View source for Recreational mathematics

{{short description|Form of entertainment in mathematics}}
{{Math topics TOC}}
'''Recreational mathematics''' is [[mathematics]] carried out for [[recreation]] (entertainment) rather than as a strictly research-and-application-based professional activity or as a part of a student's formal education. Although it is not necessarily limited to being an endeavor for [[List of amateur mathematicians|amateurs]], many topics in this field require no knowledge of advanced mathematics. Recreational mathematics involves [[mathematical puzzle]]s and [[Mathematical games|games]], often appealing to children and untrained adults and inspiring their further study of the subject.<ref>Kulkarni, D. [http://www.matholympiad.info/Documents/TeachingWithKenKen.pdf Enjoying Math: Learning Problem Solving With KenKen Puzzles] {{webarchive|url=https://web.archive.org/web/20130801080339/http://www.matholympiad.info/Documents/TeachingWithKenKen.pdf |date=2013-08-01 }}, a textbook for teaching with KenKen Puzzles.</ref>

The [[Mathematical Association of America]] (MAA) includes recreational mathematics as one of its seventeen [[Mathematical Association of America#Special Interest Groups|Special Interest Groups]], commenting:
{{Blockquote|Recreational mathematics is not easily defined because it is more than mathematics done as a diversion or playing games that involve mathematics. Recreational mathematics is inspired by deep ideas that are hidden in puzzles, games, and other forms of play. The aim of the SIGMAA on Recreational Mathematics (SIGMAA-Rec) is to bring together enthusiasts and researchers in the myriad of topics that fall under recreational math. We will share results and ideas from our work, show that real, deep mathematics is there awaiting those who look, and welcome those who wish to become involved in this branch of mathematics.<ref>[https://www.maa.org/community/sigmaas Special Interest Groups of the MAA] {{Webarchive|url=https://web.archive.org/web/20130718123507/https://www.maa.org/community/sigmaas |date=2013-07-18 }} Mathematical Association of America</ref>}}

Mathematical competitions (such as those sponsored by [[Mathematical Association|mathematical association]]s) are also categorized under recreational mathematics.

== Topics ==

Some of the more well-known topics in recreational mathematics are [[Rubik's Cube]]s, [[magic squares]], [[fractals]], [[logic puzzle]]s and [[mathematical chess problem]]s, but this area of mathematics includes the [[aesthetics]] and [[culture]] of mathematics, peculiar or amusing stories and [[mathematical coincidence|coincidences about mathematics]], and the personal lives of [[mathematician]]s.

===Mathematical games===
[[Mathematical game]]s are [[multiplayer game]]s whose rules, strategies, and outcomes can be studied and explained using [[mathematics]]. The players of the game may not need to use explicit mathematics in order to play mathematical games. For example, [[Mancala]] is studied in the mathematical field of [[combinatorial game theory]], but no mathematics is necessary in order to play it.

===Mathematical puzzles===
[[Mathematical puzzle]]s require mathematics in order to solve them. They have specific rules, as do [[multiplayer game]]s, but mathematical puzzles do not usually involve competition between two or more players. Instead, in order to solve such a [[puzzle]], the solver must find a solution that satisfies the given conditions.

[[Logic puzzle]]s and [[classical cipher]]s are common examples of mathematical puzzles. [[Cellular automata]] and [[fractals]] are also considered mathematical puzzles, even though the solver only interacts with them by providing a set of initial conditions.

As they often include or require game-like features or thinking, mathematical puzzles are sometimes also called mathematical games.

=== Mathemagics ===
[[Magic tricks]] based on mathematical principles can produce self-working but surprising effects. For instance, a [[mathemagician]] might use the [[combinatorics|combinatorial]] properties of a deck of [[Standard 52-card deck|playing cards]] to guess a volunteer's selected card, or [[Hamming codes]] to identify whether a volunteer is lying.<ref>{{Cite book|last=Teixeira|first=Ricardo|title=Mathemagics: A Magical Journey through Advanced Mathematics|publisher=World Scientific|year=2020|isbn=9789811214509|location=USA}}</ref>

