mathematical joke

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

{{quote|

Q. What's purple and commutes?

A. An abelian grape. (A pun on abelian group.)}}

Occasionally, multiple mathematical puns appear in the same jest:

{{quote|When Noah sends his animals to go forth and multiply, a pair of snakes replies "We can't multiply, we're adders" – so Noah builds them a log table.{{Cite book | url = https://books.google.com/books?id=ldX0FkgurzoC&pg=PA261 | title = Science Askew : a light-hearted look at the scientific world | isbn = 9780750307147 | last1 = Simanek | first1 = Donald E. | last2 = Holden | first2 = John C. | date = 2001-10-01| publisher = CRC Press }}}}

This invokes four double meanings: adder (snake) vs. addition (algebraic operation); multiplication (biological reproduction) vs. multiplication (algebraic operation); log (a cut tree trunk) vs. log (logarithm); and table (set of facts) vs. table (piece of furniture).{{Cite book | url = https://books.google.com/books?id=e1CwC4paHAsC&pg=PA65 | title = The Language of Comic Narratives | isbn = 9783110208337 | last1 = Ermida | first1 = Isabel | date = 2008-12-10| publisher = Walter de Gruyter }}

Other jokes create a double meaning from a direct calculation involving facetious variable names, such as this retold from Gravity's Rainbow:{{cite web | url=http://www.physicsforums.com/showthread.php?t=71753 | title=Quick and Witty! | work=Physics Forums | date=April 6, 2005 | access-date=February 28, 2013 | author=polyb}}

{{quote|

Person 1: What's the integral of {{sfrac|1|cabin}} with respect to cabin?

Person 2: A log cabin.

Person 1: No, a houseboat; you forgot to add the C!{{Cite book | url = https://books.google.com/books?id=5NwF-Gdgg9YC&pg=PA145 | title = Thomas Pynchon | isbn = 9781438116112 | last1 = Bloom | first1 = Harold | date = 2009-01-01| publisher = Infobase }}}}

The first part of this joke relies on the fact that the primitive (formed when finding the antiderivative) of the function 1/x is log(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 calculus students may forget. Thus, the indefinite integral of 1/cabin is "log(cabin) + C", or "A log cabin plus the sea", i.e., "A houseboat".

Some jokes depend on ambiguity of numeral bases.

{{quote|There are only 10 types of people in the world: those who understand binary, and those who don't.}}

This joke subverts the trope of phrases that begin with "there are two types of people in the world..." and relies on an ambiguous meaning of the expression 10, which in the binary numeral system is equal to the decimal number 2.{{Cite book | url = https://books.google.com/books?id=kELa1UaugxUC&pg=PA31 | title = The Linguistic Analysis of Jokes | isbn = 9780203406953 | last1 = Ritchie | first1 = Graeme | date = 2002-06-01| publisher = Taylor & Francis }} There are many alternative versions of the joke, such as "There are two types of people in this world. Those who can extrapolate from incomplete information."{{cite web |author=Olicity8 |title=Two Types Of People |url=https://www.wattpad.com/289691067-nerd-jokes-explained-two-types-of-people |website=Wattpad |access-date=29 April 2019}}

Another pun using different radices, asks:

{{quote|

Q. Why do mathematicians confuse Halloween and Christmas?

A. Because 31 Oct = 25 Dec.{{Cite book | url = https://books.google.com/books?id=r8i-4En_aa4C&pg=PA385 | title = Applying Uml and Patterns | isbn = 9780130925695 | last1 = Larman | first1 = Craig | year = 2002| publisher = Prentice Hall Professional }}{{Cite book | url = https://books.google.com/books?id=e1VFN1V1zAAC&pg=PA78 | title = Are You a Geek? | isbn = 9780440336280 | last1 = Collins | first1 = Tim | date = 2006-08-29| publisher = Random House Publishing }}}}

The play on words lies in the similarity of the abbreviation for October/Octal and December/Decimal, and the coincidence that both equal the same number ($31\_8\; =\; 25\_\{10\}$).

File:Pythagorean_theorem_mathematical_joke.svg

Some jokes are based on imaginary number {{mvar|i}}, treating it as if it is a real number. A telephone intercept message of "you have dialed an imaginary number, please rotate your handset ninety degrees and try again" is a typical example.{{cite book|url=https://books.google.com/books?id=vQJCfjcAn2EC&pg=PA48 |title=In the Lab |author=Elizabeth Longmier |date= 2007-05-01|publisher=Lulu Press, Incorporated |access-date=2013-06-19|isbn=9781430322160}} Another popular example is:

"What did {{pi}} say to {{mvar|i}}?

Get real.

