Mathematics and the Divine seem to correspond to diametrically opposed tendencies of the human mind. Does the mathematician not seek what is precisely defined, and do the objects intended by the mystic and the theologian not lie beyond definition? Is mathematics not Man's search for a measure, and isn’t the Divine that which is immeasurable ? The present book shows that the domains of mathematics and the Divine, which may seem so radically separated, have throughout history and across cultures, proved to be intimately related. Religious activities such as the building of temples, the telling of ritual stories or the drawing of enigmatic figures all display distinct mathematical features. Major philosophical systems dealing with the Absolute and theological speculations focussing on our knowledge of the Ultimate have been based on or inspired by mathematics. A series of chapters by an international team of experts highlighting key figures, schools and trains of thought is presented here. Chinese number mysticism, the views of Pythagoras and Plato and their followers, Nicholas of Cusa's theological geometry, Spinozism and intuitionism as a philosophy of mathematics are treated side by side among many other themes in an attempt at creating a global view on the relation of mathematics and Man’s quest for the Absolute in the course of history. · Mathematics and man's quest for the Absolute · A selective history highlighting key figures, schools and trains of thought · An international team of historians presenting specific new findings as well as general overviews · Confronting and uniting otherwise compartmentalized information
This Handbook explores the history of mathematics under a series of themes which raise new questions about what mathematics has been and what it has meant to practise it. It addresses questions of who creates mathematics, who uses it, and how. A broader understanding of mathematical practitioners naturally leads to a new appreciation of what counts as a historical source. Material and oral evidence is drawn upon as well as an unusual array of textual sources. Further, the ways in which people have chosen to express themselves are as historically meaningful as the contents of the mathematics they have produced. Mathematics is not a fixed and unchanging entity. New questions, contexts, and applications all influence what counts as productive ways of thinking. Because the history of mathematics should interact constructively with other ways of studying the past, the contributors to this book come from a diverse range of intellectual backgrounds in anthropology, archaeology, art history, philosophy, and literature, as well as history of mathematics more traditionally understood. The thirty-six self-contained, multifaceted chapters, each written by a specialist, are arranged under three main headings: 'Geographies and Cultures', 'Peoples and Practices', and 'Interactions and Interpretations'. Together they deal with the mathematics of 5000 years, but without privileging the past three centuries, and an impressive range of periods and places with many points of cross-reference between chapters. The key mathematical cultures of North America, Europe, the Middle East, India, and China are all represented here as well as areas which are not often treated in mainstream history of mathematics, such as Russia, the Balkans, Vietnam, and South America. A vital reference for graduates and researchers in mathematics, historians of science, and general historians.
Author: Lynn Gamwell
Publisher: Princeton University Press
Release Date: 2015-10-27
This is a cultural history of mathematics and art, from antiquity to the present. Mathematicians and artists have long been on a quest to understand the physical world they see before them and the abstract objects they know by thought alone. Taking readers on a tour of the practice of mathematics and the philosophical ideas that drive the discipline, Lynn Gamwell points out the important ways mathematical concepts have been expressed by artists. Sumptuous illustrations of artworks and cogent math diagrams are featured in Gamwell’s comprehensive exploration. Gamwell begins by describing mathematics from antiquity to the Enlightenment, including Greek, Islamic, and Asian mathematics. Then focusing on modern culture, Gamwell traces mathematicians’ search for the foundations of their science, such as David Hilbert’s conception of mathematics as an arrangement of meaning-free signs, as well as artists’ search for the essence of their craft, such as Aleksandr Rodchenko’s monochrome paintings. She shows that self-reflection is inherent to the practice of both modern mathematics and art, and that this introspection points to a deep resonance between the two fields: Kurt Gödel posed questions about the nature of mathematics in the language of mathematics and Jasper Johns asked “What is art?” in the vocabulary of art. Throughout, Gamwell describes the personalities and cultural environments of a multitude of mathematicians and artists, from Gottlob Frege and Benoît Mandelbrot to Max Bill and Xu Bing. Mathematics and Art demonstrates how mathematical ideas are embodied in the visual arts and will enlighten all who are interested in the complex intellectual pursuits, personalities, and cultural settings that connect these vast disciplines.
