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Galilæana. Studies in Renaissance and Early Modern Science

Focus

Vol. 23 No. 1 (2026)

The influence of practical arithmetic on the emergence of proto-symbolic algebra: A long-run survey

DOI
https://doi.org/10.57617/gal-104
Submitted
15 November 2025
Published
2026-05-22

Abstract

The development of what we may term “proto-symbolic algebra” was profoundly shaped by the tradition of practical arithmetic, particularly as it evolved through abacus mathematics. Within this milieu, algebraic problem-solving techniques became increasingly sophisticated, and symbolic representations began to emerge. While the recovery of classical mathematical works provided an ideal of mathematical generality and abstraction, the mathematics practiced in abacus schools supplied computational techniques that were essential for the operationalization of algebra. As this paper shows, key figures such as Tartaglia, Cardano and Bombelli displayed influences of abacus mathematics in their algebraic works. The persistence of practical arithmetic techniques within these works suggests that the evolution of algebra was not a linear progression from classical to modern mathematics but rather a complex synthesis of various traditions.

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