What did {{mvar|i}} say to {{pi}}?

Be rational."

Joke number 11 on Page 9,

36 Teacher Jokes,

17 pages,

October 17, 2013.

Simple K12, InfoSource Inc

Some jokes are based on stereotypes of mathematicians tending to think in complicated, abstract terms, causing them to lose touch with the "real world". These compare mathematicians to physicists, engineers, or the "soft" sciences in a form similar to an Englishman, an Irishman and a Scotsman, showing the other scientists doing something practical, while the mathematician proposes a theoretically valid but physically nonsensical solution.

{{quote|A physicist, a biologist and a mathematician are sitting in a street café watching people entering and leaving a nearby house. 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."{{Cite book | url = https://books.google.com/books?id=16MjPAH_CBYC&pg=PA542 | title = Calculus with Maple Labs : early transcendentals | isbn = 9781842650745 | last1 = Krawcewicz | first1 = Wiesław | last2 = Rai | first2 = B. | date = 2003-01-01| publisher = Alpha Science Int'l }}}}

Mathematicians are also shown as averse to making hasty generalizations from a small amount of data, even if some form of generalization seems plausible:

{{quote|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, "The sheep in Scotland are black!" "No, no, no!" says the physicist. "At least one sheep in Scotland is 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 some of the time."{{Cite book | url = https://books.google.com/books?id=PcqiXD_BxA4C&pg=PA286 | title = Concepts of Modern Mathematics | isbn = 9780486134956 | last1 = Stewart | first1 = Ian | year = 1995| publisher = Courier Corporation }}{{cite web | title=Jokebook for the Physical Sciences | website=math.bu.edu | url=https://math.bu.edu/people/jeffs/joke.html | access-date=13 October 2023}}}}

A classic joke involving stereotypes is the "Dictionary of Definitions of Terms Commonly Used in Math Lectures".[http://math.ucdenver.edu/~wcherowi/mathmajor/archive/def.html "Dictionary of Definitions of Terms Commonly Used in Math lectures."] Examples include "Trivial: If I have to show you how to do this, you're in the wrong class", "Similarly: At least one line of the proof of this case is the same as before" and "This proof is left as an exercise to the reader."

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.

{{quote|A museum visitor 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 be so precise?" 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."{{Cite book | url = https://books.google.com/books?id=ghJaYi3FELMC&pg=PT14 | title = Proofiness | isbn = 9781101443507 | last1 = Seife | first1 = Charles | date = 2010-09-23| publisher = Penguin }}}}

The joke is that the employee fails to understand the scientist's implication of the uncertainty in the age of the fossil and uses false precision.

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 scope. These constructions are generally devoid of any substantial mathematical content, besides some basic arithmetic.

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

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

$$\backslash left(\; \backslash lim\_\{x\backslash to\; 8^+\}\; \backslash frac\{1\}\{x-8\}\; =\; \backslash infty\; \backslash right)\; \backslash Rightarrow\; \backslash left(\; \backslash lim\_\{x\backslash to\; 3^+\}\; \backslash frac\{1\}\{x-3\}\; =\; \backslash omega\; \backslash right)$$

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 (conventionally used to notate the smallest infinite ordinal number).{{cite web |url=http://mgccl.com/2008/02/21/a-mathematical-look-into-the-limit-joke |title=A mathematical look into the limit joke |access-date=2008-04-19 |last=Xu |first=Chao |date=2008-02-21 |url-status=dead |archive-url=https://web.archive.org/web/20080224020052/http://mgccl.com/2008/02/21/a-mathematical-look-into-the-limit-joke |archive-date=2008-02-24 }}

An anomalous cancellation is a kind of arithmetic procedural error that gives a numerically correct answer:

• $\backslash frac\{64\}\{16\}\; =\; \backslash frac\{\backslash cancel\; 64\}\{\backslash ,\backslash ,1\backslash cancel\; 6\}\; =\; \backslash frac\{4\}\{1\}\; =\; 4$
• $\backslash sqrt[6]\{64\}\; =\; \backslash sqrt[\backslash cancel\; 6]\{\backslash cancel\{6\}4\}\; =\; \backslash sqrt\{4\}\; =\; 2$
• $\backslash frac\{\backslash mathrm\; d\}\{\backslash mathrm\; d\; x\}\backslash frac\{1\}\{x\}\; =\; \backslash frac\{\backslash cancel\backslash mathrm\; d\}\{\backslash cancel\backslash mathrm\; d\; x\}\backslash frac\; 1x\; =\; \backslash frac\{\}\{x\}\backslash frac\; 1x\; =\; -\backslash frac\; 1\{x^2\}$

A number of mathematical fallacies are part of mathematical humorous folklore. For example:

\begin{align}

b &= a \\

ab &= a^2 \\

ab - b^2 &= a^2 - b^2 \\

b(a - b) &= (a + b)(a - b) \\

b &= a + b \\

b &= b + b \\

b &= 2b \\

1 &= 2

\end{align}

This appears to prove that {{math|1=1 = 2}}, but uses division by zero to produce the result.Harro Heuser: Lehrbuch der Analysis{{snd}} Teil 1, 6th edition, Teubner 1989, {{isbn|978-3-8351-0131-9}}, page 51 (German).

