This book emerged from a discussion I had with Don Albers in the Spring of 2002, when he suggested the ideaof a book that would describe the world of the great mathematicians: “What would Newton see, if he looked out his window?” I really liked the idea, and planned to pick out a dozen or so mathematicians and write a hundred or so pages of history discussing how mathematics, society, and mathematicians interacted with one another. Before I knew it, I had written six hundred pages. I've cut those down to the present text, which is part mathematics, part mathematical biography, and part history.

My hope is to convey some of the fascinating and complex relationships between mathematicians, mathematics, and society. In these pages, you will find how world events shaped the lives of mathematicians like Archimedes and de Moivre; how artistic conventions inspired some of the mathematical investigations of Abu'l-Wafā and al-Khayyāmī; how Newton and Poincaré affected the political events of their time; and how mathematical concepts like the irrationality of 7√2 drove cultural development.

Finally, some thanks and dedication. First, to Rob Bradley of Adelphi University and Ross Gingrich of Southern Connecticut State University for suggesting the title of the book (my title was a completely uninspired “Mathematics and History”). Next, to my wife Jacqui, who listened with great forbearance as I tried to reconcile information from different sources, which often spelled and indexed the same name in different ways, or gave different dates for the same historical event, or completely different interpretations of the significance of an event.