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| 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, or from a lay person's misunderstanding of a mathematical concept. Mathematician and author [[John Allen Paulos]] in his book ''Mathematics and Humor'' described several ways that mathematics, generally considered a dry, formal activity, overlaps with humor, a loose, irreverent activity: both are forms of "intellectual play"; both have "logic, pattern, rules, structure"; and both are "economical and explicit".<ref>{{cite book|title=Mathematics and Humor|author=John Allen Paulos}}</ref>
| | Emilia Shryock is my name but you can call me something you like. For years he's been operating as a receptionist. Her family life in Minnesota. One of the very best issues in the world for me is to do aerobics and now I'm trying to earn cash with it.<br><br>Have a look at my weblog; at home std testing ([http://www.youporn-nederlandse.com/blog/117384 Click Home]) |
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| Some performers combine mathematics and jokes to entertain and/or teach math.<ref>{{cite web|url=http://www.mathscareers.org.uk/viewItem.cfm?cit_id=383215 |title=Matt Parker, math stand-up comedian |publisher=Mathscareers.org.uk |date=2011-08-04 |accessdate=2013-07-01}}</ref><ref>{{cite web|url=http://www.comedy.co.uk/guide/tv/dara_o_briain_school_hard_sums/episodes/ |title=Dara O'Briain: School of hard sums |publisher=Comedy.co.uk |date= |accessdate=2013-07-01}}</ref><ref>{{cite web|last=Schimmrich |first=Steven |url=http://hudsonvalleygeologist.blogspot.com/2011/05/dave-gorman-math-stand-up-comedy.html |title=Dave Gorman - stand-up math comedy |publisher= |date=2011-05-17 |accessdate=2013-07-01}}</ref>
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| ==Pun-based jokes==
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| [[Image:Acanthophis laevis.jpg|thumb|“We can't multiply, we're [[Vipera berus|adders]]"]]
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| Some jokes use a mathematical term with a second non-technical meaning as the punchline of a joke.
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| :Q. What's purple and commutes?
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| :A. An Abelian grape. (A pun on ''[[Abelian group]]''.)<ref name=mw-abel>{{MathWorld |title=Abelian Group |urlname=AbelianGroup}}, citing Renteln, P. and Dundes, A. "Foolproof: A Sampling of Mathematical Folk Humor." Notices Amer. Math. Soc. 52, 24-34, 2005. </ref>
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| Occasionally multiple mathematical puns appear in the same jest:
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| :"When [[Noah's Ark|Noah sends his animals]] to go forth and multiply, a pair of snakes replies “We can't multiply, we're [[Vipera berus|adders]]” — so [[Noah]] builds them a [[log table]]."<ref>{{Cite journal | url = http://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}}</ref>
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| This invokes three [[double meaning]]s: [[Vipera berus|adder (snake)]] vs. [[addition]] (algebraic operation); [[reproduction|multiplication (biological reproduction)]] vs. [[multiplication]] (algebraic operation); [[logging|log]] (cut [[tree trunk]]) vs. [[logarithm|log]] (mathematical logarithm)<ref>{{Cite journal | url = http://books.google.com/books?id=e1CwC4paHAsC&pg=PA65 | title = The Language of Comic Narratives | isbn = 9783110208337 | author1 = Ermida | first1 = Isabel | date = 2008-12-10}}</ref>
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| [[Image:Grand Turk(34).jpg|thumb|log(book) + C]]
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| Other jokes create a double meaning from a direct calculation involving facetious variable names, such as this retold from ''[[Gravity's Rainbow]]'':<ref>{{cite web | url=http://www.physicsforums.com/showthread.php?t=71753 | title=Quick and Witty! | work=Physics Forums | date=April 6, 2005 | accessdate=February 28, 2013 | author=polyb}}</ref>
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| :Person 1: What's the integral of <sup>1</sup>/<sub>cabin</sub> with respect to cabin?
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| :Person 2: A log cabin.
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| :Person 1: No, a houseboat; you forgot to add the C!<ref>{{Cite journal | url = http://books.google.com/books?id=5NwF-Gdgg9YC&pg=PA145 | title = Thomas Pynchon | isbn = 9781438116112 | author1 = Bloom | first1 = Harold | date = 2009-01-01}}</ref>
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| The first part of this joke relies on the fact that the primitive (formed when finding the [[antiderivative]]) of the function 1/''x'' is [[Natural logarithm|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]]".