Some jokes attempt a seemingly plausible, but in fact impossible, mathematical operation. For example:

Pi goes on and on and on ...

And e is just as cursed.

I wonder: Which is larger

When their digits are reversed?{{cite web |title=Pi goes on and on and on … |url=http://math.ucdenver.edu/~wcherowi/mathmajor/jff.html |website=JUST FOR FUN |publisher=Math Majors Matter |access-date=12 August 2018}}

To reverse the digits of a number's decimal expansion, we have to start at the last digit and work backwards. However, that is not possible if the expansion never ends, which is true in the case of $\backslash pi$ and $e$.

Many numbers have been given humorous names, either as pure numbers or as units of measurement. Some examples:

Sagan has been defined as "billions and billions", a metric of the number of stars in the observable universe.William Safire, [https://query.nytimes.com/gst/fullpage.html?res=9507E3DF143EF934A25757C0A962958260 ON LANGUAGE; Footprints on the Infobahn], New York Times, April 17, 1994[http://www.numericana.com/answer/sagan.htm Sizing up the Universe{{snd}} Stars, Sand and Nucleons{{snd}} Numericana]

Jenny's constant has been defined as $J\; =\; (7^\{e\; -\; 1/e\}\; -\; 9)\; \backslash cdot\; \backslash pi^2\; =\; 867.5309\backslash ldots.$ {{OEIS|A182369}}, from the pop song 867-5309/Jenny, which concerns the telephone number 867-5309.{{cite web|url=http://mathworld.wolfram.com/JennysConstant.html |title=Jenny's Constant |publisher=Wolfram MathWorld |date=2012-04-26 |access-date=2013-06-19}}

The number 42 appears prominently in the Douglas Adams trilogy The Hitchhiker's Guide to the Galaxy, where it is portrayed as "the answer to the ultimate question of life, the universe and everything".{{cite news|last=Gill|first=Peter|title=42: Douglas Adams' Amazingly Accurate Answer to Life the Universe and Everything|url=https://www.theguardian.com/books/2011/feb/03/douglas-adams-42-hitchhiker?INTCMP=SRCH|publisher=Guardian|access-date=2011-04-03|location=London|date=2011-02-03}} This number appears as a fixed value in the TIFF image file format and its derivatives (including for example the ISO standard TIFF/EP) where the content of bytes 2–3 is defined as 42: "An arbitrary but carefully chosen number that further identifies the file as a TIFF file".{{cite manual

| author = Aldus/Microsoft

| title = TIFF

| section = 1) Structure

| version = Revision 5.0

| publisher = Aldus Corporation and Microsoft Corporation

| date = 1999-08-09

| url = http://cool-palimpsest.stanford.edu/bytopic/imaging/std/tiff5.html

| access-date = 2009-06-29

| quote = The number 42 was chosen for its deep philosophical significance.

|archive-date = 2012-02-11

| archive-url = https://web.archive.org/web/20120211130146/http://cool.conservation-us.org/bytopic/imaging/std/tiff5.html

}}

The number 69 is commonly used in reference to a group of sex positions in which two people align to perform oral sex, thus becoming mutually inverted like the numerals 6 and 9. Because of this association, "69" has become an internet meme and is known as "the sex number" in certain communities.{{cite web | last=Feldman | first=Brian | title=Why 69 Is the Internet's Coolest Number (Sex) | website=Intelligencer | date=2016-06-09 | url=https://nymag.com/intelligencer/2016/06/why-69-is-the-internets-coolest-number-sex.html | access-date=2020-09-04}}

In the context of numerical humor, one classic example is the joke, "Why was six afraid of seven? Because seven eight (ate) nine!" The humor in this statement originates from a linguistic play on numbers and fundamental arithmetic.{{cite web | title=Adding Laughter to Numbers | website=Harvard.edu| url=https://tagteam.harvard.edu/remix/6331 }}

{{Main|Calculator spelling}}

Calculator spelling is the formation of words and phrases by displaying a number and turning the calculator upside down.{{Cite book | url = https://archive.org/details/amazingmathemati00bolt | url-access = registration | page = [https://archive.org/details/amazingmathemati00bolt/page/48 48] | title = The Amazing Mathematical Amusement Arcade | publisher = Cambridge University Press | isbn = 9780521269803 | last1 = Bolt | first1 = Brian | date = 1984-09-27}} The jest may be formulated as a mathematical problem where the result, when read upside down, appears to be an identifiable phrase like "ShELL OIL" or "Esso" using seven-segment display character representations where the open-top "4" is an inverted 'h' and '5' looks like 'S'. Other letters can be used as numbers too with 8 and 9 representing B and G, respectively.

