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 and inspiring their further study of the subject.^{[1]}
The Mathematical Association of America (MAA) includes recreational mathematics as one of its seventeen Special 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 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.^{[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 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.^{[4]} |
Henry Dudeney | Dudeney | 1857 | 1930 | English | Civil servant described as England's "greatest puzzlist".^{[5]} |
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. |