Rarely has the history and philosophy of mathematics been written
about by mathematicians, and the analysis of mathematical texts
themselves has been an area almost entirely unexplored. "Figures of
Thought" looks at ways in which mathematical works can be read as
texts and demonstrates that such readings provide a rich source of
philosophical issues regarding mathematics: issues which
traditional approaches to the history and philosophy of mathematics
have neglected. David Reed offers the first sustained and critical
attempt to find a consistent argument or narrative thread in
mathematical texts. He selects mathematicians from a range of
historical periods and compares their approaches to organizing and
arguing texts, using an extended commentary of Euclid's "Elements"
as a central structuring framework. In doing so, he develops new
interpretations of mathematicians' work throughout history, from
Descartes to Grothendieck and traces the implications of such an
approach for the understanding of the history and development of
mathematics.
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