An attributed example of calculator spelling, which dates from the 1970s,{{cite book|author1=Tom Dalzell|author2=Terry Victor|title=The Concise New Partridge Dictionary of Slang and Unconventional English|url=https://books.google.com/books?id=Ak6cBQAAQBAJ&q=5318008&pg=PA2060|date=27 November 2014|publisher=Taylor & Francis|isbn=978-1-317-62511-7|page=2060}} is 5318008, which when turned over spells "BOOBIES".

A mathematical limerick is an expression which, when read aloud, matches the form of a limerick. The following numerically correct example is attributed to Leigh Mercer:{{cite web|url=http://www.lhup.edu/~DSIMANEK/mayhem.htm |title=Math Mayhem |publisher=Lhup.edu |access-date=2011-06-29}}

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

This is read as follows:

{{quote|

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.}}

Another example using calculus is{{efn|The variable's name 'z' should be pronounced as zee to make a proper rhyme to 'three' and 'e'.}}:

$$\backslash int\_\{1\}^\{\backslash sqrt[3]\{3\}\}z^2\; dz\; \backslash cdot\; \backslash cos\backslash left(\backslash frac\{3\backslash pi\}\{9\}\backslash right)\; =\; \backslash log(\backslash sqrt[3]\{e\})$$

which may be read:

{{quote|

Integral z-squared dz

From one to the cube root of three

Times the cosine

of three pi over nine

Equals log of the cube root of e}}

The limerick is true if $\backslash log$ is interpreted as the natural logarithm.

Image:Mug and Torus morph.gif) and back]]

An oft-repeated joke is that topologists cannot tell a coffee cup from a doughnut,{{cite book|url=https://books.google.com/books?id=SHBj2oaSALoC&pg=PA204 |title=Differential Equations: A Dynamical Systems Approach : Higher-Dimensional Systems |date=1995-03-30 |access-date=2011-06-29|isbn=9780387943770|last1=West|first1=Beverly H|publisher=Springer }} since they are topologically equivalent: a sufficiently pliable doughnut could be reshaped (by a homeomorphism) to the form of a cup by creating a dimple and progressively enlarging it, while shrinking the hole into a handle.

Category theory is a common source of esoteric mathematical jokes, due to its high level of abstraction. Recall that a category is a kind of mathematical structure consisting of points and arrows between these points. For any concept in category theory, the dual concept reverses the directions of all arrows. The name of the dual concept is simply the name of the original concept with the prefix "co-" added in front. Thus,

{{quote|A coconut is just a nut.}}

The joke is that when the dual is taken twice, the direction of the arrows remains the same, and hence the double "co-" is redundant.

Another joke references a quote by Alfréd Rényi: "A mathematician is a device for turning coffee into theorems." If the dual is taken, the quote becomes

{{quote|A comathematician is a device for turning cotheorems into ffee.{{cite web|url=https://math.stackexchange.com/q/900390 |title=Joke explanation: "a comathematician is a device for turning cotheorems into ffee" |publisher=Mathematics StackExchange |access-date=2025-01-26}}}}

Not only are "coffee" and "theorems" dualized, their order is also swapped, since taking the dual reverses the direction of arrows.

• New Math (song)
• Spherical cow
• All horses are the same color
• When a white horse is not a horse

{{clear}}

{{Notelist}}

{{Reflist}}

• [http://mathworld.wolfram.com/topics/MathematicalHumor.html Mathematical Humor – from Mathworld]
• {{Cite journal|author=Paul Renteln and Alan Dundes|date=2004-12-08|url=https://www.ams.org/notices/200501/fea-dundes.pdf|title=Foolproof: A Sampling of Mathematical Folk Humor|journal=Notices of the AMS|volume=52|issue=1}}
• [http://www.businessinsider.com/13-math-jokes-that-every-mathematician-finds-absolutely-hilarious-2013-5 13 Jokes That Every Math Geek Will Find Hilarious]

{{DEFAULTSORT:Mathematical Joke}}

Category:In-jokes