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Revolutions And Continuity In Greek Mathematics

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Revolutions And Continuity In Greek Mathematics

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Author : Michalis Sialaros
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2018-04-23

Revolutions And Continuity In Greek Mathematics written by Michalis Sialaros and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-04-23 with History categories.

This volume brings together a number of leading scholars working in the field of ancient Greek mathematics to present their latest research. In their respective area of specialization, all contributors offer stimulating approaches to questions of historical and historiographical ‘revolutions’ and ‘continuity’. Taken together, they provide a powerful lens for evaluating the applicability of Thomas Kuhn’s ideas on ‘scientific revolutions’ to the discipline of ancient Greek mathematics. Besides the latest historiographical studies on ‘geometrical algebra’ and ‘premodern algebra’, the reader will find here some papers which offer new insights into the controversial relationship between Greek and pre-Hellenic mathematical practices. Some other contributions place emphasis on the other edge of the historical spectrum, by exploring historical lines of ‘continuity’ between ancient Greek, Byzantine and post-Hellenic mathematics. The terminology employed by Greek mathematicians, along with various non-textual and material elements, is another topic which some of the essays in the volume explore. Finally, the last three articles focus on a traditionally rich source on ancient Greek mathematics; namely the works of Plato and Aristotle.

Revolutions And Continuity In Greek Mathematics

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Author : Michalis Sialaros
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2018-04-23

Numbers And Numeracy In The Greek Polis

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Author :
language : en
Publisher: BRILL
Release Date : 2021-12-20

Numbers And Numeracy In The Greek Polis written by and has been published by BRILL this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-12-20 with History categories.

We tend to think of numbers as inherently objective and precise. Yet the diverse ways in which ancient Greeks used numbers illustrates that counting is actually shaped by context-specific and culturally-dependent choices: what should be counted and how, who should count, and how should the results be shared? This volume is the first to focus on the generation and use of numbers in the polis to quantify, communicate and persuade. Its papers demonstrate the rich insights that can be gained into ancient Greek societies by reappraising seemingly straightforward examples of quantification as reflections of daily life and cultural understandings.

The Logical Syntax Of Greek Mathematics

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Author : Fabio Acerbi
language : en
Publisher: Springer Nature
Release Date : 2021-06-21

The Logical Syntax Of Greek Mathematics written by Fabio Acerbi and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-06-21 with Mathematics categories.

The aim of this monograph is to describe Greek mathematics as a literary product, studying its style from a logico-syntactic point of view and setting parallels with logical and grammatical doctrines developed in antiquity. In this way, major philosophical themes such as the expression of mathematical generality and the selection of criteria of validity for arguments can be treated without anachronism. Thus, the book is of interest for both historians of ancient philosophy and specialists in Ancient Greek, in addition to historians of mathematics. This volume is divided into five parts, ordered in decreasing size of the linguistic units involved. The first part describes the three stylistic codes of Greek mathematics; the second expounds in detail the mechanism of "validation"; the third deals with the status of mathematical objects and the problem of mathematical generality; the fourth analyzes the main features of the "deductive machine," i.e. the suprasentential logical system dictated by the traditional division of a mathematical proposition into enunciation, setting-out, construction, and proof; and the fifth deals with the sentential logical system of a mathematical proposition, with special emphasis on quantification, modalities, and connectors. A number of complementary appendices are included as well.

Handbook Of The History And Philosophy Of Mathematical Practice

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Author : Bharath Sriraman
language : en
Publisher: Springer Nature
Release Date : 2024-04-26

Handbook Of The History And Philosophy Of Mathematical Practice written by Bharath Sriraman and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-04-26 with Mathematics categories.

