Harvard University Press
The Craft of Indo-Arabic Numerals
About this book
“A must-read.” —Joel Mokyr, Nobel Prize–winning author of A Culture of Growth: The Origins of the Modern Economy
An illuminating, fine-grained account of how Indo-Arabic numerals facilitated the spread of practical knowledge in Western Europe—reshaping both commerce and mathematics in the process.
In the thirteenth-century Mediterranean, commerce transformed as merchants shifted from Roman to Indo-Arabic numerals—an alternative that better facilitated complex calculations. It has long been known that this transition stemmed from Europe’s increasing exchanges with India, Persia, and the Arabic world. Yet much remains to be understood about how Indo-Arabic numerals—and the practical arithmetic they enabled—actually spread across Europe. As Raffaele Danna shows, it was hundreds of ordinary merchants, schoolmasters, and artisans who nurtured these changes, thereby driving key advances in both commerce and mathematics.
Drawing on an original catalog of more than 1,200 practical arithmetic manuals, Danna charts the incremental spread of the new figures with unprecedented precision. While Italian merchants were the early adopters, it took nearly three centuries for Indo-Arabic numerals to become established in northern Europe. As Danna shows, adoption did not follow the routes of maritime trade. Rather, Indo-Arabic numerals moved gradually across the continent through inland networks of practitioners. Everywhere they went, the ten figures enhanced commercial practices and facilitated the emergence of a coherent language of mathematical craft. The growing social circulation of this knowledge, in turn, had a lasting impact on the economic trajectory of Western Europe. By the late sixteenth century, even academics were absorbing lessons from the vernacular tradition—a development that led to the first major breakthroughs in European mathematical theory since antiquity.
Combining economic history with the social history of mathematics, The Craft of Indo-Arabic Numerals illuminates the integral role of practical arithmetic in both intellectual and commercial transformations across Western Europe.
Reviews
-- Joel Mokyr, Nobel Prize–winning author of A Culture of Growth: The Origins of the Modern Economy
-- Sheilagh Ogilvie, author of The European Guilds: An Economic Analysis
-- Thomas Morel, author of Underground Mathematics: Craft Culture and Knowledge Production in Early Modern Europe
-- Patrick Wallis, author of The Market for Skill: Apprenticeship and Economic Growth in Early Modern England
-- Morgan Kelly, Professor of Economics at University College Dublin
Topics
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Frontmatter
i -
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Contents
vii -
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Introduction
1 - Part 1: The emergence of practical arithmetic
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1 The Adoption of Indo-Arabic Numerals in Latin Europe
33 -
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2 Indo-Arabic Numerals and the Commercial Revolution
58 -
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3 A Mathematical Craft
86 - Part 2: The spread of practical arithmetic
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4 The Spread of Practical Arithmetic in Italy
131 -
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5 The Spread of Practical Arithmetic in Europe
184 -
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6 Indo-Arabic Numerals in Other Vernacular Sources
245 -
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Conclusion
285 -
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Note on Sources
293 -
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Notes
299 -
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Selected Bibliography
391 -
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Acknowledgments
409 -
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Index
413