===Other activities===
Other curiosities and pastimes of non-trivial mathematical interest include:
* patterns in [[juggling]]
* the sometimes profound algorithmic and geometrical characteristics of [[origami]]
* patterns and process in creating [[string figure]]s such as [[Cat's cradle]]s, etc.
* [[fractal-generating software]]

==Online blogs, podcasts, and YouTube channels==
<!-- EDITOR NOTE: This is for *notable* entries. This generally would mean that there is already a page existing for the person or thing. -->
There are many blogs and audio or video series devoted to recreational mathematics.  Among the notable are the following:
* [[Cut-the-Knot]] by [[Alexander Bogomolny]]
* [[Futility Closet]] by Greg Ross
* [https://youtube.com/@Mathologer Mathologer] by [[Burkard Polster]]
* [[Numberphile]] by [[Brady Haran]]
* [https://www.youtube.com/user/standupmaths Stand-Up Maths] by [[Matt Parker]]
* The videos of [[Vi Hart]]

==Publications==
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* The journal ''[[Eureka (University of Cambridge magazine)|Eureka]]'' published by the mathematical society of the [[University of Cambridge]] is one of the oldest publications in recreational mathematics. It has been published 60 times since 1939 and authors have included many famous mathematicians and scientists such as [[Martin Gardner]], [[John Horton Conway|John Conway]], [[Roger Penrose]], [[Ian Stewart (mathematician)|Ian Stewart]], [[Timothy Gowers]], [[Stephen Hawking]] and [[Paul Dirac]].
* The ''[[Journal of Recreational Mathematics]]'' was the largest publication on this topic from its founding in 1968 until 2014 when it ceased publication.
* ''[[List of Martin Gardner Mathematical Games columns|Mathematical Games]]'' (1956 to 1981) was the title of a long-running ''[[Scientific American]]'' column on recreational mathematics by [[Martin Gardner]].  He inspired several generations of mathematicians and scientists through his interest in mathematical recreations. "Mathematical Games" was succeeded by 25 "[[Metamagical Themas]]" columns (1981-1983), a similarly distinguished, but shorter-running, column by [[Douglas Hofstadter]], then by 78 "Mathematical Recreations" and "Computer Recreations" columns (1984 to 1991) by [[A. K. Dewdney]], then by 96 "Mathematical Recreations" columns (1991 to 2001) by [[Ian Stewart (mathematician)|Ian Stewart]], and most recently "Puzzling Adventures" by [[Dennis Shasha]].
* The [http://rmm.ludus-opuscula.org/ Recreational Mathematics Magazine], published by the [http://ludicum.org/ Ludus Association], is electronic and semiannual, and focuses on results that provide amusing, witty but nonetheless original and scientifically profound mathematical nuggets. The issues are published in the exact moments of the equinox.

== People ==
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Prominent practitioners and advocates of recreational mathematics have included professional and [[List of amateur mathematicians|amateur mathematicians]]:

