Recreational mathematics

Single pixels appear and disappear in a pattern which moves across the gif.
John Conway's game of life breeder-pattern animation.

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.

The Mathematical Association of America (MAA) has seventeen Special Interest Groups which includes a recreational math group called SIGMAA-Rec. The SIGMAA-Rec website defines recreational mathematics as, "...a broad term that covers many different areas including games, puzzles, magic, art, and more."

Although it is not necessarily limited to being an endeavor for amateurs, many topics in this field require no knowledge of advanced mathematics. Mathematical competitions (such as those sponsored by mathematical associations) are also categorized under recreational mathematics.

Areas of mathematics

An example of a mathematical puzzle that challenges players to deduce the start of a linear sequence that has changed into a continuous circle. The terms of the sequence have been expressed Algebraically.
An empty grid is filled in square-by-square using the L-shape movement of the knight chess piece to demonstrate the Knight's tour puzzle.
The Knight's tour, a mathematical chess problem, animated.

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.

History

1200s

A scan of the Liber Abaci with the problem How many pairs of rabbits are created by one pair in one year. on it.
A page of Fibonacci's Liber Abaci from the Biblioteca Nazionale di Firenze showing (in box on right) 13 entries of the Fibonacci sequence.

The Liber Abaci or Liber Abbaci was written by Leonardo of Pisa, posthumously known as Fibonacci. Multiple math puzzles are presented with one titled, How Many Pairs of Rabbits Are Created by One Pair in One Year.

1700s

Choi Seok-jeong (Korean: 최석정; Hanja: 崔錫鼎; 1646–1715) made the earliest known form of latin squares in his book Gusuryak (Koo-Soo-Ryak: Korean: 구수략; Hanja: 九數略). The mathematical-puzzle game Sudoku created in the 1970s is a special case of Latin squares.

1800s

The Lady's and Gentleman's Diary was a recreational math magazine created by Wesley S. B. Woolhouse which ran from 1704 to 1871.

1900s

The first Sudoku puzzle is developed by Howard Garns and published by Dell Magazines in May 1979, and the puzzles spread to Japan in April 1984.

Forms

Numeracy is a requirement for recreational activities, from knowing the range of people who can participate at a time to using specific areas of knowledge to participate at all. Hobbyists enjoy finding the mathematical sides of the world and creating enjoyable experiences with mathematics.

Books

Different from a singular math word problem mathematical fiction books may involve multiple problems which further build upon each other as the story progresses.

One example is a children's-book series called Usborne Puzzle Adventures.

Throughout the book, there are puzzles which you must solve for the next part of the story to make sense. Clues and evidence lurk in the words and the pictures...If you get stuck, there are extra clues to help you...They are printed in a secret way, so you will have to work out how to read them first.

— Karen Dolby, Usborne Puzzle Adventures: Danger at Demon's Cove, About this Book

Games

Young people playing a Mancala-variant called Igisoro, a traditional Rwandan game.

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.

Mathemagics

Stacks of cards are pictured with multiple of them having colored backgrounds and/or numbers to visually explain the trick.
Mathematical explanation of the Twenty-One Card Trick:
The cards are dealt into three piles which are accumulated with the pile containing the target card (shaded yellow and labelled with the step number) put in the middle. This is done three times, the middle card (*) is the one in all chosen piles.

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.

Music

Mathematics is used to create and understand music.

There are subgenres of music which are directly inspired by mathematics, such as math rock.

Math and music examples
AudioAboutGenre
Fractal Study -1 "...Fractal Study no. 1 is a soft ambient piece created by a nonlinear function." - User:Rozencrantz~commonswikiambient

Puzzles

Clumsy wagon, a puzzle that has as its core a mathematical problem that seeks to verify if it is possible for a wagon with only two points of contact to pass through a winding rail, available on the collection of Matemateca IME-USP.

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 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. These games can be done through different forms of media, such as board games, books, comics, and video games.

Other activities

Origami-inspired engineering to discover how to make self-folding structures.

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

Relationship with the sciences

A video from the Wikibook, 'Physics Explained Through a Video Game.'

The academic field of mathematics is a core-component for others, such as chemistry and physics. Whenever there is recreational play in those academic fields they include recreational mathematics as well.

Distributors

Recreational mathematics is shared in similar ways as other hobbies. Individual enthusiasts and math-related organizations will make and share what they have created and/or learned.