Author: Richard J. Oosterhoff
Publisher: Oxford University Press
Release Date: 2018-07-26
In 1503, for the first time, a student in Paris was able to spend his entire university career studying only the printed textbooks of his teacher, thanks to the works of the humanist and university reformer Jacques Lefèvre d'Étaples (c. 1455-1536). As printed books became central to the intellectual habits of following generations, Lefèvre turned especially to mathematics as a way to renovate the medieval university. Making Mathematical Culture argues this was a pivatol moment in the cultural history of Europe and explores how the rise of the printed book contributed to the growing profile of mathematics in the region. Using student manuscripts and annotated books, Making Mathematical Culture offers a new account of printed textbooks, as jointly made by masters and students, and how such collaborative practices informed approaches to mathematics.
Author: Robert H. Nelson
Publisher: Wipf and Stock Publishers
Release Date: 2015-11-11
In recent years, a number of works have appeared with important implications for the age-old question of the existence of a god. These writings, many of which are not by theologians, strengthen the rational case for the existence of a god, even as this god may not be exactly the Christian God of history. This book brings together for the first time such recent diverse contributions from fields such as physics, the philosophy of human consciousness, evolutionary biology, mathematics, the history of religion, and theology. Based on such new materials as well as older ones from the twentieth century, it develops five rational arguments that point strongly to the (very probable) existence of a god. They do not make use of the scientific method, which is inapplicable to the question of a god. Rather, they are in an older tradition of rational argument dating back at least to the ancient Greeks. For those who are already believers, the book will offer additional rational reasons that may strengthen their belief. Those who do not believe in the existence of a god at present will encounter new rational arguments that may cause them to reconsider their opinion.
Author: Mario Livio
Publisher: Simon and Schuster
Release Date: 2011-02-22
Bestselling author and astrophysicist Mario Livio examines the lives and theories of history’s greatest mathematicians to ask how—if mathematics is an abstract construction of the human mind—it can so perfectly explain the physical world. Nobel Laureate Eugene Wigner once wondered about “the unreasonable effectiveness of mathematics” in the formulation of the laws of nature. Is God a Mathematician? investigates why mathematics is as powerful as it is. From ancient times to the present, scientists and philosophers have marveled at how such a seemingly abstract discipline could so perfectly explain the natural world. More than that—mathematics has often made predictions, for example, about subatomic particles or cosmic phenomena that were unknown at the time, but later were proven to be true. Is mathematics ultimately invented or discovered? If, as Einstein insisted, mathematics is “a product of human thought that is independent of experience,” how can it so accurately describe and even predict the world around us? Physicist and author Mario Livio brilliantly explores mathematical ideas from Pythagoras to the present day as he shows us how intriguing questions and ingenious answers have led to ever deeper insights into our world. This fascinating book will interest anyone curious about the human mind, the scientific world, and the relationship between them.
Author: Ho Peng Yoke
Release Date: 2004-03-01
Though there are a number of well-written works on Chinese divination, there are none that deal with the three sophisticated devices that were employed by the Chinese Astronomical Bureau in the eleventh century and for hundreds of years thereafter. Chinese experts applied the methods associated with these devices to both weather forecasting and to the interpretation of human affairs. Hidden by a veil of secrecy, these methods have always been relatively little known other than by their names. The first work in any language to explore these three methods, known as sanshi (three cosmic boards), this book sheds light on a topic which has been shrouded in mystery for centuries, having been kept secret for many years by the Chinese Astronomical Bureau.
Author: Ravi M. Gupta
Publisher: Columbia University Press
Release Date: 2013-03-19
A vibrant example of living literature, the Bhagavata Purana is a versatile Hindu sacred text written in Sanskrit verse. Finding its present form by the tenth century C.E., the work inspired several major north Indian devotional (bhakti) traditions as well as schools of dance and drama, and continues to permeate popular Hindu art and ritual in both India and the diaspora. Introducing the Bhagavata Purana's key themes while also examining its extensive influence on Hindu thought and practice, this collection conducts the first multidimensional reading of the entire text. Each essay focuses on a key theme of the Bhagavata Purana and its subsequent presence in Hindu theology, performing arts, ritual recitation, and commentary. The authors consider the relationship between the sacred text and the divine image, the text's metaphysical and cosmological underpinnings, its shaping of Indian culture, and its ongoing relevance to contemporary Indian concerns.
