Recreational mathematics (nonfiction)

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Recreational mathematics is mathematics carried out for recreation (entertainment) rather than as a strictly research and application-based professional activity. 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.

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.

Mathematical competitions (such as those sponsored by mathematical associations) are also categorized under recreational mathematics.

History of recreational mathematics

Albrecht Heeffer, author of How algebra spoiled recreational problems: A case study in the cross-cultural dissemination of mathematics, writes in the abstract:

This paper deals with a sub-class of recreational problems which are solved by a simple memorized rule resulting from an elementary arithmetical or algebraic solution, called proto-algebraic rules. Their recreational aspect is derived from a surprise or trick solution which is not immediately obvious to the subjects involved. Around 1560 many such problems wane from arithmetic and algebra textbooks to reappear in the eighteenth century. Several hypotheses are investigated why popular Renaissance recreational problems lost their appeal. We arrive at the conclusion that the emergence of algebra as a general problem solving method changed the scope of what is considered recreational in mathematics.

An excerpt from the paper:

Most of these problems are formulated in a practical context which gives them a panache and purpose and make them acceptable within that context. For example, Thomas Digges published a book (Digges, 1579), reprinted in 1590, named An arithmeticall warlike treatise named Stratioticos compendiously teaching the science of nombers as well in fractions as integers, and so much of the rules and aequations algebraicall, and art of nombers cossicall, as are requisite for the profession of a soldier. As the title makes clear, the book is intended for army officers and every problem is thus set into the context of an army or warfare. Claiming a practical purpose was an important incentive for selling and producing textbooks on arithmetic from the sixteenth century onwards.

  • Thomas Digges (nonfiction) - English mathematician and astronomer (c. 1546 – 24 August 1595). He was the first to expound the Copernican system in English but discarded the notion of a fixed shell of immoveable stars to postulate infinitely many stars at varying distances. He was also first to postulate the "dark night sky paradox". His father was mathematician and surveyor Leonard Digges.
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