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Recreational mathematics ismathematics carried out forrecreation (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 foramateurs, many topics in this field require no knowledge of advanced mathematics. Recreational mathematics involvesmathematical puzzles andgames, often appealing to children and untrained adults and inspiring their further study of the subject.[1]
TheMathematical Association of America (MAA) includes recreational mathematics as one of its seventeenSpecial Interest Groups, commenting:
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.[2]
Mathematical competitions (such as those sponsored bymathematical associations) are also categorized under recreational mathematics.
Some of the more well-known topics in recreational mathematics areRubik's Cubes,magic squares,fractals,logic puzzles andmathematical chess problems, but this area of mathematics includes theaesthetics andculture of mathematics, peculiar or amusing stories andcoincidences about mathematics, and the personal lives ofmathematicians.
Mathematical games aremultiplayer games whose rules, strategies, and outcomes can be studied and explained usingmathematics. 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 ofcombinatorial 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 domultiplayer games, but mathematical puzzles do not usually involve competition between two or more players. Instead, in order to solve such apuzzle, the solver must find a solution that satisfies the given conditions.
Logic puzzles andclassical ciphers are common examples of mathematical puzzles.Cellular automata andfractals 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, amathemagician might use thecombinatorial properties of a deck ofplaying cards to guess a volunteer's selected card, orHamming codes to identify whether a volunteer is lying.[3]
Other curiosities and pastimes of non-trivial mathematical interest include:
There are many blogs and audio or video series devoted to recreational mathematics. Among the notable are the following:
Prominent practitioners and advocates of recreational mathematics have included professional andamateur mathematicians:
| Full name | Last name | Born | Died | Nationality | Description |
|---|---|---|---|---|---|
| Lewis Carroll (Charles Dodgson) | Carroll | 1832 | 1898 | English | Mathematician, puzzlist andAnglicandeacon best known as the author ofAlice in Wonderland andThrough the Looking-Glass. |
| Sam Loyd | Loyd | 1841 | 1911 | American | Chess problem composer and author, described as "America's greatestpuzzlist" byMartin Gardner.[4] |
| Henry Dudeney | Dudeney | 1857 | 1930 | English | Civil servant described as England's "greatest puzzlist".[5] |
| Yakov Perelman | Perelman | 1882 | 1942 | Russian | Author of manypopular science andmathematics books, includingMathematics Can Be Fun. |
| D. R. Kaprekar | Kaprekar | 1905 | 1986 | Indian | Discovered several results innumber theory, described severalclasses of natural numbers including theKaprekar,harshad andself numbers, and discovered theKaprekar's constant |
| Martin Gardner | Gardner | 1914 | 2010 | American | Popular mathematics andscience writer; author ofMathematical Games, a long-runningScientific 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 ofJournal of Recreational Mathematics, author ofMathematics on Vacation. |
| Solomon W. Golomb | Golomb | 1932 | 2016 | American | Mathematician and engineer, best known as the inventor ofpolyominoes. |
| John Horton Conway | Conway | 1937 | 2020 | English | Mathematician and inventor ofConway's Game of Life, co-author ofWinning Ways, an analysis of manymathematical games. |
| Noboyuki Yoshigahara | Yoshigahara | 1936 | 2004 | Japanese | Japan's most celebrated inventor, collector, solver, and communicator of puzzles. |
| Lee Sallows | Sallows | 1944 | English | Inventedgeomagic squares,golygons, andself-enumerating sentences. |
