the history of mathematical proof in ancient traditions

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The History Of Mathematical Proof In Ancient Traditions

Author : Karine Chemla
ISBN : 9781139510585
Genre : Philosophy
File Size : 61. 27 MB
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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.

Texts Textual Acts And The History Of Science

Author : Karine Chemla
ISBN : 9783319164441
Genre : Science
File Size : 43. 10 MB
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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.

Proofs And Types

Author : Jean-Yves Girard
ISBN : 0521371813
Genre : Computers
File Size : 58. 23 MB
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This text is an outgrowth of notes prepared by J. Y. Girard for a course at the University of Paris VII. It deals with the mathematical background of the application to computer science of aspects of logic (namely the correspondence between proposition & types). Combined with the conceptual perspectives of Girard's ideas, this sheds light on both the traditional logic material & its prospective applications to computer science. The book covers a very active & exciting research area, & it will be essential reading for all those working in logic & computer science.

The Oxford Handbook Of Generality In Mathematics And The Sciences

Author : Karine Chemla
ISBN : 9780198777267
Genre :
File Size : 33. 9 MB
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Generality is a key value in scientific discourses and practices. Throughout history, it has received a variety of meanings and of uses. This collection of original essays aims to inquire into this diversity. Through case studies taken from the history of mathematics, physics and the life sciences, the book provides evidence of different ways of understanding the general in various contexts. It aims at showing how collectives have valued generality and how they have worked with specific types of "general" entities, procedures, and arguments. The books connects history and philosophy of mathematics and the sciences at the intersection of two of the most fruitful contemporary lines of research: historical epistemology, in which values (e.g. "objectivity," "accuracy") are studied from a historical viewpoint; and the philosophy of scientific practice, in which conceptual developments are seen as embedded in networks of social, instrumental, and textual practices. Each chapter provides a self-contained case-study, with a clear exposition of the scientific content at stake. The collection covers a wide range of scientific domains - with an emphasis on mathematics - and historical periods. It thus allows a comparative perspective which suggests a non-linear pattern for a history of generality. The introductory chapter spells out the key issues and points to the connections between the chapters.

Fiscal Regimes And The Political Economy Of Premodern States

Author : Andrew Monson
ISBN : 9781316300152
Genre : History
File Size : 39. 72 MB
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Inspired by the New Fiscal History, this book represents the first global survey of taxation in the premodern world. What emerges is a rich variety of institutions, including experiments with sophisticated instruments such as sovereign debt and fiduciary money, challenging the notion of a typical premodern stage of fiscal development. The studies also reveal patterns and correlations across widely dispersed societies that shed light on the basic factors driving the intensification, abatement, and innovation of fiscal regimes. Twenty scholars have contributed perspectives from a wide range of fields besides history, including anthropology, economics, political science and sociology. The volume's coverage extends beyond Europe, the Mediterranean, and the Near East to East Asia and the Americas, thereby transcending the Eurocentric approach of most scholarship on fiscal history.

Ancient Indian Leaps Into Mathematics

Author : B.S. Yadav
ISBN : 0817646957
Genre : Mathematics
File Size : 83. 70 MB
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This book presents contributions of mathematicians covering topics from ancient India, placing them in the broader context of the history of mathematics. Although the translations of some Sanskrit mathematical texts are available in the literature, Indian contributions are rarely presented in major Western historical works. Yet some of the well-known and universally-accepted discoveries from India, including the concept of zero and the decimal representation of numbers, have made lasting contributions to the foundation of modern mathematics. Through a systematic approach, this book examines these ancient mathematical ideas that were spread throughout India, China, the Islamic world, and Western Europe.

Mathematics In Ancient Iraq

Author : Eleanor Robson
ISBN : 069109182X
Genre : History
File Size : 76. 55 MB
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"This work is an enormously significant contribution to the history of mathematics. No other work surveys the vast landscape of Mesopotamian mathematics from a position of the modern understanding of the past, incorporating the latest scholarship and yet still managing to be so accessible to nonspecialists. Robson's book is an outstanding guide that can be consulted by anyone interested in the field."--Duncan J. Melville, St. Lawrence University "A very significant contribution to the history of ancient mathematics, and to the history of mathematics in general. I anticipate this book will be very, very useful to readers outside the field and general readers, because it is very clearly and incisively written, it gives clear indications about where to find the primary sources, and it summarizes previous historiography very effectively. There is no comparable book."--Serafina Cuomo, Birkbeck College, London "A truly exciting and highly readable intellectual history of ancient Iraq. Eleanor Robson's "Mathematics in Ancient Iraq" is destined to become a classic. The book will have a wide readership among people interested in Near Eastern archaeology, the origins of writing, the history of education, and the history of science. This is truly a magnificent read."--Gary Urton, Harvard University "This is a wholly original work, the first to integrate all the recent work from the history of mathematics in this area with archaeological scholarship. The result is a remarkably rich portrayal of mathematics in ancient Iraq. The breadth of coverage is striking, both in chronological terms but also in broad intellectual ones. The book is very well written and handsomely illustrated."--Jeremy Gray, The Open University

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