Figures of Thought: Mathematics and Mathematical Texts

Figures of Thought: Mathematics and Mathematical Texts

Figures of Thought: Mathematics and Mathematical Texts

Figures of Thought: Mathematics and Mathematical Texts


Rarely has the history or 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, examines their textual strategies 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, a professional mathematician himself, offers the first sustained and critical attempt to find a consistent argument or narrative thread in mathematical texts. In doing so he develops new and fascinating interpretations of mathematicians' work throughout history, from an in-depth analysis of Euclid's Elements , to the mathematics of Descartes and right up to the work of contemporary mathematicians such as Grothendeick. He also traces the implications of this approach to the understanding of the history and development of mathematics.


Day unto day uttereth speech and night unto night declareth knowledge…


But the contemplative life is somehow above the level of humanity…

Nic. Eth. X vii

This book is the product of reflection and research undertaken over a period of twenty years under a wide variety of circumstances. It has its origins in the simple questions that David Smigelskis, Charles Wegener and Eugene Garver asked and taught me to ask at the University of Chicago two decades ago and the pleasure that accompanies the attempt to answer such questions has not diminished since. The influence of the ideas of Richard McKeon will also be evident to anyone who is familiar with them. More recently the kind and encouraging words of Stuart Shenker provided the impetus to undertake the task of combining these thoughts into a systematic whole.

Over these decades there has been a steady increase in the number of analyses of works from the 'scientific literature' and the notion that such texts can be treated as texts has become much more widespread. Readers will surely not be surprised to find in their hands an analysis which includes not only writings of Euclid and Descartes but also more modern and indeed contemporary mathematicians as well. The mathematical literature contains many wonderful examples from a range of eras and in a variety of genres. Increased awareness of the value of this literature both within and without the mathematical community is the principal objective to which this book is devoted.

Special thanks are owed to the Mathematical Institute, Angus Macintyre, Bryan Birch, Aldo and Gigi and all the others who have made my re-entry into the mathematical community so enjoyable. . .

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