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 amateurs, many topics in this field require no knowledge of advanced mathematics. Recreational mathematics involves mathematical puzzles and games, often appealing to children and untrained adults, inspiring their further study of the subject.
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.
Mathematical competitions (such as those sponsored by mathematical associations) are also categorized under recreational mathematics.
Some of the more well-known topics in recreational mathematics are Rubik's Cubes, magic squares, fractals, logic puzzles and mathematical chess problems, but this area of mathematics includes the aesthetics and culture of mathematics, peculiar or amusing stories and coincidences about mathematics, and the personal lives of mathematicians.
Mathematical games are multiplayer games 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 require mathematics in order to solve them. They have specific rules, as do multiplayer games, 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 puzzles and classical ciphers 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.
Magic tricks based on mathematical principles can produce self-working but surprising effects. For instance, a mathemagician might use the combinatorial properties of a deck of playing cards to guess a volunteer's selected card, or Hamming codes to identify whether a volunteer is lying.
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 figures such as Cat's cradles, etc.
- fractal-generating software
Online blogs, podcasts, and YouTube channels
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
- Numberphile by Brady Haran
- Mathologer by Burkard Polster
- 3Blue1Brown by Grant Sanderson
- The videos of Vi Hart
- Stand-Up Maths by Matt Parker
- The journal 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 Conway, Roger Penrose, 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.
- 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, and most recently "Puzzling Adventures" by Dennis Shasha.
- The Recreational Mathematics Magazine, published by the 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.
Prominent practitioners and advocates of recreational mathematics have included professional and amateur mathematicians:
|Full name||Last name||Born||Died||Nationality||Description|
|Lewis Carroll (Charles Dodgson)||Carroll||1832||1898||English||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||Chess problem composer and author, described as "America's greatest puzzlist" by Martin Gardner.|
|Henry Dudeney||Dudeney||1857||1930||English||Civil servant described as England's "greatest puzzlist".|
|Yakov Perelman||Perelman||1882||1942||Russian||Author of many popular science and mathematics books, including Mathematics Can Be Fun.|
|D. R. Kaprekar||Kaprekar||1905||1986||Indian||Discovered several results in number theory, described several classes of natural numbers including the Kaprekar, harshad and self numbers, and discovered the Kaprekar's constant|
|Martin Gardner||Gardner||1914||2010||American||Popular mathematics and science writer; author of Mathematical Games, a long-running Scientific American column.|
|Raymond Smullyan||Smullyan||1919||2017||American||Logician; author of many logic puzzle books including "To Mock a Mockingbird".|
|Joseph Madachy||Madachy||1927||2014||American||Long-time editor of Journal of Recreational Mathematics, author of Mathematics on Vacation.|
|Solomon W. Golomb||Golomb||1932||2016||American||Mathematician and engineer, best known as the inventor of polyominoes.|
|John Horton Conway||Conway||1937||2020||English||Mathematician and inventor of Conway's Game of Life, co-author of Winning Ways, an analysis of many mathematical games.|
|Lee Sallows||Sallows||1944||English||Invented geomagic squares, golygons, and self-enumerating sentences.|
- Kulkarni, D. Enjoying Math: Learning Problem Solving With KenKen Puzzles Archived 2013-08-01 at the Wayback Machine, a textbook for teaching with KenKen Puzzles.
- Special Interest Groups of the MAA Mathematical Association of America
- Teixeira, Ricardo (2020). Mathemagics: A Magical Journey through Advanced Mathematics. USA: World Scientific. ISBN 9789811214509.
- Loyd, Sam (1959). Mathematical Puzzles of Sam Loyd (selected and edited by Martin Gardner), Dover Publications Inc., p. xi, ISBN 0-486-20498-7
- Newing, Angela (1994), "Henry Ernest Dudeney: Britain's Greatest Puzzlist", in Guy, Richard K.; Woodrow, Robert E. (eds.), The Lighter Side of Mathematics: Proceedings of the Eugène Strens Memorial Conference on Recreational Mathematics and Its History, Cambridge University Press, pp. 294–301, ISBN 9780883855164.
- W. W. Rouse Ball and H.S.M. Coxeter (1987). Mathematical Recreations and Essays, Thirteenth Edition, Dover. ISBN 0-486-25357-0.
- 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.