{| class="wikitable sortable" style="white-space:nowrap;"
! Full name || Last name || Born || Died || Nationality
! Description
|-
| [[Lewis Carroll]] (Charles Dodgson) || Carroll || 1832 || 1898 || English
|style="white-space:normal;"| Mathematician, puzzlist and [[Anglican]] [[deacon]] best known as the author of ''[[Alice in Wonderland]]'' and ''[[Through the Looking-Glass]].''
|-
| [[Sam Loyd]] || Loyd || 1841 || 1911 || American
|style="white-space:normal;"| [[Chess problem]] composer and author, described as "America's greatest [[puzzlist]]" by [[Martin Gardner]].<ref>Loyd, Sam (1959). ''Mathematical Puzzles of Sam Loyd'' (selected and edited by [[Martin Gardner]]), Dover Publications Inc., p. xi, {{ISBN|0-486-20498-7}}</ref>
|-
| [[Henry Dudeney]] || Dudeney || 1857 || 1930 || English
|style="white-space:normal;"| [[Civil servant]] described as England's "greatest puzzlist".<ref>{{citation|contribution=Henry Ernest Dudeney: Britain's Greatest Puzzlist|first=Angela|last=Newing|title=The Lighter Side of Mathematics: Proceedings of the Eugène Strens Memorial Conference on Recreational Mathematics and Its History|year=1994|editor1-first=Richard K.|editor1-last=Guy|editor1-link=Richard K. Guy|editor2-first=Robert E.|editor2-last=Woodrow|publisher=Cambridge University Press|isbn= 9780883855164|url=https://books.google.com/books?id=-4W_5ZISxpsC&pg=PA294|pages=294–301}}.</ref>
|-
| [[Yakov Perelman]] || Perelman || 1882 || 1942 || Russian
|style="white-space:normal;"| Author of many [[popular science]] and [[popular mathematics|mathematics]] books, including ''Mathematics Can Be Fun.''
|-
| J.A.H. Hunter || Hunter || 1902 || 1986 || British
| style="white-space:normal;"| Author of ''Fun with Figures''.
|-
| [[D. R. Kaprekar]] || Kaprekar || 1905 || 1986 || Indian
|style="white-space:normal;"| Discovered several results in [[number theory]], described several [[Template:Classes of natural numbers|classes of natural numbers]] including the [[Kaprekar number|Kaprekar]], [[harshad number|harshad]] and [[self number|self]] numbers, and discovered the [[Kaprekar's constant]]
|-
| [[Martin Gardner]] || Gardner || 1914 || 2010 || American
|style="white-space:normal;"| [[Popular mathematics]] and [[Popular science|science]] writer; author of ''Mathematical Games'', a long-running ''[[Scientific American]]'' column.
|-
| [[Raymond Smullyan]] || Smullyan || 1919 || 2017 || American
|style="white-space:normal;"| Logician; author of many logic puzzle books including "[[To Mock a Mockingbird]]".
|-
| [[Joseph Madachy]] || Madachy || 1927 || 2014 || American
|style="white-space:normal;"| Long-time editor of ''[[Journal of Recreational Mathematics]]'', author of ''Mathematics on Vacation.''
|-
| [[Solomon W. Golomb]]{{nbsp|2}} || Golomb || 1932 || 2016 || American
|style="white-space:normal;"| Mathematician and engineer, best known as the inventor of [[polyominoes]].
|-
| [[John Horton Conway]]{{nbsp|2}} || Conway || 1937 || 2020 || English
|style="white-space:normal;"| Mathematician and inventor of [[Conway's Game of Life]], co-author of ''[[Winning Ways]]'', an analysis of many [[mathematical games]].
|-
| [[Noboyuki Yoshigahara]]{{nbsp|2}} || Yoshigahara || 1936 || 2004 || Japanese
|style="white-space:normal;"|  Japan's most celebrated inventor, collector, solver, and communicator of puzzles.
|-
|[[Lee Sallows]]
|Sallows
|1944
|
|English
|Invented [[Geomagic square|geomagic squares]], [[Golygon|golygons]], and [[Self-enumerating sentence|self-enumerating sentences]].
|-
|}

== See also ==
* [[List of recreational number theory topics]]
* [[Mathematics of paper folding]] ([[origami]])

== References ==
{{reflist}}

== Further reading ==
* [[W. W. Rouse Ball]] and [[H.S.M. Coxeter]] (1987). ''Mathematical Recreations and Essays'', Thirteenth Edition, Dover. {{isbn|0-486-25357-0}}.
* [[Henry Dudeney|Henry E. Dudeney]] (1967). ''536 Puzzles and Curious Problems. Charles Scribner's sons''. {{isbn|0-684-71755-7}}.
* [[Sam Loyd]] (1959. 2 Vols.). in Martin Gardner: The Mathematical Puzzles of Sam Loyd. Dover. {{OCLC|5720955}}.
* [[Raymond M. Smullyan]] (1991). ''The Lady or the Tiger? And Other Logic Puzzles''. Oxford University Press. {{isbn|0-19-286136-0}}.

==External links==
{{Wiktionary}}
*[https://mathworld.wolfram.com/topics/RecreationalMathematics.html Recreational Mathematics] from [[MathWorld]] at [[Wolfram Research]]

{{Areas of mathematics|state=collapsed}}
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[[Category:Recreational mathematics| ]]