Circles disturbed
Journal Data
| Type | SOURCE_BOOK |
|---|---|
| Publisher | Princeton University Press (US) |
| ISBN-13 | 9780691149042 |
| Open Library | OL16215176W |
| Total publications | 3 |
| Coverage period | 2012 - 2012 |
| Language | EN |
This book brings together important thinkers in mathematics, history, and philosophy to explore the relationship between mathematics and narrative. “Circles disturbed” reflect the last words of Archimedes before he was slain by a Roman soldier—“Don't disturb my circles”—words that seem to refer to two radically different concerns: that of the practical person living in the concrete world of reality, and that of the theoretician lost in a world of abstraction. Stories and theorems are, in a sense, the natural languages of these two worlds—stories representing the way we act and interact, and theorems giving us pure thought, distilled from the hustle and bustle of reality. Yet, though the voices of stories and theorems seem totally different, they share profound connections and similarities. This book delves into topics such as the way in which historical and biographical narratives shape our understanding of mathematics and mathematicians, the development of “myths of origins” in mathematics, the structure and importance of mathematical dreams, the role of storytelling in the formation of mathematical intuitions, the ways mathematics helps us organize the way we think about narrative structure, and much more.
A Streetcar Named (among Other Things) Proof
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,…
Hilbert on Theology and Its Discontents
This chapter examines the myth surrounding Paul Gordan's response to David Hilbert's finiteness theorems. A proof introduced by Hilbert in 1888 became the paradigm of modern axiomatic mathematics. In the myth, Gordan denounced Hilbert's proof, and his anathema rebounded against himself when he said, “This is not Mathematics, it is Theology!” After providing the background to the various interpretations that Gordan's comment has generated, the cha…
Circles disturbed
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A Streetcar Named (among Other Things) Proof
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,…
Hilbert on Theology and Its Discontents
This chapter examines the myth surrounding Paul Gordan's response to David Hilbert's finiteness theorems. A proof introduced by Hilbert in 1888 became the paradigm of modern axiomatic mathematics. In the myth, Gordan denounced Hilbert's proof, and his anathema rebounded against himself when he said, “This is not Mathematics, it is Theology!” After providing the background to the various interpretations that Gordan's comment has generated, the cha…
Circles disturbed