This is the first book-length analysis of the techniques and procedures of ancient mathematical commentaries. It focuses on examples in Chinese, Sanskrit, Akkadian and Sumerian, and Ancient Greek, presenting the general issues by constant detailed reference to these commentaries, of which substantial extracts are included in the original languages and in translation, sometimes for the first time. This makes the issues accessible to readers without specialized training in mathematics or in the languages involved. The result is a much richer understanding than was hitherto possible of the crucial role of commentaries in the history of mathematics in four different linguistic areas, of the nature of mathematical commentaries in general, of the contribution that the study of mathematical commentaries can make to the history of science and to the study of commentaries in general, and of the ways in which mathematical commentaries are like and unlike other kinds of commentaries.

This book focuses on the ancient Near East, early imperial China, South-East Asia, and medieval Europe, shedding light on mathematical knowledge and practices documented by sources relating to the administrative and economic activities of officials, merchants and other actors. It compares these to mathematical texts produced in related school contexts or reflecting the pursuit of mathematics for its own sake to reveal the diversity of mathematical practices in each of these geographical areas of the ancient world. Based on case studies from various periods and political, economic and social contexts, it explores how, in each part of the world discussed, it is possible to identify and describe the different cultures of quantification and computation as well as their points of contact. The thirteen chapters draw on a wide variety of texts from ancient Near East, China, South-East Asia and medieval Europe, which are analyzed by researchers from various fields, including mathematics, history, philology, archaeology and economics. The book will appeal to historians of science, economists and institutional historians of the ancient and medieval world, and also to Assyriologists, Indologists, Sinologists and experts on medieval Europe.

This book focuses on the ancient Near East, early imperial China, South-East Asia, and medieval Europe, shedding light on mathematical knowledge and practices documented by sources relating to the administrative and economic activities of officials, merchants and other actors. It compares these to mathematical texts produced in related school contexts or reflecting the pursuit of mathematics for its own sake to reveal the diversity of mathematical practices in each of these geographical areas of the ancient world. Based on case studies from various periods and political, economic and social contexts, it explores how, in each part of the world discussed, it is possible to identify and describe the different cultures of quantification and computation as well as their points of contact. The thirteen chapters draw on a wide variety of texts from ancient Near East, China, South-East Asia and medieval Europe, which are analyzed by researchers from various fields, including mathematics, history, philology, archaeology and economics. The book will appeal to historians of science, economists and institutional historians of the ancient and medieval world, and also to Assyriologists, Indologists, Sinologists and experts on medieval Europe.

This radical, profoundly scholarly book explores the purposes and nature of proof in a range of historical settings. It overturns the view that the first mathematical proofs were in Greek geometry and rested on the logical insights of Aristotle by showing how much of that view is an artefact of nineteenth-century historical scholarship. It documents the existence of proofs in ancient mathematical writings about numbers and shows that practitioners of mathematics in Mesopotamian, Chinese and Indian cultures knew how to prove the correctness of algorithms, which are much more prominent outside the limited range of surviving classical Greek texts that historians have taken as the paradigm of ancient mathematics. It opens the way to providing the first comprehensive, textually based history of proof.

The book presents the outcomes of an innovative research programme in the history of science and implements a Text Act Theory which extends Speech Act Theory, in order to illustrate a new approach to texts and textual communicative acts. It examines assertives (absolute or conditional statements, forecasts, insurance, etc.), directives, declarations and enumerations, as well as different types of textual units allowing authors to perform these acts: algorithms, recipes, prescriptions, lexical templates for terminological studies and enumerative structures. The book relies on the study of a broad range of documents of the past dealing with various domains: mathematics, zoology, medicine, lexicography. The documents examined come from scholarly sources from different parts of the world, such as China, Europe, India, Mesopotamia and are written in a variety of European languages as well as Chinese, Cuneiform and Sanskrit. This approach proves fruitful in both history of science and Text Act Theory.

