don't know."

The second logician replies: "I don't know."

The third logician replies: "Yes."

-- Peter Rowlett, via Kit Yates, via Twitter

More beer

$\aleph_0$ mathematicians walk into a bar. The first one orders a pint of beer. The second one orders half a pint of beer. The third orders a quarter of a pint of beer. The fourth one orders an eighth of a pint of beer. After hearing the seventh order, the barman pours two pints, and says, "You guys should know your limits."

Surreal variant

$\aleph_0$ mathematicians walk into a bar. The first orders one beer. The second one orders two beers. The third one orders three beers. The bartender stops them, says: "You guys are idiots," and pours out $-\dfrac 1 {12}$ of a beer.

Divergent variant

$\aleph_0$ mathematicians walk into a bar. The first one orders a pint of beer. The second one orders half a pint of beer. The third orders a third of a pint of beer. The fourth one orders a fourth of a pint of beer. The barman yells, "Get out of here, are you trying to ruin me?"


LOGIC, n. The art of thinking and reasoning in strict accordance with the limitations and incapacities of the human misunderstanding. The basis of logic is the syllogism, consisting of a major and a minor premise and a conclusion -- thus:
Major Premise: Sixty men can to a piece of work sixty times as quickly as one man.
Minor Premise: One man can dig a posthole in sixty seconds.
Conclusion: Sixty men can dig a posthole in one second.
Ambrose Bierce, The Devil's Dictionary


What goes: $3.1415 \text{baa}$?

Shepherd's pi.

Second Pizza Theorem

Q: What is the volume of a pizza whose radius is $z$ and whose thickness is $a$?
A: From Volume of Cylinder: $\text {pi} z z a$.

More $\pi$

I've memorised all the digits of pi. Now I just have to remember what order they come in.
-- (Traditional)

Proof by Contradiction

A mad scientist captures a mathematician and locks him in a room full of cans of food - but no can opener.

Checking on the cell several weeks later, the mathematician is lying dead, but he has written one last message on the dust on the floor:


If I cannot open these cans of food, I will die.


Suppose not.


The Mathematicians' Party

Once upon a time, all the mathematicians who had ever lived attended a great big party, in order to let their hair down and enjoy themselves for once.

Plenty of physicists attended, and quite a few chemists and biologists came too.

Our roving reporter was at the door, and these are some of the things he observed ...

Click on the link in the title of this section to go to the party yourself.

Optimists versus Pessimists

Consider the real interval:

$\mathbb I := \hointr a b$

An optimist regards $\mathbb I$ as half-open.

A pessimist regards $\mathbb I$ as half-closed.

Coffee Paradox

The task of making coffee is too complex to accomplish unless one has first drunk a cup of coffee.

Author Prank

I have started covering a book (Introduction to Boolean Algebras) whose authors state:

"The verification that $A$ (a Ring of Idempotents, LF) becomes a Boolean ring in this way is an amusing exercise in ring axiomatics.", p.5

It's indeed most enjoyable to watch people write out $\paren {x \oplus y} \circ \paren {x \oplus y} = x \oplus y$...

Möbius Strip

I had a fight with a Möbius strip (or Möbius band for those of a prurient mentality).

I'm ashamed to say I lost. It was completely one-sided.

Amusing names

Is there an Emma Lehmer Lemma?


Let $f = \ds \sum_{i \mathop = 0}^n a_i x^i$ be a polynomial.

If the polynomial coefficient $a_n$ of $f$ is $1$, then $f$ is monic

If the polynomial coefficient $a_{n - 1}$ of $f$ is $0$, then $f$ is depressed.

So, a polynomial of the form:

$f = x^n + a_{n-2} x^{n-2} + \cdots + a_1 x + a_0$

can be called monic depressive?


A woman sends her logician husband to the shops. "Get me a loaf of bread," she said, "and if they have eggs, get me a dozen."

The husband returns from the shop with twelve loaves of bread.

Yes or no?

A woman has a baby, and the midwife immediately hands it to her logician husband.

"Well?" says the woman, "is it a boy or a girl?"

