Making And Breaking Mathematical Sense

Author : Roi Wagner
Publisher : Princeton University Press
Page : 250 pages
File Size : 40,8 Mb
Release : 2017-01-10
Category : Mathematics
ISBN : 9780691171715

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Making and Breaking Mathematical Sense by Roi Wagner Pdf

In line with the emerging field of philosophy of mathematical practice, this book pushes the philosophy of mathematics away from questions about the reality and truth of mathematical entities and statements and toward a focus on what mathematicians actually do—and how that evolves and changes over time. How do new mathematical entities come to be? What internal, natural, cognitive, and social constraints shape mathematical cultures? How do mathematical signs form and reform their meanings? How can we model the cognitive processes at play in mathematical evolution? And how does mathematics tie together ideas, reality, and applications? Roi Wagner uniquely combines philosophical, historical, and cognitive studies to paint a fully rounded image of mathematics not as an absolute ideal but as a human endeavor that takes shape in specific social and institutional contexts. The book builds on ancient, medieval, and modern case studies to confront philosophical reconstructions and cutting-edge cognitive theories. It focuses on the contingent semiotic and interpretive dimensions of mathematical practice, rather than on mathematics' claim to universal or fundamental truths, in order to explore not only what mathematics is, but also what it could be. Along the way, Wagner challenges conventional views that mathematical signs represent fixed, ideal entities; that mathematical cognition is a rigid transfer of inferences between formal domains; and that mathematics’ exceptional consensus is due to the subject’s underlying reality. The result is a revisionist account of mathematical philosophy that will interest mathematicians, philosophers, and historians of science alike.

Author : Roi Wagner
Publisher : Princeton University Press
Page : 256 pages
File Size : 44,9 Mb
Release : 2017-01-10
Category : Mathematics
ISBN : 9781400883783

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Making and Breaking Mathematical Sense by Roi Wagner Pdf

In line with the emerging field of philosophy of mathematical practice, this book pushes the philosophy of mathematics away from questions about the reality and truth of mathematical entities and statements and toward a focus on what mathematicians actually do—and how that evolves and changes over time. How do new mathematical entities come to be? What internal, natural, cognitive, and social constraints shape mathematical cultures? How do mathematical signs form and reform their meanings? How can we model the cognitive processes at play in mathematical evolution? And how does mathematics tie together ideas, reality, and applications? Roi Wagner uniquely combines philosophical, historical, and cognitive studies to paint a fully rounded image of mathematics not as an absolute ideal but as a human endeavor that takes shape in specific social and institutional contexts. The book builds on ancient, medieval, and modern case studies to confront philosophical reconstructions and cutting-edge cognitive theories. It focuses on the contingent semiotic and interpretive dimensions of mathematical practice, rather than on mathematics' claim to universal or fundamental truths, in order to explore not only what mathematics is, but also what it could be. Along the way, Wagner challenges conventional views that mathematical signs represent fixed, ideal entities; that mathematical cognition is a rigid transfer of inferences between formal domains; and that mathematics’ exceptional consensus is due to the subject’s underlying reality. The result is a revisionist account of mathematical philosophy that will interest mathematicians, philosophers, and historians of science alike.

Author : Mircea Pitici
Publisher : Princeton University Press
Page : 242 pages
File Size : 48,7 Mb
Release : 2017-11-14
Category : Mathematics
ISBN : 9780691178639

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The Best Writing on Mathematics 2017 by Mircea Pitici Pdf

The year's finest mathematics writing from around the world This annual anthology brings together the year’s finest mathematics writing from around the world. Featuring promising new voices alongside some of the foremost names in the field, The Best Writing on Mathematics 2017 makes available to a wide audience many articles not easily found anywhere else—and you don’t need to be a mathematician to enjoy them. These writings offer surprising insights into the nature, meaning, and practice of mathematics today. They delve into the history, philosophy, teaching, and everyday occurrences of math, and take readers behind the scenes of today’s hottest mathematical debates. Here Evelyn Lamb describes the excitement of searching for incomprehensibly large prime numbers, Jeremy Gray speculates about who would have won math’s highest prize—the Fields Medal—in the nineteenth century, and Philip Davis looks at mathematical results and artifacts from a business and marketing viewpoint. In other essays, Noson Yanofsky explores the inherent limits of knowledge in mathematical thinking, Jo Boaler and Lang Chen reveal why finger-counting enhances children’s receptivity to mathematical ideas, and Carlo Séquin and Raymond Shiau attempt to discover how the Renaissance painter Fra Luca Pacioli managed to convincingly depict his famous rhombicuboctahedron, a twenty-six-sided Archimedean solid. And there’s much, much more. In addition to presenting the year’s most memorable writings on mathematics, this must-have anthology includes a bibliography of other notable writings and an introduction by the editor, Mircea Pitici. This book belongs on the shelf of anyone interested in where math has taken us—and where it is headed.

