Recreational mathematics

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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, 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

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

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.


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 activities

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

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:



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

Full nameLast nameBornDiedNationalityDescription
Lewis Carroll (Charles Dodgson)Carroll18321898EnglishMathematician, puzzlist and Anglican deacon best known as the author of Alice in Wonderland and Through the Looking-Glass.
Sam Loyd Loyd18411911American Chess problem composer and author, described as "America's greatest puzzlist" by Martin Gardner. [4]
Henry Dudeney Dudeney18571930English Civil servant described as England's "greatest puzzlist". [5]
Yakov Perelman Perelman18821942RussianAuthor of many popular science and mathematics books, including Mathematics Can Be Fun.
Dattatreya Ramchandra Kaprekar Kaprekar19051986IndianDiscovered 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 Gardner19142010American Popular mathematics and science writer; author of Mathematical Games, a long-running Scientific American column.
Raymond Smullyan Smullyan19192017AmericanLogician; author of many logic puzzle books including "To Mock a Mockingbird".
Joseph Madachy Madachy19272014AmericanLong-time editor of Journal of Recreational Mathematics , author of Mathematics on Vacation.
Solomon W. Golomb   Golomb19322016AmericanMathematician and engineer, best known as the inventor of polyominoes.
John Horton Conway   Conway19372020EnglishMathematician and inventor of Conway's Game of Life, co-author of Winning Ways , an analysis of many mathematical games.
Lee Sallows Sallows1944EnglishInvented geomagic squares, golygons, and self-enumerating sentences.

See also

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John Horton Conway English mathematician (1937–2020)

John Horton Conway was an English mathematician active in the theory of finite groups, knot theory, number theory, combinatorial game theory and coding theory. He also made contributions to many branches of recreational mathematics, most notably the invention of the cellular automaton called the Game of Life.

Martin Gardner American mathematics and science writer (1914–2010)

Martin Gardner was an American popular mathematics and popular science writer with interests also encompassing scientific skepticism, micromagic, philosophy, religion, and literature—especially the writings of Lewis Carroll, L. Frank Baum, and G. K. Chesterton. He was also a leading authority on Lewis Carroll. The Annotated Alice, which incorporated the text of Carroll's two Alice books, was his most successful work and sold over a million copies. He had a lifelong interest in magic and illusion and in 1999, MAGIC magazine named him as one of the "100 Most Influential Magicians of the Twentieth Century". He was considered the doyen of American puzzlers. He was a prolific and versatile author, publishing more than 100 books.

Sam Loyd American chess player, chess composer, puzzle author, and recreational mathematician

Samuel Loyd, was an American chess player, chess composer, puzzle author, and recreational mathematician. Loyd was born in Philadelphia but raised in New York City.

Tangram Dissection puzzle

The tangram is a dissection puzzle consisting of seven flat polygons, called tans, which are put together to form shapes. The objective is to replicate a pattern generally found in a puzzle book using all seven pieces without overlap. Alternatively the tans can be used to create original minimalist designs that are either appreciated for their inherent aesthetic merits or as the basis for challenging others to replicate its outline. It is reputed to have been invented in China sometime around the late 18th century CE and then carried over to America and Europe by trading ships shortly after. It became very popular in Europe for a time, and then again during World War I. It is one of the most widely recognized dissection puzzles in the world and has been used for various purposes including amusement, art, and education.

Three utilities problem Mathematical problem

The classical mathematical puzzle known as the three utilities problem or sometimes water, gas and electricity asks for non-crossing connections to be drawn between three houses and three utility companies in the plane. When posing it in the early 20th century, Henry Dudeney wrote that it was already an old problem. It is an impossible puzzle: it is not possible to connect all nine lines without crossing. Versions of the problem on nonplanar surfaces such as a torus or Möbius strip, or that allow connections to pass through other houses or utilities, can be solved.

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 in a logical way, in order to arrive at the correct or fun solution of the puzzle. There are different genres of puzzles, such as crossword puzzles, word-search puzzles, number puzzles, relational puzzles, and logic puzzles.

