Aldo Brigaglia

A5. Remarks on the Historiography of Mathematics

Introduction

A5. Remarks on the historiography of mathematics. Examines the key methodological debate in the historiography of mathematics since 2010, covering Unguru-Rashed on Apollonius' Conics and 'geometric algebra'.

Abstract

In this paper, I examine aspects of the methodological debate that originated in 2010, when the distinguished historian of mathematics Sabetai Unguru reviewed Roshdi Rashed’s edition of the Arabic translation of Apollonius’ Conics. In his review, Unguru criticized what Rashed calls ‘l’usage instrumental d’une autre mathématique pour commenter une oeuvre ancienne’. I consider this debate very important and will try to place it within in the discussion of the so-called ‘geometric algebra’ that goes back to the seventies, by tracing the contributions of the main figures who took part in it.

Review

The proposed paper, "Remarks on the Historiography of Mathematics," promises a timely and significant intervention into a crucial methodological debate within the history of mathematics. The author aims to scrutinize the controversy that arose in 2010 following Sabetai Unguru’s critical review of Roshdi Rashed’s edition of Apollonius’ Conics, specifically focusing on Rashed’s concept of ‘l’usage instrumental d’une autre mathématique pour commenter une oeuvre ancienne’. This central tension, concerning the appropriate use of modern mathematical frameworks when interpreting ancient texts, is correctly identified as a foundational issue for the discipline. The strength of this work lies in its intention to contextualize the Unguru-Rashed exchange within the broader, long-standing discussion surrounding ‘geometric algebra’, tracing its origins back to the 1970s. By linking a contemporary, high-profile debate to its historical antecedents and identifying the main contributors to this evolving discourse, the paper has the potential to offer a comprehensive genealogical account of key historiographical challenges. This approach is vital for understanding how different interpretive strategies have been developed and contested in the study of ancient mathematics. To maximize its impact, the paper should not merely trace contributions but also endeavor to provide a critical analysis or synthesis of the positions outlined. While the abstract clearly establishes the historical scope, it would benefit from an indication of the author's own analytical framework or a proposed resolution to these ongoing methodological dilemmas. Articulating a clear stance on "l'usage instrumental" or offering fresh perspectives on how historians might navigate the anachronism problem would significantly enhance the paper's contribution, moving beyond a historical recounting to offer new insights for current scholarly practice.

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