Author : Cary Wolfe,Adam Nocek
Publisher : Routledge
Page : 196 pages
File Size : 43,7 Mb
Release : 2021-12-27
Category : Philosophy
ISBN : 9781000533613

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Ontogenesis Beyond Complexity by Cary Wolfe,Adam Nocek Pdf

This book is based upon the collaborative efforts of the Ontogenetics Process Group (OPG) – an interdisciplinary, multi-institutional, multi-national research group that began meeting in 2017 to explore new and innovative ways of thinking the problem of complexity in living, physical, and social systems outside the algorithmic models that have dominated paradigms of complexity to date. For all the descriptive and predictive power that the complexity sciences offer (the ability to compute feedback systems, recursive networks, emergent dynamics, etc.), they also presume that the living world in all of its modalities (biological, semiotic, economic, affective, social) can be reduced to finite schema of description that delimits in advance all possible outcomes. What is proposed in this volume are conceptual architectures for the living that are not only irreducible to physico-mathematical frames of reference, but that are also as vital as the phenomena they wish to express. In short: life is more complex than complexity. What emerges from this engagement is not the ascendance of a new transcendental principle (or, what amounts to the same thing, a foundational bedrock) derived from the physico-mathematical sciences, but just the opposite: a domain in which the ontological and the epistemological domains enter a zone of strange (and unavoidable) entanglement. The chapters in this book were originally published as a special issue of Angelaki.

Author : Mircea Pitici
Publisher : Princeton University Press
Page : 288 pages
File Size : 51,9 Mb
Release : 2019-11-05
Category : Crafts & Hobbies
ISBN : 9780691198354

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The Best Writing on Mathematics 2019 by Mircea Pitici Pdf

An anthology of the year's finest writing on mathematics from around the world, featuring promising new voices as well as some of the foremost names in mathematics.

Author : Victor J. Katz,Menso Folkerts,Barnabas Hughes,Roi Wagner,J. Lennart Berggren
Publisher : Princeton University Press
Page : 593 pages
File Size : 51,7 Mb
Release : 2016-10-18
Category : Mathematics
ISBN : 9781400883202

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Sourcebook in the Mathematics of Medieval Europe and North Africa by Victor J. Katz,Menso Folkerts,Barnabas Hughes,Roi Wagner,J. Lennart Berggren Pdf

Medieval Europe was a meeting place for the Christian, Jewish, and Islamic civilizations, and the fertile intellectual exchange of these cultures can be seen in the mathematical developments of the time. This sourcebook presents original Latin, Hebrew, and Arabic sources of medieval mathematics, and shows their cross-cultural influences. Most of the Hebrew and Arabic sources appear here in translation for the first time. Readers will discover key mathematical revelations, foundational texts, and sophisticated writings by Latin, Hebrew, and Arabic-speaking mathematicians, including Abner of Burgos's elegant arguments proving results on the conchoid—a curve previously unknown in medieval Europe; Levi ben Gershon’s use of mathematical induction in combinatorial proofs; Al-Mu’taman Ibn Hūd’s extensive survey of mathematics, which included proofs of Heron’s Theorem and Ceva’s Theorem; and Muhyī al-Dīn al-Maghribī’s interesting proof of Euclid’s parallel postulate. The book includes a general introduction, section introductions, footnotes, and references. The Sourcebook in the Mathematics of Medieval Europe and North Africa will be indispensable to anyone seeking out the important historical sources of premodern mathematics.

Author : Bharath Sriraman
Publisher : Springer Nature
Page : 3221 pages
File Size : 55,5 Mb
Release : 2024-06-29
Category : Electronic
ISBN : 9783031408465

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Handbook of the History and Philosophy of Mathematical Practice by Bharath Sriraman Pdf

Author : Stefania Centrone,Deborah Kant,Deniz Sarikaya
Publisher : Springer Nature
Page : 511 pages
File Size : 51,6 Mb
Release : 2019-11-11
Category : Mathematics
ISBN : 9783030156558

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Reflections on the Foundations of Mathematics by Stefania Centrone,Deborah Kant,Deniz Sarikaya Pdf