"Yes," he replies.

The Evils of Drink

Booze and calculus don't mix.

Don't drink and derive.


A visiting Professor of Linguistics was delivering a lecture.

"In the grammars of many languages throughout the world, a double negative expresses a positive. On the other hand there are some languages, such as Russian and the English of Chaucer, in which a double negative remains a negative. However, there is not a language in the world in which a double positive can express a negative."

A voice from the back of the room piped up: "Yeah, right."

-- Taken from the Facebook page of George Takei on $9$th March $2014$, but has been around for considerably longer than that.

Rhetorical Questions

Q: What do you get when you cross a joke with a rhetorical question?
A: Quite.

Physicist Mathematician and Engineer Jokes

The Red Rubber Ball

A physicist, mathematician and engineer were asked to determine the volume of a red rubber ball.

The physicist filled a beaker with water, immersed the ball, caught the runoff and measured its volume.

The mathematician set up and solved an appropriate triple integral, then measured the diameter of the ball and plugged in the number.

The engineer looked around on his bookshelf, then asked, "Has anyone got a red rubber ball volume table? I've only got the ones for blue and purple."

The Burning Hotel

The engineer is awakened by a smell and gets up to check it. He finds a fire in the hallway, sees a nearby fire extinguisher and after extinguishing it, goes back to bed.

Later that night, the physicist gets up, again because of the smell of fire. He quickly gets up and sees the fire in the hallway. After calculating air pressure, flame temperature and humidity as well as distance to the fire and projected trajectory, he extinguishes the fire with the least amount of fluid.

Variant 1

Finally, the mathematician awakes, only again to find a fire in the hallway. He instantly sees the extinguisher and thinks, "A solution exists!", and heads back into his room.

Variant 2

The punchline has been left as an exercise for the reader.

Variant 3

The mathematician awakens, and finds another fire in the hallway. He looks out the door, then goes back to bed. The house ends up burning down, but the physicist and engineer manages to save the mathematician. When asked why he didn't put out the fire, he says: "I saw the fire, I saw the extinguisher, the solution was trivial."

Variant 4

Then the mathematician awakens, and finds that the embers of the fire are still burning. After giving much thought to the problem, he gets up and lights it up to an actual fire. Then he goes back to sleep, satisfied that the problem has been reduced to a previously solved one.

Variant 5

Then the mathematician awakens, and finds another fire in the hallway. He quickly tears pages out of his notebook, lighting them on fire one by one. He then runs down the hall sliding sheets of burning paper under the other guests' doors.

After the building burns to the ground the fire marshal asks the mathematicians how the fire spread so fast.

He responds: "I thought distributing the problem would lead to finding a solution faster."

N-Dimensional Space

A mathematician, a physicist, and an engineer attend a lecture on Minkowski space.

Getting frustrated, the engineer asks, "How do you visualize 4-dimensional space?"

"Easy," replies the physicist. "Just imagine that each point of $\R$, representing a point in time, is associated with its own 3d space."

"There's an easier way," says the mathematician. "Just imagine N-dimensional space and set $N=4$."


$\dfrac {12 + 144 + 20 + 3 \sqrt 4} 7 + \paren {5 \times 11} = 9^2 + 0$
A dozen, a gross, and a score
Plus three times the square root of four
Divided by seven
Plus five times eleven
Is nine squared and not a bit more.
-- Leigh Mercer

My cat, mathematically-trained,
Says "Your topology's too coarse-grained,
Quantum mechanics
Sends you into blind panics
Because you're not well-enough brained."

Three thousand, four hundred and sixty
Five million, six hundred and fifty
Three thousand, six hun-
Dred and seventy one
Point four seven five six one three
-- Unknown attribution

$\ds \int \limits_1^{\sqrt [3] 3} z^2 \rd z \times \cos \dfrac {3 \pi} 9 = \map \ln {\sqrt [3] e}$
Integral zee squared dee zee
From one to the cube root of three
Times the cosine
Of three pi over nine
Is the log of the cube root of e
-- Unknown attribution

I met a logician from Spain
And showed him a proof about chains
Not one to dawdle
He built me a model
A disproof that did cause me pain
-- Unknown attribution

Physics Jokes


"We don't serve faster-than-light particles in here," says the barman.

