A

**mathematical joke** is a form of humor which relies on aspects of

mathematicsMathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...

or a

stereotypeA stereotype is a popular belief about specific social groups or types of individuals. The concepts of "stereotype" and "prejudice" are often confused with many other different meanings...

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

Some jokes simply use a mathematical term with a second non-technical meaning as the punchline of a joke.

- Q. What's purple and commutes?
- A. An Abelian grape. (A pun on Abelian group
In abstract algebra, an abelian group, also called a commutative group, is a group in which the result of applying the group operation to two group elements does not depend on their order . Abelian groups generalize the arithmetic of addition of integers...

.)

Other jokes create a double meaning from a direct calculation involving facetious variable names:

- Person 1: What's the integral of
^{1}/_{cabin} with respect to cabin?
- Person 2: A 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

antiderivativeIn calculus, an "anti-derivative", antiderivative, primitive integral or indefinite integralof a function f is a function F whose derivative is equal to f, i.e., F ′ = f...

) of the function 1/x is

logThe natural logarithm is the logarithm to the base e, where e is an irrational and transcendental constant approximately equal to 2.718281828...

. 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 calculus students may forget. Thus, the indefinite integral of 1/cabin is "log|cabin| + C", or "A log cabin plus the

seaA sea generally refers to a large body of salt water, but the term is used in other contexts as well. Most commonly, it means a large expanse of saline water connected with an ocean, and is commonly used as a synonym for ocean...

", i.e., "A

houseboatA houseboat is a boat that has been designed or modified to be used primarily as a human dwelling. Some houseboats are not motorized, because they are usually moored, kept stationary at a fixed point and often tethered to land to provide utilities...

."

This type of joke was featured in an episode of

The SimpsonsThe Simpsons is an American animated sitcom created by Matt Groening for the Fox Broadcasting Company. The series is a satirical parody of a middle class American lifestyle epitomized by its family of the same name, which consists of Homer, Marge, Bart, Lisa and Maggie...

, "

Bart the Genius"Bart the Genius" is the second episode of The Simpsons first season, which originally aired on the Fox network on January 14, 1990. It was the first episode written by Jon Vitti. It was also the first ever episode to use the signature title sequence, as well as the first regular episode...

."

BartBartholomew JoJo "Bart" Simpson is a fictional main character in the animated television series The Simpsons and part of the Simpson family. He is voiced by actress Nancy Cartwright and first appeared on television in The Tracey Ullman Show short "Good Night" on April 19, 1987...

cheated on an exam and as a result was placed into a gifted school. However, since he did not have previous exposure to calculus, he was unable to see the humor in this exchange with his 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, except for Bart, laughs] Don't you get it, Bart? Differential dy = 3 r squared dr over 3, or r squared dr, or r dr r.

This joke also relies on knowledge that "hardy har har" (r dr r) is an English

onomatopoeia for laughter .

## Jokes with numeral bases

- 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. Like other

punThe pun, also called paronomasia, is a form of word play which suggests two or more meanings, by exploiting multiple meanings of words, or of similar-sounding words, for an intended humorous or rhetorical effect. These ambiguities can arise from the intentional use and abuse of homophonic,...

s, the humor is derived from an ambiguous meaning; in this case, the expression 10 in the

binary numeral systemThe binary numeral system, or base-2 number system, represents numeric values using two symbols, 0 and 1. More specifically, the usual base-2 system is a positional notation with a radix of 2...

is equal to the decimal number

two.

Another pun using different

radicesIn mathematical numeral systems, the base or radix for the simplest case is the number of unique digits, including zero, that a positional numeral system uses to represent numbers. For example, for the decimal system the radix is ten, because it uses the ten digits from 0 through 9.In any numeral...

, sometimes attributed to computer scientists, asks:

- Why do mathematicians always confuse Halloween
Hallowe'en , also known as Halloween or All Hallows' Eve, is a yearly holiday observed around the world on October 31, the night before All Saints' Day...

and ChristmasChristmas or Christmas Day is an annual holiday generally celebrated on December 25 by billions of people around the world. It is a Christian feast that commemorates the birth of Jesus Christ, liturgically closing the Advent season and initiating the season of Christmastide, which lasts twelve days...

?
- Because 31 Oct
The octal numeral system, or oct for short, is the base-8 number system, and uses the digits 0 to 7. Numerals can be made from binary numerals by grouping consecutive binary digits into groups of three...

= 25 DecThe decimal numeral system has ten as its base. It is the numerical base most widely used by modern civilizations....

.