This edited work presents contemporary mathematical practice in the foundational mathematical theories, in particular set theory and the univalent foundations. It shares the work of significant scholars across the disciplines of mathematics, philosophy and computer science. Readers will discover systematic thought on criteria for a suitable foundation in mathematics and philosophical reflections around the mathematical perspectives. The volume is divided into three sections, the first two of which focus on the two most prominent candidate theories for a foundation of mathematics. Readers may trace current research in set theory, which has widely been assumed to serve as a framework for foundational issues, as well as new material elaborating on the univalent foundations, considering an approach based on homotopy type theory (HoTT). The third section then builds on this and is centred on philosophical questions connected to the foundations of mathematics. Here, the authors contribute to discussions on foundational criteria with more general thoughts on the foundations of mathematics which are not connected to particular theories. This book shares the work of some of the most important scholars in the fields of set theory (S. Friedman), non-classical logic (G. Priest) and the philosophy of mathematics (P. Maddy). The reader will become aware of the advantages of each theory and objections to it as a foundation, following the latest and best work across the disciplines and it is therefore a valuable read for anyone working on the foundations of mathematics or in the philosophy of mathematics.

Author : Emily Rolfe Grosholz
Publisher : Springer
Page : 187 pages
File Size : 54,5 Mb
Release : 2016-11-25
Category : Philosophy
ISBN : 9783319466903

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Starry Reckoning: Reference and Analysis in Mathematics and Cosmology by Emily Rolfe Grosholz Pdf

This book deals with a topic that has been largely neglected by philosophers of science to date: the ability to refer and analyze in tandem. On the basis of a set of philosophical case studies involving both problems in number theory and issues concerning time and cosmology from the era of Galileo, Newton and Leibniz up through the present day, the author argues that scientific knowledge is a combination of accurate reference and analytical interpretation. In order to think well, we must be able to refer successfully, so that we can show publicly and clearly what we are talking about. And we must be able to analyze well, that is, to discover productive and explanatory conditions of intelligibility for the things we are thinking about. The book’s central claim is that the kinds of representations that make successful reference possible and those that make successful analysis possible are not the same, so that significant scientific and mathematical work typically proceeds by means of a heterogeneous discourse that juxtaposes and often superimposes a variety of kinds of representation, including formal and natural languages as well as more iconic modes. It demonstrates the virtues and necessity of heterogeneity in historically central reasoning, thus filling an important gap in the literature and fostering a new, timely discussion on the epistemology of science and mathematics.

Author : Paul A. Wagner,Frank Fair
Publisher : Rowman & Littlefield
Page : 153 pages
File Size : 49,9 Mb
Release : 2022-06-06
Category : Education
ISBN : 9781475862997

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The Personality of Math by Paul A. Wagner,Frank Fair Pdf

If our goal is to broaden and deepen students’ awareness and understanding of mathematics, we advance the idea that engaging students with what we metaphorically call the personality of math. That is, we think that students who engage with the math’s (1) human champions, (2) with its history and philosophy, and (3) with the nature of its problems and inferential challenges, are more likely to have a positive attitude toward math that will encourage greater learning.

Author : Mojtaba Mojtahedi,Shahid Rahman,Mohammad Saleh Zarepour
Publisher : Springer Nature
Page : 493 pages
File Size : 46,8 Mb
Release : 2021-02-09
Category : Philosophy
ISBN : 9783030536541

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Mathematics, Logic, and their Philosophies by Mojtaba Mojtahedi,Shahid Rahman,Mohammad Saleh Zarepour Pdf

This volume is a collection of essays in honour of Professor Mohammad Ardeshir. It examines topics which, in one way or another, are connected to the various aspects of his multidisciplinary research interests. Based on this criterion, the book is divided into three general categories. The first category includes papers on non-classical logics, including intuitionistic logic, constructive logic, basic logic, and substructural logic. The second category is made up of papers discussing issues in the contemporary philosophy of mathematics and logic. The third category contains papers on Avicenna’s logic and philosophy. Mohammad Ardeshir is a full professor of mathematical logic at the Department of Mathematical Sciences, Sharif University of Technology, Tehran, Iran, where he has taught generations of students for around a quarter century. Mohammad Ardeshir is known in the first place for his prominent works in basic logic and constructive mathematics. His areas of interest are however much broader and include topics in intuitionistic philosophy of mathematics and Arabic philosophy of logic and mathematics. In addition to numerous research articles in leading international journals, Ardeshir is the author of a highly praised Persian textbook in mathematical logic. Partly through his writings and translations, the school of mathematical intuitionism was introduced to the Iranian academic community.

