A mathematical joke is a form of humor which relies on aspects of mathematics or a stereotype of mathematicians to derive humor. The humor may come from a pun, or from a double meaning of a mathematical term. It may also come from a lay person's misunderstanding of a mathematical concept (which is not wholly unexpected). These jokes are frequently inaccessible to those without a mathematical bent.

Pun-based jokes

Q. Why do mathematicians like national parks?

A. Because of the natural logs.

Q. What's purple and commutes ?

A. An Abelian grape. (A pun on Abelian group.)^[1]

A more sophisticated example:

Person 1: What's the integral of ¹/_cabin?

Person 2: A natural log cabin.

Person 1: No, a houseboat ? you forgot to add the c!

The first part of this joke relies on the fact that the primitive (formed when finding the antiderivative) of the function 1/x is ln(x). The second part is then based on the fact that the antiderivative is actually a class of functions, requiring the inclusion of a constant of integration, usually denoted as C ? something which many calculus students forget. Thus, the indefinite integral of 1/cabin is "ln(cabin) + c", or "A natural log cabin plus the sea", ie. "A houseboat".

There are only 10 types of people in the world ?
those who understand binary, and those who don't.

This joke relies on the fact that mathematical expressions, just as expressions in natural languages, may have multiple meanings. When multiple meanings are available, puns are possible. In this case a pun is made using the expression 10. For non-mathematicians or non-computer programmers 10 almost always refers to the number ten. However, in binary, the expression 10 means the number two. Thus the joke says that there are only two kinds of people, those who understand binary, and those who don't. However, those who do not understand binary will certainly not get the joke. This joke is only feasible in written form; when speaking a binary number aloud, "10" would be phrased as "one zero" or simply "two", rather than "ten".

There are only 10 types of people in the world ?
those who understand binary, those who don't, and those who understand Gray code.

In Gray code, "10" would be phrased as "one zero" or simply "three", rather than "ten", adding another layer of subtlety to the joke.

A self-deprecating version is as follows:

There are only 10 types of people in the world ?
those who understand binary, and those who get laid.

The following joke refers to the original joke:

There are only 10 types of people in the world ?
those who understand ternary, those who don't, and those who mistake it for binary.

A similar joke may be played by asking the question:

If only DEAD people understand hexadecimal, how many people understand hexadecimal?

In this case, DEAD refers to a hexadecimal number (57005 base 10), not the state of being no longer alive.

Another pun using different radices, sometimes attributed to computer scientists, asks:

Why do mathematicians think Halloween and Christmas are the same?

Because 31 Oct = 25 Dec.

The humor lies in the fact that Halloween occurs on October 31 and Christmas occurs on December 25, thus equating "oct" in October and octal, and "dec" in December and decimal. (This one is also often attributed to computer scientists: Real programmers confuse Halloween and Christmas ? because dec(25) = oct(31).)

Another joke involving counting is:

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

This implies, of course, that the person making the statement is the latter.

Almost everyone knows the trite line: "Why did the chicken cross the road?" "To get to the other side". A mathematical variation follows as: "Why did the chicken cross the Möbius strip?" This joke relies on the audience knowing that since the Möbius Strip is a surface with only one "side" (i.e., one "edge"), anyone trying to give the typical answer will realize its impossibility. The answer is sometimes also given as "To get to the same side", with the same rationale.

Stereotypes of mathematicians

Some jokes are based on stereotypes of mathematicians tending to think in complicated, abstract terms, causing them to lose touch with the "real world".

Many of these jokes compare mathematicians to other professions, typically physicists, engineers, or the "soft" sciences in a form similar to those which begin "An Englishman, an Irishman and a Scotsman?" or the like. The joke generally shows the other scientist doing something practical, while the mathematician does something less useful such as making the necessary calculation but not performing the implied action.

Examples:

A mathematician and his best friend, an engineer, attend a public lecture on geometry in thirteen-dimensional space. "How did you like it?" the mathematician wants to know after the talk. "My head's spinning," the engineer confesses. "How can you develop any intuition for thirteen-dimensional space?" "Well, it's not even difficult. All I do is visualize the situation in n-dimensional space and then set n = 13."