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| ==Jokes with numeral bases==
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| :"There are only 10 types of people in the world: those who understand [[binary numeral system|binary]], and those who don't."
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| This well-known joke<ref>[https://www.thinkgeek.com/product/5aa9/ "binary people" t-shirt]</ref> mocks 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 (number)|two]] and in any arbitrary numeral system is equal to the number base in use.<ref>{{Cite journal | url = http://books.google.com/books?id=kELa1UaugxUC&pg=PA31 | title = The Linguistic Analysis of Jokes | isbn = 9780203406953 | author1 = Ritchie | first1 = Graeme | date = 2002-06-01}}</ref>
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| Another [[pun]] using different [[radix|radices]], sometimes attributed to computer scientists, asks:
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| :Why do mathematicians confuse [[Halloween]] and [[Christmas]]?
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| :Because 31 [[Octal|Oct]] = 25 [[Decimal|Dec]].<ref>{{Cite journal | url = http://books.google.com/books?id=r8i-4En_aa4C&pg=PA385 | title = Applying Uml and Patterns | isbn = 9780130925695 | author1 = Larman | first1 = Craig | year = 2002}}</ref><ref>{{Cite journal | url = http://books.google.com/books?id=e1VFN1V1zAAC&pg=PA78 | title = Are You a Geek? | isbn = 9780440336280 | author1 = Collins | first1 = Tim | date = 2006-08-29}}</ref>
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| The play on words lies in the similarity of the abbreviation for October/[[Octal]] and December/Decimal, and the coincidence that the two representations equal the same amount (31 Octal is <math>3\cdot8 + 1 = 2\cdot10 + 5 = 25</math> Decimal).
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| ==Imaginary and complex numbers==
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| In mathematics, an [[imaginary number]] is a square root of a negative quantity, such as the constant ''i'':
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| <math>i = \sqrt{ -1}</math>
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| A [[complex number]] is a quantity which can be written as the sum of a [[real number]] plus an imaginary number.
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| While a pun has been based upon the constant's name ("complex numbers are all fun and games until someone loses an i"), most jokes treat an imaginary number as if it were a fictional entity. A telephone [[intercept message]] of "you have dialled an imaginary number, please rotate your handset ninety degrees and try again" is a typical example.<ref>{{cite book|url=http://books.google.com/books?id=vQJCfjcAn2EC&pg=PA48 |title=In the Lab |author=Elizabeth Longmier |date= 2007-05-01|accessdate=2013-06-19|isbn=9781430322160}}</ref>
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| The most common application of imaginary and complex numbers to physical quantities is in [[electrical engineering]], where the imaginary component serves in [[alternating current]] calculations to represent current drawn 90° out of phase with voltage. As this [[imaginary power]] serves only to repeatedly charge and discharge [[electrical reactance|reactive]] elements such as [[capacitor]]s and [[inductor]]s, it does no useful work.<ref>{{cite book|url=http://books.google.com/books?id=GZQdJwKP3Q4C&pg=PA31 |title=Power System Analysis |author=P. P. Deo |date= 2007-01-01|accessdate=2013-06-19|isbn=9788184311242}}</ref> A utility may financially penalise a large industrial client for a low [[power factor]] which requires larger [[electrical conductor]]s to carry these out-of-phase currents.
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| A mathematical joke would describe a factory manager balking "Why should real money be paid for imaginary power?" and issuing a cheque for real money for the useful real power the factory consumes, plus a separate cheque for the square root of negative one dollars for the imaginary power the factory's owner never ordered and did not want.
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| ==Stereotypes of mathematicians==
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| 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 [[physicist]]s, [[engineer]]s, or the [[Soft science|"soft" sciences]] in a form similar to [[an Englishman, an Irishman and a Scotsman]], showing the other scientist doing something practical, while the mathematician proposes a theoretically valid but physically nonsensical solution.