The purpose of this unique handbook is to examine the transformation of the philosophy of mathematics from its origins in the history of mathematical practice to the present. It aims to synthesize what is known and what has unfolded so far, as well as to explore directions in which the study of the philosophy of mathematics, as evident in increasingly diverse mathematical practices, is headed. Each section offers insights into the origins, debates, methodologies, and newer perspectives that characterize the discipline today. Contributions are written by scholars from mathematics, history, and philosophy – as well as other disciplines that have contributed to the richness of perspectives abundant in the study of philosophy today – who describe various mathematical practices throughout different time periods and contrast them with the development of philosophy. Editorial Advisory Board Andrew Aberdein, Florida Institute ofTechnology, USA Jody Azzouni, Tufts University, USA Otávio Bueno, University of Miami, USA William Byers, Concordia University, Canada Carlo Cellucci, Sapienza University of Rome, Italy Chandler Davis, University of Toronto, Canada (1926-2022) Paul Ernest, University of Exeter, UK Michele Friend, George Washington University, USA Reuben Hersh, University of New Mexico, USA (1927-2020) Kyeong-Hwa Lee, Seoul National University, South Korea Yuri Manin, Max Planck Institute for Mathematics, Germany (1937-2023) Athanase Papadopoulos, University of Strasbourg, France Ulf Persson, Chalmers University of Technology, Sweden John Stillwell, University of San Francisco, USA David Tall, University of Warwick, UK (1941-2024) This book with its exciting depth and breadth, illuminates us about the history, practice, and the very language of our subject; about the role of abstraction, ofproof and manners of proof; about the interplay of fundamental intuitions; about algebraic thought in contrast to geometric thought. The richness of mathematics and the philosophy encompassing it is splendidly exhibited over the wide range of time these volumes cover---from deep platonic and neoplatonic influences to the most current experimental approaches. Enriched, as well, with vivid biographies and brilliant personal essays written by (and about) people who play an important role in our tradition, this extraordinary collection of essays is fittingly dedicated to the memory of Chandler Davis, Reuben Hersh, and Yuri Manin. ---Barry Mazur, Gerhard Gade University Professor, Harvard University This encyclopedic Handbook will be a treat for all those interested in the history and philosophy of mathematics. Whether one is interested in individuals (from Pythagoras through Newton and Leibniz to Grothendieck), fields (geometry, algebra, number theory, logic, probability, analysis), viewpoints (from Platonism to Intuitionism), or methods (proof, experiment, computer assistance), the reader will find a multitude of chapters that inform and fascinate. ---John Stillwell, Emeritus Professor of Mathematics, University of San Francisco; Recipient of the 2005 Chauvenet Prize Dedicating a volume to the memory of three mathematicians – Chandler Davis, Reuben Hersh, and Yuri Manin –, who went out of their way to show to a broader audience that mathematics is more than what they might think, is an excellent initiative. Gathering authors coming from many different backgrounds but who are very strict about the essays they write was successfully achieved by the editor-in-chief. The result: a great source of potential inspiration! ---Jean-Pierre Bourguignon; Nicolaas Kuiper Honorary Professor at the Institut des Hautes Études Scientifiques

Essays On Topology

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Author : Louis Funar
language : en
Publisher: Springer Nature
Release Date : 2025-07-21

Essays On Topology written by Louis Funar and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-07-21 with Mathematics categories.

This book consists of a collection of articles dedicated to Valentin Poénaru, on topology and geometry in a broad sense. Poénaru is one of the leading mathematicians whose work had an essential impact on the development of topology in France over the last forty years of the twentieth century. The special topics addressed in this volume include hyperbolic geometry, 3-manifolds, complex and symplectic geometry, differential topology, combinatorial group theory, piecewise-linear topology, algebraic geometry, knots and links, homotopy theory, braid groups, phylogenetics, the history of geometry, and the philosophy of mathematics. This collection of articles, written by well-known researchers, provides a lively insight into a number of current research topics in geometry and topology.

Anachronisms In The History Of Mathematics

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Author : Niccol- Guicciardini
language : en
Publisher: Cambridge University Press
Release Date : 2021-07-22

Anachronisms In The History Of Mathematics written by Niccol- Guicciardini and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-07-22 with History categories.

Discover essays by leading scholars on the history of mathematics from ancient to modern times in European and non-European cultures.

Geometry In History

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Author : S. G. Dani
language : en
Publisher: Springer Nature
Release Date : 2019-10-18

Geometry In History written by S. G. Dani and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-10-18 with Mathematics categories.

This is a collection of surveys on important mathematical ideas, their origin, their evolution and their impact in current research. The authors are mathematicians who are leading experts in their fields. The book is addressed to all mathematicians, from undergraduate students to senior researchers, regardless of the specialty.

Scientific Visual Representations In History

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Author : Matteo Valleriani
language : en
Publisher: Springer Nature
Release Date : 2023-01-01

Scientific Visual Representations In History written by Matteo Valleriani and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-01-01 with Science categories.

This book explores continuity and ruptures in the historical use of visual representations in science and related disciplines such as art history and anthropology. The book also considers more recent developments that attest to the unprecedented importance of scientific visualizations, such as video recordings, animations, simulations, graphs, and enhanced realities. The volume collects historical reflections concerned with the use of visual material, visualization, and vision in science from a historical perspective, ranging across multiple cultures from antiquity until present day. The focus is on visual representations such as drawings, prints, tables, mathematical symbols, photos, data visualizations, mapping processes, and (on a meta-level) visualizations of data extracted from historical sources to visually support the historical research itself. Continuity and ruptures between the past and present use of visual material are presented against the backdrop of the epistemic functions of visual material in science. The function of visual material is defined according to three major epistemic categories: exploration, transformation, and transmission of knowledge.

Brill S Companion To The Reception Of Ancient Rhetoric

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Author :
language : en
Publisher: BRILL
Release Date : 2021-12-06

Brill S Companion To The Reception Of Ancient Rhetoric written by and has been published by BRILL this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-12-06 with Literary Criticism categories.

This volume, examining the reception of ancient rhetoric, aims to demonstrate that the past is always part of the present: in the ways in which decisions about crucial political, social and economic matters have been made historically; or in organic interaction with literature, philosophy and culture at the core of the foundation principles of Western thought and values. Analysis is meant to cover the broadest possible spectrum of considerations that focus on the totality of rhetorical species (i.e. forensic, deliberative and epideictic) as they are applied to diversified topics (including, but not limited to, language, science, religion, literature, theatre and other cultural processes (e.g. athletics), politics and leadership, pedagogy and gender studies) and cross-cultural, geographical and temporal contexts.

Revolutions And Continuity In Greek Mathematics

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