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Let History into the Mathematics Classroom
This book brings together 10 experiments which introduce historical perspectives into mathematics classrooms for 11 to 18-year-olds. The authors suggest that students should not only read ancient texts, but also should construct, draw and manipulate. The different chapters refer to ancient Greek, Indian, Chinese and Arabic mathematics as well as to contemporary mathematics. Students are introduced to well-known mathematicians—such as Gottfried Leibniz and Leonard Euler—as well as to less famous practitioners and engineers. Always, there is the attempt to associate the experiments with their scientific and cultural contexts. One of the main values of history is to show that the notions and concepts we teach were invented to solve problems. The different chapters of this collection all have, as their starting points, historic problems—mathematical or not. These are problems of exchanging and sharing, of dividing figures and volumes as well as engineers’ problems, calculations, equations and congruence. The mathematical reasoning which accompanies these actions is illustrated by the use of drawings, folding, graphical constructions and the production of machines.
The Oxford Handbook of Generality in Mathematics and the Sciences
This collection of original essays aims to inquire into the diversity of Generality. 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.
Definition and Essence from Aristotle to Kant
This volume brings together 12 essays exploring the history of theories of definition and essence in Western philosophy from Aristotle to Kant. Definition and essence have been central to philosophical theorising since antiquity and remain so to this day. This volume presents a series of explorations of key authors and themes connected by a common set of questions: What are definitions and essences? What are the connections between them? What are their logical and metaphysical properties? What sorts of things have definitions and essences and what sorts of things do not? What functions do definitions and essences serve in the physical, mathematical, and human sciences? How, if at all, can we...
Science in the Forest, Science in the Past
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.
Weyl and the Problem of Space
This book investigates Hermann Weyl’s work on the problem of space from the early 1920s onwards. It presents new material and opens the philosophical problem of space anew, crossing the disciplines of mathematics, history of science and philosophy. With a Kantian starting point Weyl asks: among all the infinitely many conceivable metrical spaces, which one applies to the physical world? In agreement with general relativity, Weyl acknowledges that the metric can quantitatively vary with the physical situation. Despite this freedom, Weyl “deduces”, with group-theoretical technicalities, that there is only one “kind” of legitimate metric. This construction was then decisive for the de...
Do the Humanities Create Knowledge?
There is in certain circles a widely held belief that the only proper kind of knowledge is scientific knowledge. This belief often runs parallel to the notion that legitimate knowledge is obtained when a scientist follows a rigorous investigative procedure called the 'scientific method'. Chris Haufe challenges this idea. He shows that what we know about the so-called scientific method rests fundamentally on the use of finely tuned human judgments directed toward certain questions about the natural world. He suggests that this dependence on judgment in fact reveals deep affinities between scientific knowledge and another, equally important, sort of comprehension: that of humanistic creative endeavour. His wide-ranging and stimulating new book uncovers the unexpected unity underlying all our efforts – whether scientific or arts-based – to understand human experience. In so doing, it makes a vital contribution to broader conversation about the value of the humanities in an increasingly STEM-saturated educational culture.
The Richness of the History of Mathematics
This book, a tribute to historian of mathematics Jeremy Gray, offers an overview of the history of mathematics and its inseparable connection to philosophy and other disciplines. Many different approaches to the study of the history of mathematics have been developed. Understanding this diversity is central to learning about these fields, but very few books deal with their richness and concrete suggestions for the “what, why and how” of these domains of inquiry. The editors and authors approach the basic question of what the history of mathematics is by means of concrete examples. For the “how” question, basic methodological issues are addressed, from the different perspectives of mathematicians and historians. Containing essays by leading scholars, this book provides a multitude of perspectives on mathematics, its role in culture and development, and connections with other sciences, making it an important resource for students and academics in the history and philosophy of mathematics.
The Best Writing on Mathematics 2017
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 Lam...
Osiris, Volume 38
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. T...
Hidden Harmony—Geometric Fantasies
This book is a history of complex function theory from its origins to 1914, when the essential features of the modern theory were in place. It is the first history of mathematics devoted to complex function theory, and it draws on a wide range of published and unpublished sources. In addition to an extensive and detailed coverage of the three founders of the subject – Cauchy, Riemann, and Weierstrass – it looks at the contributions of authors from d’Alembert to Hilbert, and Laplace to Weyl. Particular chapters examine the rise and importance of elliptic function theory, differential equations in the complex domain, geometric function theory, and the early years of complex function t...
