Recreational mathematics is mathematics carried out for recreation (entertainment) rather than as a strictly research and application-based professional activity. Although it is not necessarily limited to being an endeavor for amateurs, 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. 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 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 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.
Other curiosities and pastimes of non-trivial mathematical interest include:
- 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.
In popular culture
Prominent practitioners and advocates of recreational mathematics have included:
- ^Kulkarni, D. Enjoying Math: Learning Problem Solving With KenKen PuzzlesArchived 2013-08-01 at the Wayback Machine., a textbook for teaching with KenKen Puzzles.
- ^Newing, Angela (1994), "Henry Ernest Dudeney: Britain's Greatest Puzzlist", in Guy, Richard K.; Woodrow, Robert E., 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 .
H. S. M. Coxeter: Through the Looking Glass
Harold Scott MacDonald Coxeter (1907?2003) is one of the greatest geometers of the last century, or of any century, for that matter. Coxeter was associated with the University of Toronto for sixty years, the author of twelve books regarded as classics in their field, a student of Hermann Weyl in the 1930s, and a colleague of the intriguing Dutch artist and printmaker Maurits Escher in the 1950s.
In the Author's Own Words:
"I'm a Platonist ? a follower of Plato ? who believes that one didn't invent these sorts of things, that one discovers them. In a sense, all these mathematical facts are right there waiting to be discovered."
"In our times, geometers are still exploring those new Wonderlands, partly for the sake of their applications to cosmology and other branches of science, but much more for the sheer joy of passing through the looking glass into a land where the familiar lines, planes, triangles, circles, and spheres are seen to behave in strange but precisely determined ways."
"Geometry is perhaps the most elementary of the sciences that enable man, by purely intellectual processes, to make predictions (based on observation) about the physical world. The power of geometry, in the sense of accuracy and utility of these deductions, is impressive, and has been a powerful motivation for the study of logic in geometry."
"Let us revisit Euclid. Let us discover for ourselves a few of the newer results. Perhaps we may be able to recapture some of the wonder and awe that our first contact with geometry aroused." ? H. S. M. Coxeter