This book could not have been written without the support of many individuals, starting with my wife, Jennifer, who read several complete drafts, making editorial, structural, and practical suggestions. She is always my inspiration and support.
I am exceedingly grateful to the Bogliasco Foundation for a Fellowship and Residency to complete this book at the magnificent Villa dei Pini on the aptly named Golfo Paradiso in Bogliasco, Italy. It generously provided me with ample time, luxurious comfort, and late afternoon swims in the warm Mediterranean, all in the company of my delightfully inspiring colleagues Ruby Blondell, John Eaton, Luisa Costa Gomes, Jennie MaryTai Liu, Jennifer Sachs, and Willard Spiegelman, who contributed both directly and indirectly to the final draft of this book.
Very special thanks to the caring readers of complete drafts: Michelle Bower, Julian Ferholz, and Margorie Senechal. Thanks to others who read drafts of individual chapters, often many chapters: Robyn Arianrhod, Steve Batterson, Kenneth Bleeth, Charles Burnett, Barry Cipra, David Cox, Robert Dawson, Florin Diacu, Rafaella Franci, Fernando Gouvea, Emily Grosholz, Phil Holmes, Jens Høyrup, Gizem Karaali, Mikhail Katz, Catherine Mazur-Jefferies, Barry Mazur, Peter Meredith, Kim Plofker, and Siobhan Roberts. And thanks to my expert consultants for informative and encouraging correspondence, and conversations: Stanislas Dehaene, David Geary, Daniel Kahneman, George Lakoff, Steven Pinker, Ian Stewart, David Tall, and Elisabetta Ulivi.
I consider myself a mathematics journalist embedded with the learned troupes. So I thank the real scholars who have labored over the history of symbols to uncover (p.234) what had been intellectually lost for hundreds of years. Stephen Chrisomalis for his doctoral dissertation, “The Comparative History of Numerical Notation” (McGill, 2003), which lists 1,047 academic publications about numerals and numeral systems, numeral notation, and numeration. This was vastly helpful in my research. Paolo Vian of the Biblioteca Apostolica Vaticana. Clay Institute, Project Guttenberg, OpenLibrary.org, University of Chicago Digital Preservation Collection, The European Cultural Heritage Online (ECHO), The New York Public Library Digital Gallery, Liberty Fund, PhilSci Archive, Biblioteca Apostolica Vaticana, Archivio di Stato de Firenze, Biblioteca Marucelliana Firenze, Biblioteca Nazionale Centrale Firenze, Universita degli Studi di Pavia, and so on. Gallica (the online rare books library of the Bibliothèque National de France), Scribd.com, Ancientlibrary.com, the Perseus Digital Library, Centro di Ricerca Matematica Ennio De Giorgi (for Bombelli’s L’Algebra), and Biblioteca della Scuola Normale Superiore for allowing me to do research from my home that, a decade ago, would have taken years in rare books rooms of libraries halfway around the world, and to Jonathan Bennett, who maintains a site for the translations of correspondences of mathematicians and philosophers at www.earlymoderntexts.com. And to the real scholars no longer with us, who labored over the history of symbols to uncover what had been intellectually lost for hundreds of years: Florian Cajori, Sir Thomas Heath, Louis Charles Karpinski, and Karl Menninger. Many thanks to Marek Čtrnáct, the translator for the Czech edition, for catching a heap of English typos in the last moments of production.
Special thanks goes to my editor, Vickie Kearn, for her resolute support, and to my agent, Andrew Stewart, who saw this project’s potential in my very brief proposal.
To the Mazur Jefferies family: Catherine, Tom, Sophie, Yelena, and Ned. To the Marshall family: Tamina, Scott, and Lena. To my brother Barry and sisters-in-law Carole Joffe and Grechen Mazur, for their constant encouragement.