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Galilæana. Studies in Renaissance and Early Modern Science

Focus

Vol. 23 No. 1 (2026)

The several faces and the interlaced roots of the “New Algebra”

DOI
https://doi.org/10.57617/gal-100
Submitted
30 October 2025
Published
2026-05-22

Abstract

Who compares Euler’s algebra with that of al-Khwārizmī will see more differences than kinship. Al-Khwārizmī uses natural language, while Euler calculates within the syntax of algebraic symbolism. Al-Khwārizmī has a single unknown (a word), Euler as many as he needs, represented by non-linguistic signs. Al-Khwārizmī deals with the unknown and its second power, Euler knows no limits. Al-Khwārizmī’s coefficients are numerically fixed, those of Euler may have undetermined values. When al-Khwārizmī operates on a composite expression, he needs roundabout ways; Euler has the parenthesis. The parenthesis mostly goes unmentioned when the characteristics of the “new algebra” are discussed. The rest is familiar. However, the unfolding of the various characteristics is largely left in the dark. The whole seems to have emerged fully grown from the minds of Viète and Descartes. The aim of the paper is to trace the emergence of the various characteristic features of the New Algebra from the 14th-century beginnings of abbacus algebra. The process is far from linear – before the arrival of German coß we cannot even speak of “stops and goes” on the road toward some aim. After Christoph Rudolff we probably can; in this final phase, the mostly neglected roles of Michael Stifel and Valentin Mennher are taken up.

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