A mathematical joke is a form of humor which relies on aspects of mathematics or a stereotype of mathematicians. 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".
Humor of mathematicians may be classified into the esoteric and exoteric categories. Esoteric jokes rely on the intrinsic knowledge of mathematics and its terminology. Exoteric jokes are intelligible to the outsiders, and most of them compare mathematicians with representatives of other disciplines or with common folk.
|Rebus for "I ate some pie."|
Some jokes 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.)
Occasionally, multiple mathematical puns appear in the same jest:
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).
Person 1: What's the integral of 1/ 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 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".
Jokes with numeral bases
Some jokes depend on ambiguity of numeral bases.
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. 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."
Another pun using different radices, asks:
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 amount ().
Some jokes are based on imaginary number 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. Another popular example is: "What did π say to i? Get real. What did i say to π? Be rational." 
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". 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 scientist doing something practical, while the mathematician proposes a theoretically valid but physically nonsensical solution.
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."
Mathematicians are also shown as averse to making hasty generalizations from a small amount of data, 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. 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."
A classic joke involving stereotypes is the "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" and "Similarly: At least one line of the proof of this case is the same as before."
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.
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."
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.
Mock mathematical reasoning
|Premise I:||Knowledge is power.|
|Premise II:||Power corrupts.|
|Conclusion:||Therefore, knowledge corrupts.|
Another set of jokes relate to the absence of mathematical reasoning, or misinterpretation of conventional notation:
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).
An anomalous cancellation is a kind of arithmetic procedural error that gives a numerically correct answer:
A number of mathematical fallacies are part of mathematical humorous folklore. For example:
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?
To reverse the digits of a number's decimal expansion, we have to start at the last digit and work backwards. However, that's not possible if the expansion never ends, as for and .
The mathematical constant 42 appears throughout 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". 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".
Calculator spelling is the formation of words and phrases by displaying a number and turning the calculator upside down. 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.
Doughnut and coffee mug topology joke
An oft-repeated joke is that topologists cannot tell a coffee cup from a doughnut, 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.
- John Allen Paulos. Mathematics and Humor.
- "Matt Parker, math stand-up comedian". Mathscareers.org.uk. 2011-08-04. Retrieved 2013-07-01.
- "Dara O'Briain: School of hard sums". Comedy.co.uk. Retrieved 2013-07-01.
- Schimmrich, Steven (2011-05-17). "Dave Gorman – stand-up math comedy". Retrieved 2013-07-01.
- Paul Renteln, Alan Dundes, Foolproof: A Sampling of Mathematical Folk Humor, NOTICES OF THE AMS, VOLUME 52, NUMBER 1, 2005, pp. 24-34.
- Simanek, Donald E.; Holden, John C. (2001-10-01). Science Askew : a light-hearted look at the scientific world. ISBN 9780750307147.
- Ermida, Isabel (2008-12-10). The Language of Comic Narratives. ISBN 9783110208337.
- polyb (April 6, 2005). "Quick and Witty!". Physics Forums. Retrieved February 28, 2013.
- Bloom, Harold (2009-01-01). Thomas Pynchon. ISBN 9781438116112.
- Ritchie, Graeme (2002-06-01). The Linguistic Analysis of Jokes. ISBN 9780203406953.
- Olicity8. "Two Types Of People". Wattpad. Retrieved 29 April 2019.
- Larman, Craig (2002). Applying Uml and Patterns. ISBN 9780130925695.
- Collins, Tim (2006-08-29). Are You a Geek?. ISBN 9780440336280.
- Elizabeth Longmier (2007-05-01). In the Lab. ISBN 9781430322160. Retrieved 2013-06-19.
- Joke number 11 on Page 9, 36 Teacher Jokes, 17 pages, October 17, 2013. Simple K12, InfoSource Inc
- Krawcewicz, Wiesław; Rai, B. (2003-01-01). Calculus with Maple Labs : early transcendentals. ISBN 9781842650745.
- Stewart, Ian (1995). Concepts of Modern Mathematics. ISBN 9780486134956.
- "Dictionary of Definitions of Terms Commonly Used in Math lectures."
- Seife, Charles (2010-09-23). Proofiness. ISBN 9781101443507.
- Lawless, Andrew (2005). Plato's Sun. ISBN 9780802038098.
- Xu, Chao (2008-02-21). "A mathematical look into the limit joke". Archived from the original on 2008-02-24. Retrieved 2008-04-19.
- Harro Heuser: Lehrbuch der Analysis – Teil 1, 6th edition, Teubner 1989, ISBN 978-3-8351-0131-9, page 51 (German).
- "Pi goes on and on and on …". JUST FOR FUN. Math Majors Matter. Retrieved 12 August 2018.
- William Safire, ON LANGUAGE; Footprints on the Infobahn, New York Times, April 17, 1994
- Sizing up the Universe – Stars, Sand and Nucleons – Numericana
- "Jenny's Constant". Wolfram MathWorld. 2012-04-26. Retrieved 2013-06-19.
- Gill, Peter (2011-02-03). "42: Douglas Adams' Amazingly Accurate Answer to Life the Universe and Everything". London: Guardian. Retrieved 2011-04-03.
- Aldus/Microsoft (1999-08-09). "1) Structure". TIFF. Revision 5.0. Aldus Corporation and Microsoft Corporation. Archived from the original on 2012-02-11. Retrieved 2009-06-29.
The number 42 was chosen for its deep philosophical significance.
- Bolt, Brian (1984-09-27). The Amazing Mathematical Amusement Arcade. Cambridge University Press. p. 48. ISBN 9780521269803.
- "Math Mayhem". Lhup.edu. Retrieved 2011-06-29.
- West, Beverly H (1995-03-30). Differential Equations: A Dynamical Systems Approach : Higher-Dimensional Systems. ISBN 9780387943770. Retrieved 2011-06-29.
- A Sampling of Mathematical Folk Humor
- Mathematical Humor – from Mathworld
- Paul Renteln and Alan Dundes (2004-12-08). "Foolproof: A Sampling of Mathematical Folk Humor" (PDF). Notices of the AMS. 52 (1).
- 13 Jokes That Every Math Geek Will Find Hilarious