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 An amateur () is generally considered a person who pursues an avocation independent from their source of income. Amateurs and their pursuits are also described as popular, informal, self-taught, user-generated, DIY, and hobbyist. History H ...

, many topics in this field require no knowledge of advanced mathematics. Recreational mathematics involves

mathematical puzzle Mathematical puzzles make up an integral part of recreational mathematics. They have specific rules, but they do not usually involve competition between two or more players. Instead, to solve such a puzzle, the solver must find a solution that sati ...

s and

games A game is a Structure, structured type of play (activity), play usually undertaken for entertainment or fun, and sometimes used as an Educational game, educational tool. Many games are also considered to be Work (human activity), work (such as p ...

, 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 A special interest group (SIG) is a community within a larger organization with a shared interest in advancing a specific area of knowledge, learning or technology where members cooperate to effect or to produce solutions within their particular f ...

, commenting: Mathematical competitions (such as those sponsored by

mathematical association The Mathematical Association is a professional society concerned with mathematics education in the UK. History It was founded in 1871 as the Association for the Improvement of Geometrical Teaching and renamed to the Mathematical Association in ...

s) are also categorized under recreational mathematics.

Topics

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

magic squares In mathematics, especially historical and recreational mathematics, a square array of numbers, usually positive integers, is called a magic square if the sums of the numbers in each row, each column, and both main diagonals are the same. The " ...

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 puzzle A logic puzzle is a puzzle deriving from the mathematics, mathematical field of deductive reasoning, deduction. History The logic puzzle was first produced by Charles Lutwidge Dodgson, who is better known under his pen name Lewis Carroll, the a ...

s 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 game A mathematical game is a game whose rules, strategies, and outcomes are defined by clear mathematics, mathematical parameters. Often, such games have simple rules and match procedures, such as tic-tac-toe and dots and boxes. Generally, mathemati ...

s are

multiplayer game A game is a structured type of play usually undertaken for entertainment or fun, and sometimes used as an educational tool. Many games are also considered to be work (such as professional players of spectator sports or video games) or art (su ...

s 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 Combinatorial game theory is a branch of mathematics and theoretical computer science that typically studies sequential games with perfect information. Research in this field has primarily focused on two-player games in which a ''position'' ev ...

, but no mathematics is necessary in order to play it.

Mathematical puzzles

Mathematical puzzle Mathematical puzzles make up an integral part of recreational mathematics. They have specific rules, but they do not usually involve competition between two or more players. Instead, to solve such a puzzle, the solver must find a solution that sati ...

s require mathematics in order to solve them. They have specific rules, as do

s, but mathematical puzzles do not usually involve competition between two or more players. Instead, in order to solve such a

puzzle A puzzle is a game, problem, or toy that tests a person's ingenuity or knowledge. In a puzzle, the solver is expected to put pieces together ( or take them apart) in a logical way, in order to find the solution of the puzzle. There are differe ...

, the solver must find a solution that satisfies the given conditions.

Logic puzzle A logic puzzle is a puzzle deriving from the mathematics, mathematical field of deductive reasoning, deduction. History The logic puzzle was first produced by Charles Lutwidge Dodgson, who is better known under his pen name Lewis Carroll, the a ...

s and

classical cipher In cryptography, a classical cipher is a type of cipher that was used historically but for the most part, has fallen into disuse. In contrast to modern cryptographic algorithms, most classical ciphers can be practically computed and solved by hand ...

s are common examples of mathematical puzzles.

Cellular automata A cellular automaton (pl. cellular automata, abbrev. CA) is a discrete model of computation studied in automata theory. Cellular automata are also called cellular spaces, tessellation automata, homogeneous structures, cellular structures, tessel ...

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 Magic, which encompasses the subgenres of close-up magic, parlor magic, and stage magic, among others, is a performing art in which audiences are entertained by tricks, effects, or illusions of seemingly impossible feats, using natural mea ...

based on mathematical principles can produce self-working but surprising effects. For instance, a

mathemagician A mathemagician is a mathematician who is also a magician. The term "mathemagic" is believed to have been introduced by Royal Vale Heath with his 1933 book "Mathemagic"."Mathemagic" by Royal Vale Heath and Jerome Sydney Meyer, Simon and Schuster, ...

might use the

combinatorial Combinatorics is an area of mathematics primarily concerned with counting, both as a means and as an end to obtaining results, and certain properties of finite structures. It is closely related to many other areas of mathematics and has many ...

properties of a deck of

playing cards A playing card is a piece of specially prepared card stock, heavy paper, thin cardboard, plastic-coated paper, cotton-paper blend, or thin plastic that is marked with distinguishing motifs. Often the front (face) and back of each card has a Pap ...

to guess a volunteer's selected card, or

Hamming codes In computer science and telecommunications, Hamming codes are a family of linear error-correcting codes. Hamming codes can detect one-bit and two-bit errors, or correct one-bit errors without detection of uncorrected errors. By contrast, the ...