A mathematician, a biologist and a physicist are sitting in a street café watching people entering and leaving the house on the other side of the street. First they see two people entering the house. Time passes. After a while they notice three people leaving the house. The physicist says, "The measurement wasn't accurate." The biologist says, "They must have reproduced." The mathematician says, "If one more person enters the house then it will be empty."

An example of a joke relying on mathematicians' propensity for not taking the implied action is as follows:

A mathematician, an engineer and a chemist are at a conference. They are staying in adjoining rooms. One evening they are downstairs in the bar. The mathematician goes to bed first. The chemist goes next, followed a minute or two later by the engineer. The chemist notices that in the corridor outside their rooms a rubbish bin is ablaze. There is a bucket of water nearby. The chemist starts concocting a means of generating carbon dioxide in order to create a makeshift extinguisher but before he can do so the engineer arrives, dumps the water on the fire and puts it out. The next morning the chemist and engineer tell the mathematician about the fire. She admits she saw it. They ask her why she didn't put it out. She replies contemptuously "there was a fire and a bucket of water: a solution obviously existed."

Mathematicians are also shown as averse to making sweeping generalizations from a small amount of data, preferring instead to state only that which can be logically deduced from the given information ? even if some form of generalization seems plausible:

An astronomer, a physicist and a mathematician are on a train in Scotland. The astronomer looks out of the window, sees a black sheep standing in a field, and remarks, "How odd. Scottish sheep are black." "No, no, no!" says the physicist. "Only some Scottish sheep are black." The mathematician rolls his eyes at his companions' muddled thinking and says, "In Scotland, there is at least one field, containing at least one sheep, at least one side of which appears black from here."

A variant has the punchline "No," says the mathematician, "all we can say is that there is at least half of a black sheep in Scotland." Another variant with cows was featured in the book The Curious Incident of the Dog in the Night-time by Mark Haddon.

Pure mathematicians are mainly concerned with the properties of the abstract systems under study, not their actual applications. However, such applications are sometimes found in mathematics itself, resulting in new insights as old problems are cast in new light. In striving not to miss such connections, mathematicians often see problems in novel (but theoretically valid) ways, which unfortunately are not always as illuminating as one could wish for:

A sociologist, a physicist and a mathematician are all given equal amounts of fencing, and are asked to enclose the greatest area. The sociologist pauses for a moment and decides to enclose a square area with his fence. The physicist, realizing he can fence off a greater amount of land with the same amount of fencing, promptly sets his fence in the form of a circle, and smiles. "I'd like to see you beat that!" he says to the mathematician. The mathematician, in response, takes a very small piece of his own fencing, and wraps it around himself, proclaiming, "I define my location to be outside of the fence!"

A small set of jokes involves only mathematicians, such as the following involving statisticians:

Three statisticians go duck hunting. Their dog chases out a duck and it starts to fly. The first statistician aims and takes his shot, and it misses a foot too high. The second statistician aims and takes his shot, and it misses a foot too low. The third statistician says, "We got him!"

The humor there is derived from the fact that the average of the shots hits the duck, and so it is dead.

An engineer and a physicist are in a hot-air balloon. After a few hours they lose track of where they are and descend to get directions. They yell to a jogger, "Hey, can you tell us where we're at?" After a few moments the jogger responds, "You're in a hot-air balloon." The engineer says, "You must be a mathematician." The jogger, shocked, responds, "yeah, how did you know I was a mathematician?" "Because, it took you far too long to come up with your answer, it was 100% correct, and it was completely useless."

Non-mathematician's math

The next category of jokes comprises those that exploit common misunderstandings of mathematics, or the expectation that most people have only a basic mathematical education, if any.

Examples:

A visitor to the Royal Tyrell Museum was admiring a Tyrannosaurus fossil, and asked a nearby museum employee how old it was. "That skeleton's sixty-five million and three years, two months and eighteen days old," the employee replied. "How can you know it that well?" she asked. "Well, when I started working here, I asked a scientist the exact same question, and he said it was sixty-five million years old ? and that was three years, two months and eighteen days ago."

In the above example, the humor is that the employee fails to understand the scientist's implication of the uncertainty in the age of the fossil.