The book presents the outcomes of an innovative research programme in the history of science and implements a Text Act Theory which extends Speech Act Theory, in order to illustrate a new approach to texts and textual communicative acts. It examines assertives (absolute or conditional statements, forecasts, insurance, etc.), directives, declarations and enumerations, as well as different types of textual units allowing authors to perform these acts: algorithms, recipes, prescriptions, lexical templates for terminological studies and enumerative structures. The book relies on the study of a broad range of documents of the past dealing with various domains: mathematics, zoology, medicine, lexicography. The documents examined come from scholarly sources from different parts of the world, such as China, Europe, India, Mesopotamia and are written in a variety of European languages as well as Chinese, Cuneiform and Sanskrit. This approach proves fruitful in both history of science and Text Act Theory.

How do Documents Become Sources? Perspectives from Asia and Science Florence Bretelle-Establet From Documents to Sources in Historiography The present volume develops a specific type of critical analysis of the written documents that have become historians' sources. For reasons that will be explained later, the history of science in Asia has been taken as a framework. However, the issue addressed is general in scope. It emerged from reflections on a problem that may seem common to historians: why, among the huge mass of written documents available to historians, some have been well studied while others have been dismissed or ignored? The question of historical sources and their (unequal) use in historiography is not new. Which documents have been used and favored as historical sources by historians has been a key historiographical issue that has occupied a large space in the historical production of the last four decades, in France at least.

two main (interacting) ways. They constitute that with which exploration into problems or questions is carried out. But they also constitute that which is exchanged between scholars or, in other terms, that which is shaped by one (or by some) for use by others. In these various dimensions, texts obviously depend on the means and technologies available for producing, reproducing, using and organizing writings. In this regard, the contribution of a history of text is essential in helping us approach the various historical contexts from which our sources originate. However, there is more to it. While shaping texts as texts, the practitioners of the sciences may create new textual resources that intimately relate to the research carried on. One may think, for instance, of the process of introduction of formulas in mathematical texts. This aspect opens up a wholerangeofextremelyinterestingquestionstowhichwewillreturnatalaterpoint.But practitioners of the sciences also rely on texts produced by themselves or others, which they bring into play in various ways. More generally, they make use of textual resources of every kind that is available to them, reshaping them, restricting, or enlarging them. Among these, one can think of ways of naming, syntax of statements or grammatical analysis, literary techniques, modes of shaping texts or parts of text, genres of text and so on.Inthissense, thepractitionersdependon, anddrawon, the"textualcultures"available to the social and professional groups to which they belong.

How do Documents Become Sources? Perspectives from Asia and Science Florence Bretelle-Establet From Documents to Sources in Historiography The present volume develops a specific type of critical analysis of the written documents that have become historians' sources. For reasons that will be explained later, the history of science in Asia has been taken as a framework. However, the issue addressed is general in scope. It emerged from reflections on a problem that may seem common to historians: why, among the huge mass of written documents available to historians, some have been well studied while others have been dismissed or ignored? The question of historical sources and their (unequal) use in historiography is not new. Which documents have been used and favored as historical sources by historians has been a key historiographical issue that has occupied a large space in the historical production of the last four decades, in France at least.

This book explores the hypothesis that the types of inscription or text used by a given community of practitioners are designed in the very same process as the one producing concepts and results. The book sets out to show how, in exactly the same way as for the other outcomes of scientific activity, all kinds of factors, cognitive as well as cultural, technological, social or institutional, conjoin in shaping the various types of writings and texts used by the practitioners of the sciences. To make this point, the book opts for a genuinely multicultural approach to the texts produced in the context of practices of knowledge. It is predicated on the conviction that, in order to approach any topic in the history of science from a theoretical point of view, it may be fruitful to consider it from a global perspective. The book hence does not only gather papers dealing with geometrical papyri of antiquity, sixteenth century French books in algebra, seventeenth century scientific manuscripts and paintings, eighteenth and nineteenth century memoirs published by European academies or scientific journals, and Western Opera Omnia. It also considers the problems of interpretation relating to reading Babylonian clay tablets, Sanskrit oral scriptures and Chinese books and illustrations. Thus it enables the reader to explore the diversity of forms which texts have taken in history and the wide range of uses they have inspired.

This volume will be of interest to historians, philosophers of science, linguists and anthropologists.