Mathematical puzzle Type of 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 satisfies the given conditions. Mathematical puzzles require mathematics to solve them. Logic puzzles are a common type of mathematical puzzle.

Henry Dudeney

Henry Ernest Dudeney was an English author and mathematician who specialised in logic puzzles and mathematical games. He is known as one of the country's foremost creators of mathematical puzzles.

Verbal arithmetic, also known as alphametics, cryptarithmetic, cryptarithm or word addition, is a type of mathematical game consisting of a mathematical equation among unknown numbers, whose digits are represented by letters of the alphabet. The goal is to identify the value of each letter. The name can be extended to puzzles that use non-alphabetic symbols instead of letters.

Marjorie Rice American amateur mathematician

Marjorie Ruth Rice was an American amateur mathematician most famous for her discoveries of pentagonal tilings in geometry. Rice was born February 16, 1923 in St. Petersburg, Florida, and died July 2, 2017 in San Diego, California, where she was living with her son and his wife.

Richard K. Guy British mathematician

Richard Kenneth Guy was a British mathematician. He was a professor in the Department of Mathematics at the University of Calgary. He is known for his work in number theory, geometry, recreational mathematics, combinatorics, and graph theory. He is best known for co-authorship of Winning Ways for your Mathematical Plays and authorship of Unsolved Problems in Number Theory. He published more than 300 scholarly articles. Guy proposed the partially tongue-in-cheek "strong law of small numbers", which says there are not enough small integers available for the many tasks assigned to them – thus explaining many coincidences and patterns found among numerous cultures. For this paper he received the MAA Lester R. Ford Award.

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Eureka is a journal published annually by The Archimedeans, the Mathematical Society of Cambridge University. It is one of the oldest recreational mathematics publications still in existence. Eureka includes many mathematical articles on a variety different topics – written by students and mathematicians from all over the world – as well as a short summary of the activities of the society, problem sets, puzzles, artwork and book reviews.

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Wilhelm Ahrens was a German mathematician and writer on recreational mathematics.

David Anthony Klarner was an American mathematician, author, and educator. He is known for his work in combinatorial enumeration, polyominoes, and box-packing.

Gary Antonick ( is an American journalist and recreational mathematician who for many years wrote a puzzle-based column called "Numberplay" for the New York Times.

Taking Sudoku Seriously: The math behind the world's most popular pencil puzzle is a book on the mathematics of Sudoku. It was written by Jason Rosenhouse and Laura Taalman, and published in 2011 by the Oxford University Press. The Basic Library List Committee of the Mathematical Association of America has suggested its inclusion in undergraduate mathematics libraries. It was the 2012 winner of the PROSE Awards in the popular science and popular mathematics category.

<i>The Tower of Hanoi – Myths and Maths</i>

The Tower of Hanoi – Myths and Maths is a book in recreational mathematics, on the tower of Hanoi, baguenaudier, and related puzzles. It was written by Andreas M. Hinz, Sandi Klavžar, Uroš Milutinović, and Ciril Petr, and published in 2013 by Birkhäuser, with an expanded second edition in 2018. The Basic Library List Committee of the Mathematical Association of America has suggested its inclusion in undergraduate mathematics libraries.


  1. Kulkarni, D. Enjoying Math: Learning Problem Solving With KenKen Puzzles Archived 2013-08-01 at the Wayback Machine , a textbook for teaching with KenKen Puzzles.
  2. Special Interest Groups of the MAA Mathematical Association of America
  3. Teixeira, Ricardo (2020). Mathemagics: A Magical Journey through Advanced Mathematics. USA: World Scientific. ISBN   9789811214509.
  4. Loyd, Sam (1959). Mathematical Puzzles of Sam Loyd (selected and edited by Martin Gardner), Dover Publications Inc., p. xi, ISBN   0-486-20498-7
  5. Newing, Angela (1994), "Henry Ernest Dudeney: Britain's Greatest Puzzlist", in Guy, Richard K.; Woodrow, Robert E. (eds.), 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 .

Further reading