Two mathematicians are in a bar. The first one says to the second that the average person knows very little about basic math. 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 agrees, and goes off mumbling to herself. The first guy returns and the second proposes a bet to prove his point. 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." Then, while walking away, she turns back and says, "Plus a constant!"

In the above example, the humor is that the waitress, chosen as an example of someone not expected to know much mathematics beyond adding up the bill, turns out to know enough calculus to correct the mathematician's omission.

Mock mathematics

A form of mathematical humor comes from using mathematical tools (both abstract symbols and physical objects such as calculators) in various ways which transgress their intended ambit. These constructions are generally devoid of any "real" mathematics, besides some basic arithmetic.

Mock mathematical reasoning

A set of equivocal jokes applies mathematical reasoning to situations where it is not entirely valid. Many of these are based on a combination of well-known quotes and basic logical constructs such as syllogisms:

Example:

|Premise I: || Knowledge is power. |- | Premise II: || Power corrupts. |- | Conclusion: || Therefore, knowledge corrupts. |} There are also a number of joke proofs, such as the proof that women are evil:

| Women are the product of time and money: || women = time \times money |- | Time is money: || time = money |- | So women are money squared: || women = money^2 |- | Money is the root of all evil: || money = \sqrt{evil} |- | So women are absolutely evil: || women = (\sqrt{evil})^2 = |evil| |}

Another set of jokes relate to the absence of mathematical reasoning, or misinterpretation of conventional notation:

Examples:

\left( \lim_{x\to 8^+} \frac{1}{x-8} = \infty \right) \Rightarrow \left( \lim_{x\to 3^+} \frac{1}{x-3} = \omega \right)

That is, the limit as x goes to 8 from above is a sideways 8 or the infinity sign, in the same way that the limit as x goes to three from above is a sideways 3 or the Greek letter omega.^[2]

\frac{\sin{x}}{n} = \frac{\mbox{si}\, x}{1} = 6

(That is, the "n" in "sin" cancels with the "n" in the denominator, giving "six" and 1 respectively.) See also Anomalous cancellation.

Calculator spelling

Tangential to mathematics is calculator spelling: words and phrases formed by entering a number and turning the calculator upside down. Due to their crudeness and relative simplicity (requiring only basic calculator skills to achieve), these are usually spread by schoolchildren. Often the words are accompanied by stories involving numbers that lead to the "final solution". A favorite word to spell is hello, which is 0.1134 or 0.7734. Dropping the 0 and changing the number to an integer results in another child's favorite. Another favorite is the spelling of 'I sell boobs' on the calculator which is the number 5800877351. A classical joke in Dutch is to ask a person the product of two times 36541867. The answer, 73083734 reads 'heleboel' (a whole lot) when turned upside down.

Math limericks

A Math Limerick is an expression which, when read aloud, matches the form of a limerick. The following is an example which closely matches the form of a limerick:

\int_{1}^{\sqrt[3]{3}} t^2\, dt \,\times\, \cos \frac{3 \pi}{9} \,=\, \ln \sqrt[3]{e}

which reads as follows:

The integral t-squared dt

From one to the cube root of three

Times the cosine

Of three pi over nine

Equals log of the cube root of e

Another, attributed to Leigh Mercer:^[3]

\frac{12 + 144 + 20 + 3 \times \sqrt{4}}{7} + 5 \times 11 = 9^2 + 0

This is read as follows

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

Maths Jokes in the Media

From the Simpsons Episode 7, Season 2,

Teacher: So y = r cubed over 3. And if you determine the rate of change in this curve correctly, I think you'll be pleasantly surprised.

[The class laughs except for Bart who appears confused.]

Teacher: Don't you get it, Bart? Derivative dy = 3 r squared dr over 3, or r squared dr, or r dr r.

See also

• Funny numbers
• Ralph P. Boas, Jr
• The Complexity of Songs
• Tom Lehrer's satirical songs "Lobachevsky" and "New Math".
• Proof by intimidation
• Spherical cow

Notes

Further reading

External links

• Mathematical Humor ? From Mathworld
• A Sampling of Mathematical Folk Humor

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