Cultural accounts of scientific ideas and practices have increasingly come to be welcomed as a corrective to previous-and still widely held-theories of scientific knowledge and practices as universal. The editors caution, however, against the temptation to overgeneralize the work of culture, and to lapse into a kind of essentialism that flattens the range and variety of scientific work. The book refers to this tendency as culturalism. The contributors to the volume model a new path where historicized and cultural accounts of scientific practice retain their specificity and complexity without falling into the traps of culturalism. They examine, among other issues, the potential of using notions of culture to study behavior in financial markets; the ideology, organization, and practice of earthquake monitoring and prediction during China's Cultural Revolution; the history of quadratic equations in China; and how studying the "glass ceiling" and employment discrimination became accepted in the social sciences. Demonstrating the need to understand the work of culture as a fluid and dynamic process that directly both shapes and is shaped by scientific practice, Cultures without Culturalism makes an important intervention in science studies. Contributors. Bruno Belhoste, Karine Chemla, Caroline Ehrhardt, Fa-ti Fan,Kenji Ito, Evelyn Fox Keller, Guillaume Lachenal, Donald MacKenzie, Mary S. Morgan, Nancy J. Nersessian, David Rabouin, Hans-Joerg Rheinberger, Claude Rosental, Koen Vermeir

This book sheds light on the variety of mathematical cultures in general. To do so, it concentrates on cultures of computation and quantification in the ancient world, mainly in ancient China, South Asia, and the Ancient Near East and offers case studies focused on numbers, quantities, and operations, in particular in relation to mathematics as well as administrative and economic activities. The various chapters focus on the different ways and contexts of shaping numbers and quantities, and on the procedures applied to them. The book places special emphasis on the processes of emergence of place-value number systems, evidenced in the three geographical areas under study All these features yield essential elements that will enable historians of mathematics to further capture the diversity of computation practices in their contexts, whereas previous historical approaches have tended to emphasize elements that displayed uniformity within "civilizational" blocks. The book includes editions and translations of texts, some of them published here for the first time, maps, and conventions for editions of ancient texts. It thereby offers primary sources and methodological tools for teaching and learning. The volume is aimed at historians and philosophers of science and mathematics, historians of the ancient worlds, historians of economics, sinologists, indologists, assyriologists, as well as undergraduate, graduate students and teachers in mathematics, the history and philosophy of science and mathematics, and in the history of ancient worlds.

This radical, profoundly scholarly book explores the purposes and nature of proof in a range of historical settings. It overturns the view that the first mathematical proofs were in Greek geometry and rested on the logical insights of Aristotle by showing how much of that view is an artefact of nineteenth-century historical scholarship. It documents the existence of proofs in ancient mathematical writings about numbers and shows that practitioners of mathematics in Mesopotamian, Chinese and Indian cultures knew how to prove the correctness of algorithms, which are much more prominent outside the limited range of surviving classical Greek texts that historians have taken as the paradigm of ancient mathematics. It opens the way to providing the first comprehensive, textually based history of proof.

Cultural accounts of scientific ideas and practices have increasingly come to be welcomed as a corrective to previous—and still widely held—theories of scientific knowledge and practices as universal. The editors caution, however, against the temptation to overgeneralize the work of culture, and to lapse into a kind of essentialism that flattens the range and variety of scientific work. The book refers to this tendency as culturalism. The contributors to the volume model a new path where historicized and cultural accounts of scientific practice retain their specificity and complexity without falling into the traps of culturalism. They examine, among other issues, the potential of using notions of culture to study behavior in financial markets; the ideology, organization, and practice of earthquake monitoring and prediction during China's Cultural Revolution; the history of quadratic equations in China; and how studying the "glass ceiling" and employment discrimination became accepted in the social sciences. Demonstrating the need to understand the work of culture as a fluid and dynamic process that directly both shapes and is shaped by scientific practice, Cultures without Culturalism makes an important intervention in science studies. Contributors. Bruno Belhoste, Karine Chemla, Caroline Ehrhardt, Fa-ti Fan,Kenji Ito, Evelyn Fox Keller, Guillaume Lachenal, Donald MacKenzie, Mary S. Morgan, Nancy J. Nersessian, David Rabouin, Hans-Jörg Rheinberger, Claude Rosental, Koen Vermeir