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| :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."<ref>{{Cite journal | url = http://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}}</ref>
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| Mathematicians are also shown as averse to making sweeping [[generalization]]s from a small amount of data, even if some form of generalization seems plausible:
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| :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. All the sheep in Scotland 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 some of the time."<ref>{{Cite journal | url = http://books.google.com/books?id=PcqiXD_BxA4C&pg=PA286 | title = Concepts of Modern Mathematics | isbn = 9780486134956 | author1 = Stewart | first1 = Ian | year = 1995}}</ref>
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| A classic joke involving stereotypes is the "Dictionary of Definitions of Terms Commonly Used in Math Lectures."<ref>Calculus Humor, [http://www.calculushumor.com/3/post/2012/06/dictionary-of-definitions-of-terms-commonly-used-in-math-lectures.html?utm_source=Wikipedia%3A%2BMath%2BJokes&utm_medium=Wikipedia%2BCite&utm_campaign=Wikipedia%2BMath%2BJokes%2BLink-2 Dictionary of Definitions of Terms Commonly Used in Math Lectures] from [http://www.calculushumor.com/?utm_source=Wikipedia%3A%2BMath%2BJokes&utm_medium=Wikipedia%2BCite-2&utm_campaign=Wikipedia%2BMath%2BJokes%2BLink-3 Calculus humor]</ref> Examples include "Trivial: If I have to show you how to do this, you're in the wrong class" and "Similarly: At least one line of the proof of this case is the same as before."
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| ==Non-mathematician's math==
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| 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.
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| :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 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."<ref>{{Cite journal | url = http://books.google.com/books?id=ghJaYi3FELMC&pg=PT14 | title = Proofiness | isbn = 9781101443507 | author1 = Seife | first1 = Charles | date = 2010-09-23}}</ref>
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| The joke is that the employee fails to understand the scientist's implication of the [[Significant figures|uncertainty]] in the age of the fossil and uses [[false precision]].
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| ==Mock mathematics==
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| 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.
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| ===Mock mathematical reasoning===
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| 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 [[logic]]al constructs such as [[syllogism]]s:
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| :{|
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| |''Premise I:'' || Knowledge is power.
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| |-
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| | ''Premise II:'' || Power corrupts.
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| |-
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| | ''Conclusion:'' || Therefore, knowledge corrupts.''
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| |}<ref>{{Cite journal | url = http://books.google.com/books?id=W-9NNTtd9NUC&pg=PA143 | title = Plato's Sun | isbn = 9780802038098 | author1 = Lawless | first1 = Andrew | year = 2005}}</ref>
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| Another set of jokes relate to the absence of mathematical reasoning, or misinterpretation of conventional notation:
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| :<math>\left( \lim_{x\to 8^+} \frac{1}{x-8} = \infty \right) \Rightarrow \left( \lim_{x\to 3^+} \frac{1}{x-3} = \omega \right)</math>
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| 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.<ref>{{cite web|url=http://mgccl.com/2008/02/21/a-mathematical-look-into-the-limit-joke |title=A mathematical look into the limit joke |accessdate=2008-04-19 |last=Xu |first=Chao |date=2008-02-21 }}</ref>
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| :<math>\frac{d}{dx} (x) = \frac{1}{x}x = 1</math>
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| 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.
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| Another variant of this joke cancels out digits within the numerator and denominator of a fraction:
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| :<math>\frac{6 4}{1 6} = \frac{/\!\!\!{6}\;{4}}{{1}\;/\!\!\!{6}} = \frac{4}{1} = 4</math>
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| This produces the correct answer, but uses improper arithmetic.
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| ===Mathematical fallacies===
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| A number of [[mathematical fallacies]] are part of mathematical humorous folklore. For example:
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| :<math>
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| \begin{align}
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| a &= b \\
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| a^2 &= b^2 \\
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| ab - b^2 &= a^2 - b^2 \\
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| b(a - b) &= (a + b)(a - b) \\
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| b &= a + b \\
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| b &= b + b \\
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| b &= 2b \\
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| 1 &= 2
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| \end{align}
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| </math>
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| This appears to prove that {{math|1=1 = 2}}, but uses incorrect algebraic manipulations (specifically, [[division by zero]]) to produce the result.<ref>Harro Heuser: ''Lehrbuch der Analysis - Teil 1'', 6th edition, Teubner 1989, ISBN 978-3-8351-0131-9, page 51 (German).</ref>
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| See also: [[All horses are the same color]].
