What is “geometric algebra”, and what has it been in historiography?

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Abstract

Following the lead of Hans Georg Zeuthen (not that of Tannery, as often
claimed), many historians of mathematics since the outgoing nineteenth century
have referred to “geometric algebra” as a constituent of ancient Greek theoretical geometry. In the 1930s, Otto Neugebauer added that this geometric algebra was indeed a translation of a Babylonian numerical algebra, necessitated by the discovery of irrational ratios. Then, beginning in 1969, the notion was attacked, first by Árpád Szabó, Michael Mahoney and Sabetai Unguru. In particular the views of the latter have since been accepted as the “new orthodoxy”.
As analysis of the writings of the actors involved shows, these have rarely
read each other’s works with much care. That already holds for many of those
who have claimed inspiration from Zeuthen, but those who have criticized the
idea have felt even less obliged to show that they knew what they spoke about.
The paper deals with this relationship between the participants in the debate.
It is not intended to discuss who is right when it comes to analysis of the
historical material.
Original languageEnglish
Publication date15 Jan 2016
Number of pages44
Publication statusPublished - 15 Jan 2016
EventHistoire de l’historiographie de l’algèbre : Séminaire Histoire et Philosophie des Mathématiques - Université Paris Diderot, Paris, France
Duration: 11 Jan 201611 Jan 2016

Seminar

SeminarHistoire de l’historiographie de l’algèbre
LocationUniversité Paris Diderot
Country/TerritoryFrance
CityParis
Period11/01/201611/01/2016

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