People

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

Full nameLast nameBornDiedNationality Description
Alcuin of YorkAlcuin735804English Clergyman, scholar, and teacher; author of Propositiones ad Acuendos Juvenes.
Lewis Carroll (Charles Dodgson)Carroll18321898English Mathematician, puzzlist and Anglican deacon best known as the author of Alice in Wonderland and Through the Looking-Glass.
Sam LoydLoyd18411911American Chess problem composer and author, described as "America's greatest puzzlist" by Martin Gardner.
W.W. Rouse BallBall18501925British Author of Mathematical Recreations and Essays, continuously published since 1892.
Henry DudeneyDudeney18571930English Civil servant described as England's "greatest puzzlist".
Yakov PerelmanPerelman18821942Russian Author of many popular science and mathematics books, including Mathematics Can Be Fun.
J.A.H. HunterHunter19021986British Author of Fun with Figures.
D. R. KaprekarKaprekar19051986Indian Discovered 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 GardnerGardner19142010American Popular mathematics and science writer; author of Mathematical Games, a long-running Scientific American column.
Raymond SmullyanSmullyan19192017American Logician; author of many logic puzzle books including "To Mock a Mockingbird".
Joseph MadachyMadachy19272014American Long-time editor of Journal of Recreational Mathematics, author of Mathematics on Vacation.
Solomon W. Golomb  Golomb19322016American Mathematician and engineer, best known as the inventor of polyominoes.
Noboyuki Yoshigahara  Yoshigahara19362004Japanese Japan's most celebrated inventor, collector, solver, and communicator of puzzles.
Vladimir Arnold  Arnold19372010Russian Prolific mathematician and educator; author of Problems for children from 5 to 15.
John Horton Conway  Conway19372020English Mathematician and inventor of Conway's Game of Life, co-author of Winning Ways, an analysis of many mathematical games.
Lee Sallows Sallows 1944 English Invented geomagic squares, golygons, and self-enumerating sentences.
Ian Stewart Stewart 1945 British Mathematician and author; his work includes the Mathematical Recreations column for Scientific American and numerous books on recreational mathematics.
Peter Winkler Winkler 1946 American Mathematician and author of several books on recreational mathematics.

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:

Publications

See also

References

  1. ↑ About SIGMAA-Rec, MAA, 2018, archived from the original on 2026-04-16
  2. ↑ Kulkarni, D. Enjoying Math: Learning Problem Solving With KenKen Puzzles Archived 2013-08-01 at the Wayback Machine, a free and online-textbook for teaching with KenKen Puzzles.
  3. ↑ Abaci, Liber (2002), "12", Fibonacci's Liber Abaci A Translation into Modern English of Leonardo Pisano's Book of Calculation, translated by Sigler, Laurence, Springer, pp. 404–405, ISBN 978-0-387-95419-6
  4. ↑ O'Connor, J J; Robertson, E F (March 2022), Choi Seok-jeong, Scotland: School of Mathematics and Statistics at the University of St Andrews, archived from the original on 2026-07-28, retrieved 2026-08-06, a free and online biography-article.
  5. ↑ Italia, Iona (2005), The Rise of Literary Journalism in the Eighteenth Century: Anxious Employment, vol. 3 of Routledge Studies in Eighteen-Century Literature (illustrated ed.), USA and Canada: Psychology Press, p. 5, ISBN 9780415343923
  6. ↑ Pegg Jr., Ed (2005-09-15), Sudoku Variations, MAA, archived from the original on 2026-08-03, retrieved 2026-08-06, a free online article on the history of Sudoku.
  7. ↑ Dolby, Karen, Danger At Demon's Cove, Usborne Puzzle Adventures, Tulsa, Oklahoma: EDC Publishing, ISBN 0746001797
  8. ↑ Teixeira, Ricardo (2020). Mathemagics: A Magical Journey through Advanced Mathematics. USA: World Scientific. ISBN 9789811214509.
  9. ↑ Liu, Xiang; Gattas, Joseph M; Chen, Yan (2016-11-10), One-DOF Superimposed Rigid Origami with Multiple States, vol. 6, Scientific Reports, doi:10.1038/srep36883, PMC 5103280, PMID 27830732, archived from the original on 2025-03-08 – via nature
  10. ↑ Loyd, Sam (1959). Mathematical Puzzles of Sam Loyd (selected and edited by Martin Gardner), Dover Publications Inc., p. xi, ISBN 0-486-20498-7
  11. ↑ 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