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| ===Humorous numbers===
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| {{main|List of humorous units of measurement}}
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| [[Sagan (number)]] has been defined as "billions and billions", a metric of the number of stars in the observable universe.<ref>[[William Safire]], [http://query.nytimes.com/gst/fullpage.html?res=9507E3DF143EF934A25757C0A962958260 ON LANGUAGE; Footprints on the Infobahn], ''[[New York Times]]'', April 17, 1994</ref><ref>[http://www.numericana.com/answer/sagan.htm Sizing up the Universe - Stars, Sand and Nucleons - Numericana]</ref>
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| Similarly, [[867-5309/Jenny|Jenny's constant]] has been defined as <math>J = (7^{e - 1/e} - 9) \cdot \pi^2 = 867.5309...</math> {{OEIS|A182369}}, a [[fictitious telephone number|fictional telephone number]].<ref>{{cite web|url=http://mathworld.wolfram.com/JennysConstant.html |title=Jenny's Constant |publisher=Wolfram MathWorld |date=2012-04-26 |accessdate=2013-06-19}}</ref>
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| The mathematical constant [[42 (number)|42]] appears throughout the [[Douglas Adams]] trilogy ''[[The Hitchhiker's Guide to the Galaxy]]'', where it is portrayed as "the answer to life, the universe and everything".<ref>{{cite news|last=Gill|first=Peter|title=42: Douglas Adams' Amazingly Accurate Answer to Life the Universe and Everything|url=http://www.guardian.co.uk/books/2011/feb/03/douglas-adams-42-hitchhiker?INTCMP=SRCH|publisher=Guardian|accessdate=2011-04-03|location=London|date=2011-02-03}}</ref>
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| The 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".<ref>{{cite manual
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| | author = Aldus/Microsoft
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| | title = TIFF
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| | section = 1) Structure
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| | version = Revision 5.0
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| | publisher = Aldus Corporation and Microsoft Corporation
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| | date = 1999-08-09
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| | url = http://cool-palimpsest.stanford.edu/bytopic/imaging/std/tiff5.html
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| | accessdate = 2009-06-29
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| | quote = The number 42 was chosen for its deep philosophical significance.
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| }}</ref>
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| ===Calculator spelling===
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| {{main|Calculator spelling}}
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| Calculator spelling is the formations of words and phrases by displaying a number and turning the [[calculator]] upside down.<ref>{{Cite journal | url = http://books.google.com/books?id=vIxed-m4_bQC&pg=PA48 | title = The Amazing Mathematical Amusement Arcade | isbn = 9780521269803 | author1 = Bolt | first1 = Brian | date = 1984-09-27}}</ref> 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|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 used as numbers too with 8 and 9 representing B and G, respectively.
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| ===Limericks===
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| A mathematical limerick is an expression which, when read aloud, matches the form of a [[Limerick (poetry)|limerick]]. The following example is attributed to [[Leigh Mercer]]:<ref>{{cite web|url=http://www.lhup.edu/~DSIMANEK/mayhem.htm |title=Math Mayhem |publisher=Lhup.edu |date= |accessdate=2011-06-29}}</ref>
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| :<math> \frac{12 + 144 + 20 + 3 \sqrt{4}}{7} + (5 \times 11) = 9^2+0</math>
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| This is read as follows:
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| : A [[dozen]], a [[Gross (unit)|gross]], and a [[20 (number)|score]]
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| : Plus three times the square root of four
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| : Divided by seven
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| : Plus five times eleven
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| : Is nine squared and not a bit more.
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| ==Doughnut and coffee mug topology joke==
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| [[Image:Mug and Torus morph.gif|thumb|right|240px|A continuous deformation (homeomorphism) of a coffee cup into a doughnut ([[torus]]) and back.]]
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| An oft-repeated joke is that [[topologist]]s can't tell a [[coffee cup]] from a [[doughnut]],<ref>{{cite book|url=http://books.google.com/books?id=SHBj2oaSALoC&pg=PA204 |title=Differential Equations: A Dynamical Systems Approach : Higher-Dimensional Systems |date=1995-03-30 |accessdate=2011-06-29|isbn=9780387943770|author1=West|first1=Beverly H}}</ref> since 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.
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| ==See also==
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| *[[Inherently funny words#Funny numbers|Funny numbers]]
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| *[[New Math (song)]]
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| *[[Spherical cow]]
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| *[[Mathematical fallacy]]
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| ==References==
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| {{Reflist}}
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| ==External links==
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| * [http://www.ams.org/notices/200501/fea-dundes.pdf A Sampling of Mathematical Folk Humor]
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| * [http://mathworld.wolfram.com/topics/MathematicalHumor.html Mathematical Humor — from Mathworld]
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| * {{Cite journal|author=Paul Renteln and Alan Dundes|date=2004-12-08|url=http://www.ams.org/notices/200501/fea-dundes.pdf|format=PDF|title=Foolproof: A Sampling of Mathematical Folk Humor|journal=Notices of the AMS|volume=52|issue=1}}
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| {{DEFAULTSORT:Mathematical Joke}}
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| [[Category:Jokes]]
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| [[Category:Mathematical humor]]
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