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 ) is the Japanese art of paper folding. In modern usage, the word "origami" is often used as an inclusive term for all folding practices, regardless of their culture of origin. The goal is to transform a flat square sheet of paper into a ...

* patterns and process in creating

string figure A string figure is a design formed by manipulating twine, string on, around, and using one's fingers or sometimes between the fingers of multiple people. String figures may also involve the use of the mouth, wrist, and feet. They may consist o ...

s such as

Cat's cradle ''Cat's Cradle'' is a satirical postmodern novel, with science fiction elements, by American writer Kurt Vonnegut. Vonnegut's fourth novel, it was first published on March 18, 1963, exploring and satirizing issues of science, technology, the p ...

s, 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 ''Futility Closet'' is a blog, podcast, and database started in 2005 by editorial manager and publishing journalist Greg Ross. As of February 2021 the database totaled over 11,000 items. They range over the fields of history, literature, langu ...

by Greg Ross
Mathologer
by Burkard Polster * The videos of Vi Hart
Stand-Up Maths
by

Matt Parker Matthew Thomas Parker (born 22 December 1980) is an Australian recreational mathematics, recreational mathematician, author, comedian, YouTube personality and Science communication, science communicator based in the United Kingdom. His book ''H ...

Numberphile ''Numberphile'' is an Educational entertainment, educational YouTube channel featuring videos that explore topics from a variety of fields of mathematics. In the early days of the channel, each video focused on a specific number, but the channe ...

Brady Haran Brady John Haran (born 18 June 1976) is an Australian-British independent filmmaker and video journalist who produces educational videos and documentary films for his YouTube channels, the most notable being ''Computerphile'' and ''Numberph ...

Publications

* The journal ''

Eureka Eureka often refers to: * Eureka (word), a famous exclamation attributed to Archimedes * Eureka effect, the sudden, unexpected realization of the solution to a problem Eureka or Ureka may also refer to: History * Eureka Rebellion, an 1854 g ...

'' 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 Martin Gardner (October 21, 1914May 22, 2010) was an American popular mathematics and popular science writer with interests also encompassing magic, scientific skepticism, micromagic, philosophy, religion, and literatureespecially the writin ...

, 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 Stephen William Hawking (8January 194214March 2018) was an English theoretical physics, theoretical physicist, cosmologist, and author who was director of research at the Centre for Theoretical Cosmology at the University of Cambridge. Between ...

and

Paul Dirac Paul Adrien Maurice Dirac ( ; 8 August 1902 – 20 October 1984) was an English mathematician and Theoretical physics, theoretical physicist who is considered to be one of the founders of quantum mechanics. Dirac laid the foundations for bot ...

. * The ''

Journal of Recreational Mathematics The ''Journal of Recreational Mathematics'' was an American journal dedicated to recreational mathematics, started in 1968. It had generally been published quarterly by the Baywood Publishing Company, until it ceased publication with the last issue ...

'' was the largest publication on this topic from its founding in 1968 until 2014 when it ceased publication. * ''

Mathematical Games A mathematical game is a game whose rules, strategies, and outcomes are defined by clear mathematics, mathematical parameters. Often, such games have simple rules and match procedures, such as tic-tac-toe and dots and boxes. Generally, mathemati ...

'' (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

. 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 Alexander Keewatin Dewdney (August 5, 1941 – March 9, 2024) was a Canadian mathematician, computer scientist, author, filmmaker, and conspiracy theorist. Dewdney was the son of Canadian artist and author Selwyn Dewdney and art therapist Irene D ...

, 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 ''MathWorld'' is an online mathematics reference work, created and largely written by Eric W. Weisstein. It is sponsored by and licensed to Wolfram Research, Inc. and was partially funded by the National Science Foundation's National Science ...

Wolfram Research Wolfram Research, Inc. ( ) is an American Multinational corporation, multinational company that creates computational technology. Wolfram's flagship product is the technical computing program Wolfram Mathematica, first released on June 23, 1988. ...

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