Recreational mathematics is mathematics 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 enjoyment, amusement, or ple ...

(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 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 structured form 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 games) or art (su ...

, often appealing to children and untrained adults, inspiring their further study of the subject. The Mathematical Association of America (MAA) includes recreational mathematics as one of its seventeen Special Interest Groups, 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 Cube The Rubik's Cube is a 3-D combination puzzle originally invented in 1974 by Hungarian sculptor and professor of architecture Ernő Rubik. Originally called the Magic Cube, the puzzle was licensed by Rubik to be sold by Pentangle Puzzles in t ...

magic squares In 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 'order' of the magic square is the number ...

fractals In mathematics, a fractal is a 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 scales, as ill ...

logic puzzle A logic puzzle is a puzzle deriving from the mathematical field of deduction. History The logic puzzle was first produced by Charles Lutwidge Dodgson, who is better known under his pen name Lewis Carroll, the author of ''Alice's Adventures in W ...

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

aesthetics Aesthetics, or esthetics, is a branch of philosophy Philosophy (from , ) is the systematized study of general and fundamental questions, such as those about existence, reason, Epistemology, knowledge, Ethics, values, Philosophy of ...

and

culture Culture () is an umbrella term which encompasses the social behavior, institutions, and norms found in human societies, as well as the knowledge, beliefs, arts, laws, customs, capabilities, and habits of the individuals in these grou ...

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 game A game is a structured form 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 games) or art (suc ...

s 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 The mancala games are a family of two-player turn-based strategy board games played with small stones, beans, or seeds and rows of holes or pits in the earth, a board or other playing surface. The objective is usually to capture all or som ...

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. Study has been largely confined to two-player games that have a ''position'' that the playe ...

, 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 arrive at the correct or fun solution of the puzzle ...

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

Logic puzzle A logic puzzle is a puzzle deriving from the mathematical field of deduction. History The logic puzzle was first produced by Charles Lutwidge Dodgson, who is better known under his pen name Lewis Carroll, the author of ''Alice's Adventures in W ...

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

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

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 fi ...

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 ...

* 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 f ...

* patterns and process in creating

string figure A string figure is a design formed by manipulating 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 of sin ...

s such as

Cat's cradle Cat's cradle is a game involving the creation of various string figures between the fingers, either individually or by passing a loop of string back and forth between two or more players. The true origin of the name is debated, though the fi ...

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 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, language, ...

by Greg Ross *

Numberphile ''Numberphile'' is an 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 channel has since expanded its s ...

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 '' Periodic Videos'' and '' Numb ...

* Mathologer by

Burkard Polster Burkard Polster (born 26 February 1965 in Würzburg) is a German mathematician who runs and presents the ''Mathologer'' channel on YouTube. Polster earned a doctorate from the University of Erlangen–Nuremberg in 1993 under the supervision of K ...

3Blue1Brown 3Blue1Brown is a math YouTube channel created and run by Grant Sanderson. The channel focuses on teaching higher mathematics from a visual perspective, and on the process of discovery and inquiry-based learning in mathematics, which Sanderson c ...

by Grant Sanderson * The videos of

Vi Hart Victoria Hart (born 1988), commonly known as Vi Hart (), is an American mathematician and YouTuber. They describe themselves as a "recreational mathemusician" and are well-known for creating mathematical videos on YouTube. Hart founded the virt ...

Stand-Up Maths
by Matt Parker

Publications

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

University of Cambridge , mottoeng = Literal: From here, light and sacred draughts. Non literal: From this place, we gain enlightenment and precious knowledge. , established = , other_name = The Chancellor, Masters and Schola ...

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 scientific skepticism, micromagic, philosophy, religion, and literatureespecially the writings of L ...

, John Conway,

Roger Penrose Sir Roger Penrose (born 8 August 1931) is an English mathematician, mathematical physicist, philosopher of science and Nobel Laureate in Physics. He is Emeritus Rouse Ball Professor of Mathematics in the University of Oxford, an emeritus f ...

, Ian Stewart,

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

, Stephen Hawking and

Paul Dirac Paul Adrien Maurice Dirac (; 8 August 1902 – 20 October 1984) was an English theoretical physicist who is regarded as one of the most significant physicists of the 20th century. He was the Lucasian Professor of Mathematics at the Unive ...

. * 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 mathematical parameters. Often, such games have simple rules and match procedures, such as Tic-tac-toe and Dots and Boxes. Generally, mathematical games ne ...

'' (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 famous scientists, including Albert Einstein and Nikola Tesla, have contributed articles to it. In print since 1845, it i ...

'' 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 ''Metamagical Themas'' is an eclectic collection of articles that Douglas Hofstadter wrote for the popular science magazine ''Scientific American'' during the early 1980s. The anthology was published in 1985 by Basic Books. The volume is subst ...

" columns (1981-1983), a similarly distinguished, but shorter-running, column by

Douglas Hofstadter Douglas Richard Hofstadter (born February 15, 1945) is an American scholar of cognitive science, physics, and comparative literature whose research includes concepts such as the sense of self in relation to the external world, consciousness, an ...

, 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 ''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 company that creates computational technology. Wolfram's flagship product is the technical computing program Wolfram Mathematica, first released on June 23, 1988. Other products include ...

The Unreasonable Utility of Recreational Mathematics
by

David Singmaster David Breyer Singmaster (born 1938) is an emeritus professor of mathematics at London South Bank University, England. A self-described metagrobologist, he has a huge personal collection of mechanical puzzles and books of brain teasers. He is m ...

{{Authority control