Author : Taner Edis
Publisher : Pitchstone Publishing (US&CA)
Page : 301 pages
File Size : 48,8 Mb
Release : 2021-11-09
Category : Body, Mind & Spirit
ISBN : 9781634312127

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Weirdness! by Taner Edis Pdf

In a world where science faces challenges from creationists and climate change deniers, and where social media is awash with wild conspiracy theories, it is no longer enough for scientists, pundits, and activists to simply ask the public to trust science. Rather, all must better understand how science works, and why science is essential. By exploring many of the odd beliefs embraced by large sections of the public that are rejected by the scientific mainstream, Weirdness! makes a case for science that goes beyond popular slogans. It takes seriously claims that paranormal phenomena, such as psychic abilities and mythical creatures, might be real, but demonstrates how such phenomena would extend beyond the laws of nature. It rejects a sharp boundary between science and religion, while explaining how to negotiate their real differences. Denials of science cause no end of trouble, but so too does placing blind trust in science. As Weirdness! reminds readers, science should not be seen as a mechanism that takes in data and spits out truth—indeed, what we get wrong about how the world works is often as interesting as what we get right.

Author : Virginia Kinnear,Mun Yee Lai,Tracey Muir
Publisher : Springer
Page : 284 pages
File Size : 43,5 Mb
Release : 2017-12-12
Category : Education
ISBN : 9789811071539

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Forging Connections in Early Mathematics Teaching and Learning by Virginia Kinnear,Mun Yee Lai,Tracey Muir Pdf

This edited book promotes thinking, dialogue, research and theorisation on multiple ways of making connections in mathematics teaching and learning in early childhood education. The book addresses some key challenges in research, policy and practice in early childhood mathematics education. It examines diverse ways for learning experiences to connect young children to mathematics, and the importance of forging connections between mathematics and young children’s lives as key elements in their engagement with mathematics. Each chapter provides research or theoretical provocations and pedagogical implications for connecting children’s lived experiences and ways of learning in mathematics teaching. The chapters are drawn from a range of international authors who raise important ideas within the overall context of current research and consider the theoretical and practical implications of their research. As such, the book advances current thinking on mathematics teaching and learning for children in the early years from birth to eight years with an emphasis on children aged birth to 5 years. It considers the purpose and value in connecting mathematics teaching and learning to children’s lives, and provides provocations for both educators and researchers on the many under-researched and under-represented aspects of early years mathematics teaching and learning.

Author : Susanna Berger,Daniel Garber
Publisher : Springer Nature
Page : 321 pages
File Size : 44,6 Mb
Release : 2022-02-15
Category : Philosophy
ISBN : 9783030846213

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Teaching Philosophy in Early Modern Europe by Susanna Berger,Daniel Garber Pdf

This book examines how philosophy was taught in the early modern period in Europe. It breaks new ground in a number of ways. Firstly, it seeks to bring text-based scholars in the history of philosophy together with social and cultural historians to examine the interaction between tradition and innovation in the early modern classroom, the site where traditional views of the world were transmitted to the generation that was to give birth to modern philosophy and science. Secondly, it draws together scholars who are centered on ideas and words with other scholars who focus on the role of images in the classroom and the intellectual world in this central period of history. The volume advances our understanding of how philosophy was understood and transmitted in this rich and crucial era. The principal audience for Teaching Philosophy are historians of science, philosophy, art, visual culture, and print culture. The chapters are written in a tone accessible to upper-level undergraduates and graduate students. It also reaches non-specialist readers interested in subjects including the “scientific revolution,” the organization of information, and Renaissance and Baroque visual art.

Author : Richard J. Oosterhoff,José Ramón Marcaida,Alexander Marr
Publisher : University of Pittsburgh Press
Page : 346 pages
File Size : 53,6 Mb
Release : 2021-11-09
Category : Science
ISBN : 9780822988465

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Ingenuity in the Making by Richard J. Oosterhoff,José Ramón Marcaida,Alexander Marr Pdf

Ingenuity in the Making explores the myriad ways in which ingenuity shaped the experience and conceptualization of materials and their manipulation in early modern Europe. Contributions range widely across the arts and sciences, examining objects and texts, professions and performances, concepts and practices. The book considers subjects such as spirited matter, the conceits of nature, and crafty devices, investigating the ways in which ingenuity acted in and upon the material world through skill and technique. Contributors ask how ingenuity informed the “maker’s knowledge” tradition, where the perilous borderline between the genius of invention and disingenuous fraud was drawn, charting the ambitions of material ingenuity in a rapidly globalizing world.