## 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.

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 language | English |
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Publication date | 15 Jan 2016 |

Number of pages | 44 |

Publication status | Published - 15 Jan 2016 |

Event | Histoire de l’historiographie de l’algèbre : Séminaire Histoire et Philosophie des Mathématiques - Université Paris Diderot, Paris, France Duration: 11 Jan 2016 → 11 Jan 2016 |

### Seminar

Seminar | Histoire de l’historiographie de l’algèbre |
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Location | Université Paris Diderot |

Country/Territory | France |

City | Paris |

Period | 11/01/2016 → 11/01/2016 |