A tachyon goes into a bar.

Quantum Mechanics

Heisenberg and Schrödinger in a car speeding down the freeway. Predictably, they are stopped by a traffic policeman.

"Do you know how fast you were going?" asked the cop.

"No, but I know exactly where I was," replied Heisenberg.

"You were actually travelling at 85 miles per hour," admonished the cop, sternly.

"Oh great," replied Heisenberg, angrily. "Now I'm lost!"

Deciding to give the car an inspection, the cop opens the trunk.

"Did you know you've got a dead cat in here?" he asks.

"Well, I do now!" replied Schrödinger.

Computer Science Jokes

Natural Numbers

Q: "Why do computer scientists have nine fingers?"
A: "Zero, one, two, three, four; five, six, seven, eight, nine."

Computer Prayer

Our Program which art in Memory,
"Hello World!" be Thy Name.
Thy Operating System come, Thy Commands be done,
at the Printer as it is on the Screen.
Give us this day our Data Dump,
and forgive us our I/O Errors
as we backup those whose Files are faulty.
Lead us not into frustration, and deliver us from email
for Thine is the Algorithm, the Application, and the Solution,
looping forever and ever.

Computer Encoding

Link to a ROT26 encoder:

Computer Programming

There are only two really difficult things in computer programming: cache invalidation, naming things, and off-by-one errors.

Law of Small Numbers

Everything is fast for small values of $n$.

Diophantus Updated

Amanda is $21$ years older than her son John.

In $6$ years from now, Amanda will be $5$ times as old as John.

Where is John's father?

Let $M$ be the age in years of Amanda now.

Let $C$ be the age in years of John now.


\(\ds M\) \(=\) \(\ds C + 21\)
\(\ds M + 6\) \(=\) \(\ds 5 \paren {C + 6}\)
\(\ds \leadsto \ \ \) \(\ds C + 21 + 6\) \(=\) \(\ds 5 \paren {C + 6}\) substituting for $M$
\(\ds \leadsto \ \ \) \(\ds C + 27\) \(=\) \(\ds 5 C + 30\) simplifying
\(\ds \leadsto \ \ \) \(\ds -3\) \(=\) \(\ds 4 C\) subtracting $C + 30$ from both sides
\(\ds \leadsto \ \ \) \(\ds C\) \(=\) \(\ds -\frac 3 4\)

So John is $-\dfrac 3 4$ years old, that is, $-9$ months.

That is, John will be born in $9$ months time.

So, right now, John's father is inside Amanda.


Q: What goes: two bloody thirds?
A: A vulgar fraction.


An engineer, physicist and mathematician visit a farm.

The farmer gives them a challenge to enclose his sheep with the smallest amount of fence possible.

The engineer starts and makes a circle, declaring: "A circle has the greatest area compared to the circumference".

Next goes the physicist. He extends the fence infinitely far before reducing the fence, forcing the sheep next to one another before declaring "This circle is as small as it can get."

Lastly goes the mathematician, who has pondered upon it all. He builds a small fence around himself before declaring: "I define myself as on the outside."

Word Problems

Pat's first day in school:

Teacher: Pat, if I give you two apples, and then I give you another apple, how many apples will you have?
Pat: I'll have four apples, Miz.
Teacher: No, it's three.
Pat: No, Miz, I'll have four.
Teacher: NO Pat, two plus one equals three -- what on earth makes you think it's four?
Pat: I already have an apple in my lunch box.


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


Gödel's First Incompleteness Theorem: Any effectively generated theory capable of expressing elementary arithmetic cannot be both consistent and.

Cauchy Condescension Test

It obviously converges, but I can't be bothered to explain why.


I'm going to this year's Fibonacci convention.
It'll be as big as the last two put together.

It's worse than that

This Fibonacci joke is as bad as the last two you heard combined.


