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Recreational mathematics is an umbrella term for mathematics carried out for recreation, self-education and self-entertainment, rather than as a fully serious professional activity. It often involves mathematical puzzles and games.
Many topics in this field require no knowledge of advanced mathematics and recreational mathematics often appeals to children and untrained adults, inspiring their further study of the subject.
Some of the more well-known topics in recreational mathematics are 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 a mathematical game, because mathematicians can study it using 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 don't 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 are a common type of mathematical puzzle. Conway's Game of Life and fractals are also considered mathematical puzzles, even though the solver only interacts with them by providing a set of initial conditions.
Sometimes, mathematical puzzles are referred to as mathematical games as well.
Other curiosities and pastimes of non-trivial mathematical interest:
- Juggling (juggling patterns)
- Origami (many mathematical results, some deep)
- Cat's cradle and other string figures
- 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 is the largest publication on this topic.
- "Mathematical Games" was the title of a long-running column on the subject by Martin Gardner (1914-2010), in Scientific American. He inspired several generations of mathematicians and scientists, through his interest in mathematical recreations. "Mathematical Games" (1956-1981) was succeeded by "Metamagical Themas" (1981-19??), a similarly distinguished, but shorter-running, column by Douglas Hofstadter, then by "Mathematical Recreations" (19??-????), a column by Ian Stewart, and most recently "Puzzling Adventures" (????-present) by Dennis Shasha.
- In popular culture
- In the Doctor Who episode "42", the Doctor completes a sequence of happy primes, then complains that schools no longer teach recreational mathematics.
- The Curious Incident of the Dog in the Nighttime, a book about a young boy with Asperger syndrome, discusses many mathematical games and puzzles.
The foremost advocates of recreational mathematics have included:
- Lewis Carroll, author, mathematician and puzzlist
- John Horton Conway, mathematician and inventor of Conway's Game of life
- Henry Dudeney, regarded as England's greatest puzzlist
- Martin Gardner, author of Mathematical Games, a long running column in Scientific American
- Vi Hart, creator of online recreational mathematics videos
- Sam Loyd, regarded as America's greatest puzzlist
- Joseph Madachy, long-time editor of Journal of Recreational Mathematics, author of Mathematics on Vacation and Madachy's Mathematical Recreations
- Clifford A. Pickover, author of numerous books on recreational mathematics
- Marilyn vos Savant, author of "Ask Marilyn", a long running column in PARADE
- Malba Tahan, pseudonym of Júlio César de Mello e Souza, author of several books figuring recreational mathematics, including The Man Who Counted
- Yakov Perelman, Russian author of many popular science books, including Mathematics Can Be Fun
- D. R. Kaprekar, Indian mathematician
- Solomon W. Golomb, best known as the inventor of polyominoes.
- Kulkarni, D. Enjoying Math: Learning Problem Solving With KenKen Puzzles, A textbook for teaching with KenKen Puzzles.
- 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.
- Igor Kokcharov (2012). Math Puzzles for MBAs. eBook for iPad. ISBN 9781623141318.
- Recreational Mathematics from MathWorld at Wolfram Research
- Mathematical treasure hunt on the Internet by CIJM (for highschool students and general public)
- QEDcat - fun mathematical resources by Burkard Polster and Marty Ross.
- mathpuzzle.com by Ed Pegg, Jr.
- Puzzles of the Month by Gianni A. Sarcone
- The Unreasonable Utility of Recreational Mathematics by David Singmaster
- Nick's Mathematical Puzzles
- Cotpi Weekly Puzzles
- Knot a Braid of Links
- Project Eureka - collection of mathematical problems and puzzles
- Vi Hart's YouTube channel
- A+Click: Math problems with difficulty level adapted to students' age