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Circles DisturbedThe Interplay of Mathematics and Narrative$
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Apostolos Doxiadis and Barry Mazur

Print publication date: 2012

Print ISBN-13: 9780691149042

Published to Princeton Scholarship Online: October 2017

DOI: 10.23943/princeton/9780691149042.001.0001

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A Streetcar Named (among Other Things) Proof

A Streetcar Named (among Other Things) Proof

From Storytelling to Geometry, via Poetry and Rhetoric

(p.281) Chapter 10 A Streetcar Named (among Other Things) Proof
Circles Disturbed

Apostolos Doxiadis

, Apostolos Doxiadis, Barry Mazur
Princeton University Press

This chapter traces the origins of deductive mathematical proof in classical Greece by drawing on the tradition of Jean-Pierre Vernant and G. E. R. Lloyd. It first considers how certain rhetorical concepts, methods, and patterns were instrumental to mathematical proof before discussing various cognitive modes, or stations, in historical development. The streetcar-named-Desire metaphor is used to examine certain cognitive aspects of the narrative, along with the linearity and nonlinearity of the narrative surface. The chapter then explores the role of narrative and poetic storytelling in the process of demonstration in Greek forensic rhetoric, along with the use of chiasmus and ring-composition as cognitive tools. Finally, it shows how both the macrostructure and the microstructure of the first proofs in Greek deductive mathematics were affected by forensic rhetoric, as this was shaped under the influence of the cognitive mechanisms of narrativity and the forms of poetic storytelling.

Keywords:   proof, Greece, Jean-Pierre Vernant, G. E. R. Lloyd, narrative, poetic storytelling, forensic rhetoric, chiasmus, deductive mathematics

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