The geographical distribution of so‐called “recreational” mathematical problems does not respect ideas about distinct mathematical cultures. The familiar conclusion is that they reflect “age‐old cultural relations between Eastern and Western civilizations” (Hermelink 1978). This inference is indubitably true but does not exhaust the matter. The reasons that these kinds of problems reflect relations between civilizations that are less visible in other mathematical sources are informative, both regarding the conditions and nature of mathematical activity in different civilizations and about the sense (or nonsense) of the concept of distinct mathematical cultures.
“Recreational problems” are pure in the sense that they do not deal with real applications, however much they speak in the idiom of everyday (some examples will be cited later). Nonetheless, their social basis is in the world of know‐how, not that of know‐why (the world of “productive,” not that of “theoretical” knowledge, in...
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References
The transcultural nature of recreational mathematics is discussed in:
Hermelink, H. Arabic Recreational Mathematics as a Mirror of Age‐Old Cultural Relations Between Eastern and Western Civilizations. Proceedings of the First International Symposium for the History of Arabic Science, April 5–12, 1976. Vol. II, Papers in European Languages. Ed. A. Y. al‐Hassan Aleppo: Institute for the History of Arabic Science, Aleppo University, 1978. 44–92.
A highly useful (though by necessity incomplete) survey of the occurrence of single recreational (and other) problem types will be found in:
Tropfke, Johannes. Geschichte der Elementarmathematik. 4. Auflage. Band 1: Arithmetik und Algebra. Vollständig neu bearbeitet von Kurt Vogel, Karin Reich, Helmuth Gericke. Berlin and New York: W. de Gruyter, 1980.
A broad treatment of the relation between oral and literate culture types is
Ong, Walter J. Orality and Literacy. The Technologizing of the Word. London and New York: Methuen, 1982.
A general discussion of the concept of subscientific mathematics (yet without a clear distinction between subscientific and scholasticized traditions), with extensive bibliography and source quotations, is
Høyrup, Jens. Sub‐Scientific Mathematics. Observations on a Pre‐Modern Phenomenon. History of Science 28 (1990): 63–86.
The scholastization process in Babylonian algebra is investigated in:
Høyrup, Jens. Algebra in the Scribal School–Schools in Babylonian Algebra? NTM. Schriftenreihe für Geschichte der Naturwissenschaften, Technik und Medizin, N. S. 4 (1993): 201–18.
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Høyrup, J. (2008). Mathematics, Practical and Recreational. In: Selin, H. (eds) Encyclopaedia of the History of Science, Technology, and Medicine in Non-Western Cultures. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-4425-0_8747
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