The humor lies in the similarity of the abbreviation for October/

OctalThe octal numeral system, or oct for short, is the base-8 number system, and uses the digits 0 to 7. Numerals can be made from binary numerals by grouping consecutive binary digits into groups of three...

and December/Decimal, and the coincidence that the two representations equal the same amount (31 Octal is 3*8 + 1 = 25 Decimal).

## 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 compare mathematicians to other professions, typically

physicistA physicist is a scientist who studies or practices physics. Physicists study a wide range of physical phenomena in many branches of physics spanning all length scales: from sub-atomic particles of which all ordinary matter is made to the behavior of the material Universe as a whole...

s,

engineerAn engineer is a professional practitioner of engineering, concerned with applying scientific knowledge, mathematics and ingenuity to develop solutions for technical problems. Engineers design materials, structures, machines and systems while considering the limitations imposed by practicality,...

s, or the "soft" sciences in a form similar to

an Englishman, an Irishman and a Scotsman"An Englishman, an Irishman and a Scotsman" is the opening line of a category of joke popular in Ireland and the United Kingdom. The nationalities involved may vary, though they are most usually restricted to those within the UK and Ireland, and the number of people involved is usually three or...

. 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 physicist, a biologist and a mathematician 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 is a rubbish bin that 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."

The last sentence is also a dig at

proofs of existenceIn mathematics, an existence theorem is a theorem with a statement beginning 'there exist ..', or more generally 'for all x, y, ... there exist ...'. That is, in more formal terms of symbolic logic, it is a theorem with a statement involving the existential quantifier. Many such theorems will not...

, which merely show that a certain object must exist but are entirely unhelpful in constructing such an object.

An example of a joke by

Bill BaileyBill Bailey is an English comedian, musician and actor. As well as his extensive stand-up work, Bailey is well known for his appearances on Black Books, Never Mind the Buzzcocks, Have I Got News for You, and QI.Bailey was listed by The Observer as one of the 50 funniest acts in British comedy in...

highlighting mathematicians' habits of creating hypothetical situations with little real-world applications (such as

ad infinitumAd infinitum is a Latin phrase meaning "to infinity."In context, it usually means "continue forever, without limit" and thus can be used to describe a non-terminating process, a non-terminating repeating process, or a set of instructions to be repeated "forever," among other uses...

situations) is as follows:

- An infinite number of mathematicians walk into a bar. The first goes up to the bartender and says, "I'll have a pint of lager, please." Each next one says, "and I'll have half of what he's having." The bartender says, "You're all idiots," and pulls two pints.

This joke also relies on the fact that the infinite sum

is equal to 2 (and that one wouldn't expect most bartenders to know this).

Mathematicians are also shown as averse to making sweeping

generalizationA generalization of a concept is an extension of the concept to less-specific criteria. It is a foundational element of logic and human reasoning. Generalizations posit the existence of a domain or set of elements, as well as one or more common characteristics shared by those elements. As such, it...

s 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
Scotland is a country that is part of the United Kingdom. Occupying the northern third of the island of Great Britain, it shares a border with England to the south and is bounded by the North Sea to the east, the Atlantic Ocean to the north and west, and the North Channel and Irish Sea to the...

. The astronomer looks out of the window, sees a black sheepIn the English language, black sheep is an idiom used to describe an odd or disreputable member of a group, especially within a family. The term has typically been given negative implications, implying waywardness...

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 sheep, at least one side of which appears to be black from here."

## Non-mathematician's math

This 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 museum visitor was admiring a Tyrannosaurus
Tyrannosaurus meaning "tyrant," and sauros meaning "lizard") is a genus of coelurosaurian theropod dinosaur. The species Tyrannosaurus rex , commonly abbreviated to T. rex, is a fixture in popular culture. It lived throughout what is now western North America, with a much wider range than other...

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."

The joke is that the employee fails to understand the scientist's implication of the

uncertaintyThe significant figures of a number are those digits that carry meaning contributing to its precision. This includes all digits except:...

in the age of the fossil and uses

false precisionFalse precision occurs when numerical data are presented in a manner that implies better precision than is actually the case; since precision is a limit to accuracy, this often leads to overconfidence in the accuracy as well.In science and engineering, convention dictates that...

.

## 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 substantial mathematical content, 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

logicIn philosophy, Logic is the formal systematic study of the principles of valid inference and correct reasoning. Logic is used in most intellectual activities, but is studied primarily in the disciplines of philosophy, mathematics, semantics, and computer science...

al constructs such as

syllogismA syllogism is a kind of logical argument in which one proposition is inferred from two or more others of a certain form...

s:

**Example:**
Premise I: |
Knowledge is power. |

Premise II: |
Power corrupts. |

Conclusion: |
Therefore, knowledge corrupts. |

Another example:

SchoolA school is an institution designed for the teaching of students under the direction of teachers. Most countries have systems of formal education, which is commonly compulsory. In these systems, students progress through a series of schools...

is a practice for future life, and practice makes a man

perfect, but nobody is perfect, So Why Practice???