A horse walks into a bar and orders a beer. The bartender asks him, "Would you like that in a glass?" The horse replies, "I think not." And POOF! he disappears.
Philosophy students will no doubt find this joke hilarious, because René Descartes' most famous saying was I think therefore I am. But to tell you that before the rest of the joke would be putting Descartes before the horse.


Hardy-Weinberg Equation:

$p^2 + 2 p q + q^2 = 1$

Easy-Weinberg Equation:

$p = 1$

Wives and Mistresses

An engineer, a physicist and a mathematician were talking in the pub.

"It's a disaster," said the engineer. "My wife's just found out about my mistress. And after all that calculation -- to the last decimal place -- of times and places and schedules, and she goes and reads my notebook!"

"I completely understand," replied the physicist. "My mistress just found out about my wife -- she came to my lab and found the apparatus for the industrial diamonds I manufactured for our anniversary the other month -- like a fool I'd left the die for the engraving of our names entwined in a heart, and now the cat is out of the bag."

"Dunno what you're complaining about," said the mathematician complacently. "My wife and my mistress both know all about each other."

"But doesn't that cause all sorts of problems?" exclaimed the engineer.

"Surely that's a foolish situation!" opined the physicist.

"Not at all," said the mathematician insouciantly. "When I'm not with my wife, she thinks I'm with my mistress. And when I'm not with my mistress, she thinks I'm with my wife. But in fact I'm actually in the library getting some mathematics done."

Contour Integrals

What's the value of:

$\ds \oint_\CC \map {\operatorname {Europe} } z \rd z$

where $\CC$ is a closed contour circling Western Europe?

By the Residue Theorem, the integral is zero. The Poles are in Eastern Europe.

(Comment: They're not, actually, freedom of movement within the European Community has allowed for them to move at will throughout the continent and there are indeed many Poles in Western Europe. But they can be considered removable.)

That famous chicken

Why did the chicken cross the Möbius strip?

To get to the other ... -- no, wait ...

Separated at birth?

KarlWilhelmFeuerbach.jpg EvaristeGalois.jpg
Karl Wilhelm Feuerbach Évariste Galois

On meticulousness

Why should I have to "dot my "i"s and cross my "t"s?

I know that $\mathbf i \cdot \mathbf i = 1$ and $\mathbf t \times \mathbf t = \mathbf 0$.

-- Fargle

Scottish Sheep are Black

A trainload of scientists have just crossed the border from England into Scotland. (Substitute a frontier of your choice.)

Looking out of the window, an anthropologist sees a black sheep.

Anthropologist: "Ooh look! Sheep in Scotland are black."
Logician: "Well, at least some sheep in Scotland are black."
Chemist: "On this occasion, we have observed that the experiment resulted in a sheep which is black. Until we have repeated the experiment in strictly controlled conditions, we cannot be certain that it will always result in a black sheep."
Statistician: "Oh come on! The entirety of the sample space consists of sheep which are black. It's perfectly appropriate from that to deduce that, to a considerable degree of accuracy, that all sheep in Scotland are black."
Physicst: "No, you're talking rubbish. At this stage, all we can tell with any certainty is that Scotland contains at least one sheep which is black."
Mathematician: "Now let's be strictly accurate here. What we do know is that in Scotland there exists at least one sheep, and this sheep is black on at least one side."

Height and Length

Several engineers are trying to erect a flagpole, but are having a very difficult job of it.

Their directions were to cut the pole to a certain height. However, once the pole is standing straight up, they are having a hard time cutting the pole down to the correct height, by the awkwardness of using a saw on a ladder.

A mathematician walks by and asks what they're doing. They tell her. She helpfully (and a bit condescendingly) explains that it would be much easier to cut the pole to the right size before setting it upright.

As she walks away, the engineers look at each other, annoyed.

"Figures that a mathematician wouldn't know the difference between height and length."

Sex is Fun

Let $e^{x / n} = \dfrac \d {\d x} \map f u$.


