Recreational mathematics is

mathematics Mathematics is a field of study that discovers and organizes methods, Mathematical theory, theories and theorems that are developed and Mathematical proof, proved for the needs of empirical sciences and mathematics itself. There are many ar ...

carried out for

recreation Recreation is an activity of leisure, leisure being discretionary time. The "need to do something for recreation" is an essential element of human biology and psychology. Recreational activities are often done for happiness, enjoyment, amusement, ...

(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. The

Mathematical Association of America The Mathematical Association of America (MAA) is a professional society that focuses on mathematics accessible at the undergraduate level. Members include university A university () is an educational institution, institution of tertiary edu ...

(MAA) includes recreational mathematics as one of its seventeen Special Interest Groups, commenting: Mathematical competitions (such as those sponsored by mathematical associations) are also categorized under recreational mathematics.

Topics

Some of the more well-known topics in recreational mathematics are Rubik's Cubes, magic squares,

fractals In mathematics, a fractal is a Shape, geometric shape containing detailed structure at arbitrarily small scales, usually having a fractal dimension strictly exceeding the topological dimension. Many fractals appear similar at various scale ...

, logic puzzles and mathematical chess problems, but this area of mathematics includes the

aesthetics Aesthetics (also spelled esthetics) is the branch of philosophy concerned with the nature of beauty and taste (sociology), taste, which in a broad sense incorporates the philosophy of art.Slater, B. H.Aesthetics ''Internet Encyclopedia of Ph ...

and

culture Culture ( ) is a concept that encompasses the social behavior, institutions, and Social norm, norms found in human societies, as well as the knowledge, beliefs, arts, laws, Social norm, customs, capabilities, Attitude (psychology), attitudes ...

of mathematics, peculiar or amusing stories and coincidences about mathematics, and the personal lives of

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, mathematical structure, structure, space, Mathematica ...

Mathematical games

Mathematical games are multiplayer games whose rules, strategies, and outcomes can be studied and explained using

. The players of the game may not need to use explicit mathematics in order to play mathematical games. For example,

Mancala Mancala ( ''manqalah'') is a family of two-player Turns, rounds and time-keeping systems in games, turn-based Strategy game, strategy board games played with small stones, beans, marbles or seeds and rows of holes or pits in the earth, a board ...

is studied in the mathematical field of combinatorial game theory, but no mathematics is necessary in order to play it.

Mathematical puzzles

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

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.

Mathemagics

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 activities

Other curiosities and pastimes of non-trivial mathematical interest include: * patterns in

juggling Juggling is a physical skill, performed by a juggler, involving the manipulation of objects for recreation, entertainment, art or sport. The most recognizable form of juggling is toss juggling. Juggling can be the manipulation of one object o ...

* 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 Alexander Bogomolny (January 4, 1948 July 7, 2018) was a Soviet Union, Soviet-born Israeli Americans, Israeli-American mathematician. He was Professor Emeritus of Mathematics at the University of Iowa, and formerly research fellow at the Moscow ...

by Alexander Bogomolny * Futility Closet by Greg Ross
Mathologer
by Burkard Polster * The videos of Vi Hart
Stand-Up Maths
by Matt Parker * Numberphile by Brady Haran

Publications

* The journal '' Eureka'' published by the mathematical society of the

University of Cambridge The University of Cambridge is a Public university, public collegiate university, collegiate research university in Cambridge, England. Founded in 1209, the University of Cambridge is the List of oldest universities in continuous operation, wo ...

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 Sir Roger Penrose (born 8 August 1931) is an English mathematician, mathematical physicist, Philosophy of science, philosopher of science and Nobel Prize in Physics, Nobel Laureate in Physics. He is Emeritus Rouse Ball Professor of Mathematics i ...

, Ian Stewart,

Timothy Gowers Sir William Timothy Gowers, (; born 20 November 1963) is a British mathematician. He is the holder of the Combinatorics chair at the Collège de France, a director of research at the University of Cambridge and a Fellow of Trinity College, Camb ...

, 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 ''Scientific American'', informally abbreviated ''SciAm'' or sometimes ''SA'', is an American popular science magazine. Many scientists, including Albert Einstein and Nikola Tesla, have contributed articles to it, with more than 150 Nobel Pri ...

'' 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 Douglas Richard Hofstadter (born 15 February 1945) is an American cognitive and computer scientist whose research includes concepts such as the sense of self in relation to the external world, consciousness, analogy-making, Strange loop, strange ...

, 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. * Th
Recreational Mathematics Magazine
published by th
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.

People

Prominent practitioners and advocates of recreational mathematics have included professional and amateur mathematicians:

References

External links

Recreational Mathematics
from MathWorld at Wolfram Research {{Authority control