This is a quote by

Green DayGreen Day is an American punk rock band formed in 1987. The band consists of lead vocalist and guitarist Billie Joe Armstrong, bassist and backing vocalist Mike Dirnt, and drummer Tre Cool...

's frontman

Billie Joe ArmstrongBillie Joe Armstrong is an American rock musician and occasional actor, best known as the lead vocalist, main songwriter and lead guitarist for the American punk rock band Green Day...

.

Another states: Women are time and money. Since time equals money, women are money squared. Since money is the

root of all evil-Money:* First Epistle to Timothy in the New Testament , which contains the phrase, "The love of money is a root of all kinds of evil"...

, women equal the square root of evil squared. The square root and the second power cancel, thus women equal evil.

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

**Examples:**
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.

The "d's" from the first part of the equation are cancelled out and leave only one over x times x, equaling one. The first and last part of the equation are correct: the derivative of a first degree variable is 1, however the intermediate process is not mathematically sound, as "d" is not an algebraic expression but an operator.

### Calculator spelling

Calculator spelling is the formations of words and phrases by entering a number and turning the

calculatorAn electronic calculator is a small, portable, usually inexpensive electronic device used to perform the basic operations of arithmetic. Modern calculators are more portable than most computers, though most PDAs are comparable in size to handheld calculators.The first solid-state electronic...

upside down. The words can be accompanied by stories involving numbers that lead to the solution.

For example: 142 workers and 154 civilians fought over 69 oil fields for 5 days. What did they fight over?

14215469 x 5 = 71077345, which, when read upside down, appears roughly to be "ShELL OIL." This only appears correctly when the open top '

4' is used by the calculator.

## Math limericks

A math limerick is an expression which, when read aloud, matches the form of a

limerickA limerick is a kind of a witty, humorous, or nonsense poem, especially one in five-line or meter with a strict rhyme scheme , which is sometimes obscene with humorous intent. The form can be found in England as of the early years of the 18th century...

. The following example is attributed to Leigh Mercer:

This is read as follows:

- A dozen
A dozen is a grouping of approximately twelve. The dozen may be one of the earliest primitive groupings, perhaps because there are approximately a dozen cycles of the moon or months in a cycle of the sun or year...

, a grossA gross is equal to a dozen dozen, i.e. 12 × 12 = 144.It can be used in duodecimal counting. The use of gross likely originated from the fact that 144 can be counted on the fingers using the fingertips and first two joints of each finger when marked by the thumb of one hand. The other hand...

, and a score20 is the natural number following 19 and preceding 21. A group of twenty units may also be referred to as a score.-In mathematics:*20 is the basis for vigesimal number systems....

- Plus three times the square root of four
- Divided by seven
- Plus five times eleven
- Is nine squared and not a bit more.

## Donut and coffee mug topology joke

An often-repeated joke is that topologists can't tell a

coffee cupA coffee cup may refer to a type of container from which coffee is consumed. Coffee cups are typically made of glazed ceramic, and have a single handle, allowing for portability while still hot...

from a

doughnutA doughnut or donut is a fried dough food and is popular in many countries and prepared in various forms as a sweet snack that can be homemade or purchased in bakeries, supermarkets, food stalls, and franchised specialty outlets...

, since a sufficiently pliable doughnut could be reshaped (by a

homeomorphismIn the mathematical field of topology, a homeomorphism or topological isomorphism or bicontinuous function is a continuous function between topological spaces that has a continuous inverse function. Homeomorphisms are the isomorphisms in the category of topological spaces—that is, they are...

) to the form of a cup by creating a dimple and progressively enlarging it, while shrinking the hole into a handle.

## See also

- Funny numbers
- Ralph P. Boas, Jr.
- The Complexity of Songs
"The Complexity of Songs" was an article published by Donald Knuth, an example of an in-joke in computer science, namely, in computational complexity theory...

- Tom Lehrer
Thomas Andrew "Tom" Lehrer is an American singer-songwriter, satirist, pianist, mathematician and polymath. He has lectured on mathematics and musical theater...

- New Math (song)
- Spherical cow
Spherical cow is a metaphor for highly simplified scientific models of complex real life phenomena.-Jokes:The phrase comes from a joke about theoretical physicists:It is told in many variants...

## External links