\(\ds \sqrt [n] {e^x}\) \(=\) \(\ds \dfrac \d {\d x} \map f u\)
\(\ds \leadsto \ \ \) \(\ds \paren {\sqrt [n] {e^x} }^n\) \(=\) \(\ds \paren {\dfrac \d {\d x} \map f u}^n\)
\(\ds \leadsto \ \ \) \(\ds e^x\) \(=\) \(\ds \paren {\dfrac \d {\d x} \map f u}^n\)
\(\ds \leadsto \ \ \) \(\ds \int e^x\) \(=\) \(\ds \int \paren {\dfrac \d {\d x} \map f u}^n\)
\(\ds \leadsto \ \ \) \(\ds \int e^x\) \(=\) \(\ds \map f u^n\)

Purists are entitled of course to quibble that the left hand side should really read $\ds \int e^x \rd x$.


Bibhorr is an Indian mathematician widely known for invention of Bibhorr formula.

Affiliated to Indira Gandhi National Open University.

Bibhorr Formula

Bibhorr angle in right triangle.

Consider a right triangle $\triangle$ $ABC$ such that $AB$, $BC$ and $AC$ are the shortest, medium and longest sides respectively. Here, $AC$ is the hypotenuse.

Now, for this triangle the angle opposite $BC$ (Bibhorr angle) is given as:

$\text{Bibhorr angle } = \dfrac {90 \left({AC + BC - AB}\right)^2} {BC^2 + 1.5 AC \left({AC + BC - AB}\right)}$ (in degrees)


$\text{Bibhorr angle } = \dfrac {\dfrac{π}{2} \left({AC + BC - AB}\right)^2} {BC^2 + 1.5 AC \left({AC + BC - AB}\right)}$ (in radians)

The above equation is the Bibhorr formula

Animal Crackers

All the animals in the zoo boarded a flight one day, in order to go on safari.

As they settled themselves down, the drinks and the drugs were broken out, and gradually, practically everybody on that flight was more or less inebriated, the worse for wear, stoned, out of it, off their box, and whatever other glorious euphemisms you care to use.

The elephants had imbibed more beer than would completely inundate a sizeable village; the monkeys were off their nuts on weed, the snakes were utterly plastered on whisky, and the giraffes were falling down on the vast quantities of wine they had guzzled.

All, that is, except for the King of the Jungle.

The head stewardess, who was having trouble keeping her passengers under control, approached him, saying:

"It's jolly nice that at least one of you has stayed sober. Maybe you can help keep order."

"Well ma'am," he replied, "it's very important that I do stay sober and clear-headed if we are to make it to our destination in the most efficient manner.

"You see," he continued, "the shortest distance between two points is taken by the straight lion in the plane."

-- Matt Westwood, $2$ March $2019$


Young Herbert was failing in mathematics, and his parents did not know what to do with him.

They had heard that Catholic schools imposed some proper discipline upon the pupils, so (despite having no spiritual leanings in that direction) they sent Herbert there.

Surprisingly enough, he had been there only a matter of weeks when it was noticed that he had seriously started to apply himself, and his grades dramatically improved.

Taking his son out on a fishing trip as a reward, Herbert's father mentioned this increase in performance, and congratulated him.

"Well Dad," said Herbert, "it's like this. When I saw the guy nailed to the plus sign, I knew they meant business."

Form Follows Function

Form follows function, did you say?

Not in my dictionary it doesn't.

The perpetrator of this joke should be charged

"Oh, no!" said one atom to the other. "I've lost one of my electrons!"
"Are you sure?" said the other atom.
"Yes, I'm positive!"

Albert Einstein's lecture tour

Some years ago, Albert Einstein did a lecture tour ranging over the whole of the United States.

It was a long tour, and he presented the same lecture every night.

In fact, it was such a long tour that his driver said to him, "Do you know, I've seen you present this lecture so often, I reckon I could do it myself."

"Go on then, said Albert, always game for a laugh.

So indeed, this is what happened.

Instead of Albert Einstein presenting the lecture, that evening his driver presented it for him.

And he presented it absolutely flawlessly, and received a hearty round of applause at the end.

But then one of the members of the audience asked a question.

