# Defence of a "Shocking" Point of View

@inproceedings{Hartner2016DefenceOA, title={Defence of a "Shocking" Point of View}, author={Willy Hartner}, year={2016} }

In his paper "On the Need to Rewrite the History of Greek Mathematics" Sabetai Unguru severely criticizes the views of Tannery, Zeuthen, Neugebauer and myself on the "Geometrical Algebra" of the Greeks. Unguru summarizes our position in one sentence: "Greek 'geometric algebra' is nothing but 'Babylonian algebra' in geometrical attire", and he starts to prove that this position is historically unacceptable. Unguru states his objections very clearly. The object of the present paper is to defend… Expand

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#### 12 Citations

Mathematical Conquerors, Unguru Polarity, and the Task of History

- Mathematics, Philosophy
- 2020

We compare several approaches to the history of mathematics recently proposed by Blasjo, Fraser--Schroter, Fried, and others. We argue that tools from both mathematics and history are essential for a… Expand

Philosophical Origins in Mathematics ? Árpád Szabó Revisited

Since the turn of the 19 th and 20 th centuries when systematic research on antique Greek mathematics began, the general tone of historiographical work in the field has been dominated by the… Expand

Situating the Debate on “Geometrical Algebra” within the Framework of Premodern Algebra

- Medicine, Mathematics
- Science in Context
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A new reading of Heron's practice is offered, the significance of contextualizing “premodern algebra” is highlighted, and the origins of algebraic reasoning should be sought in the problem-solving practice, rather than in the theorem-proving tradition. Expand

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- Mathematics
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The geometrical algebra hypothesis was once the received interpretation of Greek mathematics. In recent decades, however, it has become anathema to many. I give a critical review of all arguments… Expand

Autonomy of Geometry

- Mathematics
- 2020

In this paper we present three aspects of the autonomy of geometry. (1) An argument for the geometric as opposed to the ‘geometric algebraic’ interpretation of Euclid’s Books I and II; (2) Hilbert’s… Expand

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

- Mathematics, Philosophy
- 2016

Much ink has been spilled these last 50 years over the notion (or whatever it is) of “geometric algebra” – sometimes in disputes so hot that one would believe it to be blood. However, nobody has… Expand

Phenomenology of diagrams in Book II of the Elements.

- Philosophy, Mathematics
- 2020

In this paper, we provide an interpretation of Book II of the Elements from the perspective of figures which are represented and not represented on the diagrams. We show that Euclid's reliance on… Expand

Theodorus’ proofs of incommensurabilities with Gnomons

- Mathematics
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An ‘infinite decreasing sequence of Gnomons’ is characteristic, according to Proclus, of incommensurability, hence David Fowler's idea to reconstruct Theodorus’ proofs of incommensurabilities,… Expand

Taming the Unknown: A History of Algebra from Antiquity to the Early Twentieth Century

- History
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Reviewed Title: Katz, Victor J. and Karen Hunger Parshall. Taming the Unknown: A History of Algebra from Antiquity to the Early Twentieth Century. Princeton, NJ: Princeton University Press, 2014. 485… Expand

The Mathematics of High School Physics

- Sociology
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In the seventeenth and eighteenth centuries, mathematicians and physical philosophers managed to study, via mathematics, various physical systems of the sublunar world through idealized and… Expand