Can we still smile?

 [ Hardy and Littlewood]

John Littlewood lived through the 1918–1919 flu pandemic, yet he appears not to have remarked on it in print. Nor can we find mention of it by Godfrey Hardy in A Mathematician’s Apology—though Hardy did write about the ravages of WW I.

Today, Ken and I thought you might like some fun comments that are not about the current pandemic.

This is not to say we are ignoring it. We are all fighting the virus in one way or another. Our hearts go out to those of you fighting it directly. We are all worried about ourselves and others. We are stuck at home, at least most of us. We are all in this terrible time together. We hope you all are safe and well.

We thought we would list a few jokes and stories that you might enjoy. We wrote recently about one kind of mathematical joke that can be given various proportions of pure levity and mathematical content. Our friends Lance Fortnow and Bill Gasarch, plus commenters in their item, collected some jokes on the computer science side.

Littlewood’s notion of “mathematical joke” leaned more on mathematical content, though his memoir A Mathematician’s Miscellany includes many funny stories as well. At the end of his introduction to the book, he wrote:

A good mathematical joke is better, and better mathematics, than a dozen mediocre papers.

We will start at the levity end. This is almost a math joke:

The Daily News published a story saying that one-half of the MP (Members of Parliament) were crooks.
The Government took great exception to that and demanded a retraction and an apology.
The newspaper responded the next day with an apology and reported that one-half of the MPs were not crooks.

We like this one, even if it is not really a hardcore math one. It does rely on the fact that ${\frac{1}{2} + \frac{1}{2} = 1.}$

Jokes and More

The following are some examples that we hope you all like. They are from a variety of sources:

• Jokes that mathematicians think are funny.

• Some are from StackExchange.

• Others are from Andrej Cherkaev’s page.

We have lightly edited a few.

${\bullet }$ “My age is two billion years old,” said Paul Erdös. The point is:

When I was seventeen years old it was said the earth was two billion years old. Now they say it is four billion years old. So my age is about two billion years old.

${\bullet }$ There was a statistician that drowned crossing a river ${\dots}$ It was 3 feet deep on average.

${\bullet }$ An infinite number of mathematicians walk into a bar. The first one orders a beer. The second orders half a beer. The third orders a third of a beer. The bartender bellows, “Get the heck out of here, are you trying to ruin me?”

${\bullet }$ An chemist, a physicist, and a mathematician are stranded on an island when a can of food rolls ashore. The chemist and the physicist comes up with many ingenious ways to open the can. Then suddenly the mathematician gets a bright idea: “Assume we have a can opener ${\dots}$

${\bullet }$ A theorist decides she wants to learn more about practical problems. She sees a seminar with the title: “The Theory of Gears.” So she goes. The speaker stands up and begins, “The theory of gears with a finite number of teeth is well known ${\dots}$

${\bullet }$ The reason that every major university maintains a department of mathematics is that it is cheaper to do this than to institutionalize all those people.

Regarding the last one, Littlewood did after all write in his book:

Mathematics is a dangerous profession; an appreciable proportion of us go mad.

This appears to have been a playful swipe at Hardy’s decision to leave Cambridge for Oxford. It was couched in a discussion of events that would seem to have had tiny probabilities before they happened.

The last two we’ve picked out from the above sites verge into philosophy:

${\bullet }$ The cherry theorem: Question: What is a small, red, round thing that has a cherry pit inside?

${\bullet}$ René Descartes went into his favorite bar and the bartender asked, “would you like your usual drink tonight, Monsieur Descartes?” Descartes replied “I think not.” Then he promptly ceased to exist.

Wrong Derivations, Right Results

Littlewood’s standards for a “mathematical joke” were higher than ours, but we will start by adapting an example from this MathOverflow discussion of Littlewood-style jokes. Sometimes we can play a joke on ourselves by deriving a result we know is right but with an incorrect proof. Here is the example:

${\bullet}$ Casting out 6’s. Suppose we want to simplify the fraction ${\frac{166}{664}}$. We can use the rule of casting out 6’s to get

$\displaystyle \frac{166}{664} = \frac{16}{64} = \frac{1}{4}.$

The rule works quite generally:

$\displaystyle \frac{1666}{6664} = \frac{16666}{66664} = \frac{166666}{666664} = \cdots$

$\displaystyle \frac{26}{65} = \frac{266}{665} = \frac{2666}{6665} = \frac{26666}{66665} = \cdots$

You can even turn the paper upside down and cast out the ${6}$‘s that you see then:

$\displaystyle \frac{19}{95} = \frac{199}{995} = \frac{1999}{9995} = \frac{19999}{99995} = \cdots$

$\displaystyle \frac{49}{98} = \frac{499}{998} = \frac{4999}{9998} = \frac{49999}{99998} = \cdots$

Note, this is a joke: The rule of course does not actually work all the time:

$\displaystyle \frac{56}{65} = \frac{5}{5} = 1.$

We thought to try to come up with our own examples, or at least blend in other sources. It once struck me (Ken), on reading a column by Martin Gardner on difference equations, that they give a “convincing proof” of ${0^0 = 1}$. Consider the powers of a natural number ${k}$, say ${k = 5}$. Take differences like so:

$\displaystyle \begin{array}{ccccccccccc} 1 & & 5 & & 25 & & 125 & & 625 & & \dots\\ & 4 & & 20 & & 100 & & 500 & & \dots\\ & & 16 & & 80 & & 400 & & \dots & & \\ & & & 64 & & 320 & & \dots & & &\\ & & & & 256 & & & & \\ & & & & & \ddots & & & \end{array}$

The powers of ${k-1}$ always appear on the bottom diagonal. Thus we have: ${(k-1)^0 = 1}$, ${(k-1)}$, ${(k-1)^2}$, and so on. Now do this for ${k = 1}$:

$\displaystyle \begin{array}{ccccccccccc} 1 & & 1 & & 1 & & 1 & & 1 & & \dots\\ & 0 & & 0 & & 0 & & 0 & & \dots\\ & & 0 & & 0 & & 0 & & \dots & & \\ & & & 0 & & 0 & & \dots & & &\\ & & & & 0 & & & & \\ & & & & & \ddots & & & \end{array}$

The diagonal now holds the powers of ${0}$. It thus follows that ${0^0 = 1}$.

Open Problems

What are your favorite mathematical jokes? Please send them to us. Be safe. Be well.

[fixed equations in last main section]

April 27, 2020 9:29 am

“God exists since mathematics is consistent. The Devil exists since we cannot prove it” A. Weil

April 27, 2020 9:52 am

Joke 1:
A computer programmer leaves work and heads for home. Being the good husband that he is, he calls his wife and asks if there’s anything she needs him to pick up on the way.
Yes, a gallon of milk and, Oh, if they have eggs, get a dozen.
Later he arrives home and stumbles into the kitchen burdened with a dozen gallons of milk. His wife, perplexed, asks him “why in the world did you buy 12 gallons of milk?”

———————————————
Joke 2:
Give an an anagram of Banch-Tarski
Banach-Tarski Banach-Tarski
———————————————-
Joke 3: Actually a category of jokes.
In FILL IN (the future, a prison, a comedians convention, a comedy club)
they have numbered all of the jokes. Alice and Bob go there. Alice knows about
the numbers, Bob does not. So they hear
84 (laughter)
18 (some laughter)
The joke can end several ways

17 (BIG LAUGHS)
Bob- why did that one get such a big laugh
Alice- They hand’t heard it before
OR
Alice- its the way he told it

OR

17 (groans)
Bob- Why didn’t they like that one?
Alice- Its an old joke. Might have been better in Roman Numerals
OR
Alice- he didn’t tell it right
OR
Alice- he blew the punchline
OR

There are many other endings- make up your own.

3. April 27, 2020 12:42 pm

I could knot say that the joke about “not theory” is my favourite.

Best and be well

Dick

April 27, 2020 4:58 pm

What does a drowning number theorist say?
log log log log…

May 2, 2020 11:50 am

Dear Douglas:

Very funny. What does a drowning theorist say?

I am not sure…

Best and be well

Dick

5. April 28, 2020 7:37 pm

You can write your own setup, but the punchline is: “Assume a spherical cow, radiating milk in all directions uniformly…”. From the multivariate harmonic analysis folks at the University of Wisconsin-Madison, circa 1980.

May 2, 2020 11:48 am

Dear drdaniel:

Thanks. Yes this is a great example: Assume a spherical cow… Wonderful.

Best, and be well

Dick

April 30, 2020 3:39 pm

“It is impossible to separate a cube into two cubes, or a fourth power into two fourth powers, or in general, any power higher than the second, into two like powers.
I have discovered a truly marvelous proof of this, which this margin is too narrow to contain.”
P. de Fermat

7. May 26, 2020 6:09 am

Here is a joke I invented (based on a famous one) and had mixed reaction.

A young mathematician comes to present to a famous mathematician his theorem. “You are absolutely wrong,” the famous mathematician dismissed the young one.

Next enters another young mathematician and presents precisely the opposite theorem. “You are absolutely wrong” replies the famous mathematician.

The famous mathematician’s husband interferes. “How could you tell both of them that they are wrong,” he says. “They have made completely opposite claims, one of them must be right!”

“You are also wrong,” replied the famous mathematician.

May 26, 2020 7:58 am

Dear Gil:

Thanks for the joke. I liked the idea of the joke. There could have been ten young mathematicians all with various claims and they all still can be wronged. Am I might abut that?

The student A presents their theorem T to the famous mathematician M. M says “You are absolutely wrong”. Next student B presents their theorem not T. Then M says the same “You are absolutely wrong”. The famous mathematician’s husband interferes. “How could you tell both of them that they are wrong,” he says. “They have made completely opposite claims, one of them must be right!”

“You are also wrong,” replied the famous mathematician M.

Hmmm not better statement of the joke.

Best anyway and be safe

Dick

8. June 2, 2020 1:22 pm

Q: Why don’t mathematicians have a name for a 2-sided figure?

9. June 2, 2020 1:23 pm

Q: Why don’t mathematicians have a name for a 2-sided figure?
A: Because they can’t let bi-gons be bi-gons.