It was a big and complicated question, requiring a deep and thorough understanding of quantum mechanics for it to be answered adequately.

But the driver was completely unfazed.

He replied, "The question you have asked is so elementary, and has such an obvious answer, that ..." (pointing at Albert Einstein) "... even my driver can answer it."


Coffee and Doughnuts

A topologist is a mathematician who can't tell his doughnut from his coffee mug.

Affirming the Consequent

A professor of logic says, "Class, if you know what 'affirming the consequent' means, then raise your hand."

A student raises her hand.

The professor says, "You know what it means?"

She replies, "No, why would you think I do?"

Even More Beer

Dedekind infinite bottles of beer on the wall,

Dedekind infinite bottles of beer,

Take one down, and pass it around,

Dedekind infinite bottles of beer on the wall.

Proof Methods

Proof by Triviality

It trivially follows that $P \ne NP$.

Proof by Example

Thus $\powerset S$ is strictly larger than $S$ as is seen in the example $S=\{0,1\}$.

Proof by Exercise

The proof is left as a trivial exercise for the reader.

Proof by Non-Existent Citation

For the proof of Fermat's Last Theorem, see Fermat's commentary on Arithmetica.

Proof by Margin Size

This theorem has a truly marvelous proof which this margin is too narrow to contain.

Proof by Authority

Fermat said that this theorem is true, and who are we to argue?

Proof by Reduction to Wrong Problem

To see that $P \ne NP$, we simply reduce to the Chinese Remainder Theorem.

Proof by Generalization in the Obvious Way

To prove Fermat's Last Theorem, we simply generalize his proof of the $n=4$ case in the obvious way.

Proof by Lack of Counterexample

Computer programs haven't found a counter example all the way to $n=3,000,000$, so it must hold for all $n$.

Proof by Simple Corollary

Thus there is no surjection from $S$ to $\powerset S$.

The Continuum Hypothesis follows as a simple corollary.

Proof by Ontological Argument

The greatest proof that ZF implies Choice exists in the mind.

If it didn't exist in reality then a greater proof would exist, a contradiction.

Thus, the greatest proof of ZF implying Choice exists in reality.

Proof by Gruesome Predicate

Let '$x$ is griemann' mean '$x$ is green and was first observed before January 1, 3000, or the Riemann Hypothesis holds'.

All emeralds thus far observed have been griemann, as they have been green and observed before January 1, 3000.

By philosophical induction, all emeralds observed in the future will be griemann. Thus, after January 1, 3000, the Riemann Hypothesis will hold.

Proof by Curry's Paradox

Observe the proposition 'This proposition is true, therefore $P \ne NP$.'

Assume for contradiction that it isn't true.

Then its premise is false, making it true.

Thus the proposition is true, validating its premise.

Therefore $P \ne NP$.

Proof by Inspection

Upon simple inspection, one sees that the Continuum Hypothesis holds.

Proof by Conjecture

Let us make the following bold conjecture: $P \ne NP$.

Proof by Conjecture Reference

It has been boldly conjectured that $P \ne NP$.

Proof by Recollection

Recall the proof for the Riemann Hypothesis previously elaborated.

Proof by Being an Engineer

As this is an engineering class, we will leave it to the mathematicians to prove that this function is differentiable.

Proof by Thwarting Satan

Any doubts that you have about this theorem are just the work of Satan.

We must stay strong in our belief of a proof.

Proof by Inter-Universal Teichmuller Theory

It is a trivial implication of these papers that the abc conjecture holds.

Proof by Publishing in Your Own Journal

The result must be true.

It was published in a journal of which I am chief editor.

Proof by Terence Tao

Terence Tao is working on a proof, so while a proof is presently unknown, we trust that we will have one soon.

Proof by Assuming the Necessary Assumptions

Assuming the necessary assumptions, it follows that the function is differentiable.

Proof by Repetition

The result follows by baseless assertion.

In other words, by baseless assertion, the result follows.

Hence, by baseless assertion, we can assume the result.

Proof by Impossible Exhaustion

Thus, this property holds for all sets, as we see by exhaustively checking each set.