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(Article I.3.) On a Collection of Geometrical Riddles and Their Role in the Shaping of Four to Six “Algebras”

In: Selected Essays on Pre- and Early Modern Mathematical Practice

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  • Jens Høyrup

    (Roskilde University, Section for Philosophy and Science Studies)

Abstract

For more than a century, there has been some discussion about whether medieval Arabic al-jabr (and hence also later European algebra) has its roots in Indian or Greek mathematics. Since the 1930s, the possibility of Babylonian ultimate roots has entered the debate. This article presents a new approach to the problem, pointing to a set of quasi-algebraic riddles that appear to have circulated among Near Eastern practical geometers since c. 2000 bce, and which inspired first the so-called “algebra” of the Old Babylonian scribal school and later the geometry of Elements II (where the techniques are submitted to theoretical investigation). The riddles also turn up in ancient Greek practical geometry and Jaina mathematics. Eventually they reached European (Latin and abbaco) mathematics via the Islamic world. However, no evidence supports a derivation of medieval Indian algebra or the original core of al-jabr from the riddles.

Suggested Citation

  • Jens Høyrup, 2019. "(Article I.3.) On a Collection of Geometrical Riddles and Their Role in the Shaping of Four to Six “Algebras”," Springer Books, in: Selected Essays on Pre- and Early Modern Mathematical Practice, chapter 0, pages 67-116, Springer.
    • Handle: RePEc:spr:sprchp:978-3-030-19258-7_4
    DOI: 10.1007/978-3-030-19258-7_4
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