The History of Mathematical Proof in Ancient Traditions PDF Download
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Author: Karine Chemla
Publisher: Cambridge University Press
ISBN: 1139510584
Category : Philosophy
Languages : en
Pages : 522
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Book Description
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.
Author: Karine Chemla
Publisher: Cambridge University Press
ISBN: 1139510584
Category : Philosophy
Languages : en
Pages : 522
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Book Description
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.
Author: Karine Chemla
Publisher:
ISBN: 9781139518581
Category : MATHEMATICS
Languages : en
Pages : 614
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Book Description
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.
Author: Euclid
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 544
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Book Description
"The book includes introductions, terminology and biographical notes, bibliography, and an index and glossary" --from book jacket.
Author: Geoffrey Ernest Richard Lloyd
Publisher: Cambridge University Press
ISBN: 1108420044
Category : History
Languages : en
Pages : 137
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Book Description
Cross-cultural examination of notions and practices of rationality in ancient and modern societies, drawing on philosophy, ethnography and cognitive science.
Author: Bernard Lightman
Publisher: University of Pittsburgh Press
ISBN: 0822990075
Category : Science
Languages : en
Pages : 376
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Book Description
Before the advent of radio, conceptions of the relationship between science and religion circulated through periodicals, journals, and books, influencing the worldviews of intellectuals and a wider public. In this volume, historians of science and religion examine that relationship through diverse mediums, geographic contexts, and religious traditions. Spanning within and beyond Europe and North America, chapters emphasize underexamined regions—New Zealand, Australia, India, Argentina, Sri Lanka, Egypt, and the Ottoman Empire—and major religions of the world, including Christianity, Hinduism, Buddhism, Confucianism, and Islam; interactions between those traditions; as well as atheism, monism, and agnosticism. As they focus on evolution and human origins, contributors draw attention to European scientists other than Darwin who played a significant role in the dissemination of evolutionary ideas; for some, those ideas provided the key to understanding every aspect of human culture, including religion. They also highlight central figures in national contexts, many of whom were not scientists, who appropriated scientific theories for their own purposes. Taking a local, national, transnational, and global approach to the study of science and religion, this volume begins to capture the complexity of cultural engagement with evolution and religion in the long nineteenth century.
Author: Philip Beeley
Publisher: Routledge
ISBN: 1000207471
Category : Literary Criticism
Languages : en
Pages : 389
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Book Description
Libraries and archives contain many thousands of early modern mathematical books, of which almost equally many bear readers’ marks, ranging from deliberate annotations and accidental blots to corrections and underlinings. Such evidence provides us with the material and intellectual tools for exploring the nature of mathematical reading and the ways in which mathematics was disseminated and assimilated across different social milieus in the early centuries of print culture. Other evidence is important, too, as the case studies collected in the volume document. Scholarly correspondence can help us understand the motives and difficulties in producing new printed texts, library catalogues can illuminate collection practices, while manuscripts can teach us more about textual traditions. By defining and illuminating the distinctive world of early modern mathematical reading, the volume seeks to close the gap between the history of mathematics as a history of texts and history of mathematics as part of the broader history of human culture.
Author: Brian Greer
Publisher: Open Book Publishers
ISBN: 1805113240
Category : Education
Languages : en
Pages : 352
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Book Description
Mathematics is an activity—something we do—not just something inert that we study. This rich collection begins from that premise to explore the various social influences, institutional forces and lived realities that shape and mould the study and practice of mathematics, and are moulded by it in turn. These twenty-one essays explore questions of mathematics as a topic of philosophy, but also the nature and purpose of mathematics education and the role of mathematics in moulding citizens. It challenges the biases and prejudices inherent within uninformed histories of mathematics, including problems of white supremacy, the denial of cultural difference and the global homogenization of teaching methods. In particular, the book contrasts the effectiveness of mathematics and science in modelling physical phenomena and solving technical problems with its ineffectiveness in modelling social phenomena and solving human problems, and urges us to consider how mathematics might better meet the urgent crises of our age. The book addresses anybody who is interested in reflecting on the role of mathematics in society from different perspectives. It allows mathematicians to ponder about the cultural connections of mathematics and provides new perspectives for philosophical, sociological and cultural studies of mathematics. Because of the book’s emphasis on education in mathematics, it is especially interesting for mathematics teachers and teacher educators to challenge their understanding of the subject.
Author: Geoffrey E. R. Lloyd
Publisher: HAU Books
ISBN: 1912808412
Category : Social Science
Languages : en
Pages : 291
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Book Description
This collection brings together leading anthropologists, historians, philosophers, and artificial-intelligence researchers to discuss the sciences and mathematics used in various Eastern, Western, and Indigenous societies, both ancient and contemporary. The authors analyze prevailing assumptions about these societies and propose more faithful, sensitive analyses of their ontological views about reality—a step toward mutual understanding and translatability across cultures and research fields. Science in the Forest, Science in the Past is a pioneering interdisciplinary exploration that will challenge the way readers interested in sciences, mathematics, humanities, social research, computer sciences, and education think about deeply held notions of what constitutes reality, how it is apprehended, and how to investigate it.
Author: Gert Schubring
Publisher: Springer
ISBN: 303001617X
Category : Education
Languages : en
Pages : 201
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Book Description
This contributed volume investigates the active role of the different contexts of mathematics teaching on the evolution of the practices of mathematical concepts, with particular focus on their foundations. The book aims to deconstruct the strong and generally wide-held conviction that research in mathematics constitutes the only driving force for any progress in the development of mathematics as a field. In compelling and convincing contrast, these chapters aim to show the productive function of teaching, showcasing investigations from countries and regions throughout various eras, from Old Babylonia through the 20th Century. In so doing, they provide a critical reflection on the foundations of mathematics, as well as instigate new research questions, and explore the interfaces between teaching and research.
Author: James Evans
Publisher: University of Chicago Press
ISBN: 0226827887
Category : History
Languages : en
Pages : 419
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Book Description
Perceptively explores the shifting intersections between algorithmic systems and human practices in the modern era. How have algorithmic systems and human practices developed in tandem since 1800? This volume of Osiris deftly addresses the question, dispelling along the way the traditional notion of algorithmic “code” and human “craft” as natural opposites. Instead, algorithms and humans have always acted in concert, depending on each other to advance new knowledge and produce social consequences. By shining light on alternative computational imaginaries, Beyond Craft and Code opens fresh space in which to understand algorithmic diversity, its governance, and even its conservation. The volume contains essays by experts in fields extending from early modern arithmetic to contemporary robotics. Traversing a range of cases and arguments that connect politics, historical epistemology, aesthetics, and artificial intelligence, the contributors collectively propose a novel vocabulary of concepts with which to think about how the history of science can contribute to understanding today’s world. Ultimately, Beyond Craft and Code reconfigures the historiography of science and technology to suggest a new way to approach the questions posed by an algorithmic culture—not only improving our understanding of algorithmic pasts and futures but also unlocking our ability to better govern our present.