Author: Ida H. Stamhuis
Publisher: Springer Science & Business Media
Release Date: 2012-12-06
This volume is written as a reaction to the worldwide decreasing interest in the natural sciences. It addresses many intriguing questions. How is the changing image of the distinct sciences experienced by the general public, by the scientists themselves, or in disciplines in which natural sciences are applied? How can it be connected to the phenomenon of the low number of women in science? It is of interest to researchers, teachers, and students of natural sciences, the history of science, and philosophy.
Author: Erhard Scholz
Publisher: Springer Science & Business Media
Release Date: 1989-10-01
Diese Arbeit enthiilt zwei grof3ere Fallstudien zur Beziehung zwischen theo retischer Mathematik und Anwendungen im 19. Jahrhundert. Sie ist das Ergebnis eines mathematikhistorischen Forschungsprojekts am Mathemati schen Fachbereich der Universitiit-Gesamthochschule Wuppertal und wurde dort als Habilitationsschrift vorgelegt. Ohne das wohlwollende Interesse von Herrn H. Scheid und den Kollegen der Abteilung fUr Didaktik der Mathema tik ware das nicht moglich gewesen: Inhaltlich verdankt sie - direkt oder indirekt - vielen Beteiligten et was. So wurde mein Interesse an den kristallographischen Symmetriekon zepten, dem Thema der ersten Fallstudie, durch Anregungen und Hinweise von Herrn E. Brieskorn geweckt. Sowohl von seiner Seite als auch von Herrn J. J. Burckhardt stammen uberdies viele wert volle Hinweise zum Manuskript von Kapitel I. Herrn C. J. Scriba mochte ich fur seine die gesamte Arbeit betreffenden priizisen Anmerkungen danken und Herrn W. Borho ebenso fUr seine ubergreifenden Kommentare und Vorschlage. Beziiglich der in Kapitel II behandelten projektiven Methoden in der Baustatik des 19. Jahrhunderts gilt mein besonderer Dank den Herren K. -E. Kurrer und T. Hiinseroth fUr ihre zum Teil sehr detaillierten Anmerkungen aus dem Blickwinkel der Geschichte der Bauwissenschaften. Schliefilich geht mein Dank an alle nicht namentlich Erwiihnten, die in Gesprachen, technisch oder auch anderweitig zur Fertig stellung dieser Arbeit beigetragen haben. Fur die vorliegende Publikation habe ich einen Anhang mit einer Skizze von in unserem Zusammenhang besonders wichtig erscheinenden Aspekten der Theorie der kristallographischen Raumgruppen hinzugefUgt. Ich hoffe, daB er zum Verstiindnis des mathematischen Hintergrunds der historischen Arbeiten des ersten Kapitels beitragt.
This book is not a conventional history of mathematics as such, a museum of documents and scientific curiosities. Instead, it identifies this vital science with the thought of those who constructed it and in its relation to the changing cultural context in which it evolved. Particular emphasis is placed on the philosophic and logical systems, from Aristotle onward, that provide the basis for the fusion of mathematics and logic in contemporary thought. Ettore Carruccio covers the evolution of mathematics from the most ancient times to our own day. In simple and non-technical language, he observes the changes that have taken place in the conception of rational theory, until we reach the lively, delicate and often disconcerting problems of modern logical analysis. The book contains an unusual wealth of detail (including specimen demonstrations) on such subjects as the critique of Euclid's fifth postulate, the rise of non-Euclidean geometry, the introduction of theories of infinite sets, the construction of abstract geometry, and-in a notably intelligible discussion-the development of modern symbolic logic and meta-mathematics. Scientific problems in general and mathematical problems in particular show their full meaning only when they are considered in the light of their own history. This book accordingly takes the reader to the heart of mathematical questions, in a way that teacher, student and layman alike will find absorbing and illuminating. The history of mathematics is a field that continues to fascinate people interested in the course of creativity, and logical inference quite part and in addition to those with direct mathematical interests. Ettore Carruccio, who until his retirement was professor of philosophy at the University of Turin. He has made many contributions to mathematical and logical theory as well as to the history of the science. Isabel Quigly was the literary editor of The Tablet for many years.
In an original and compelling examination of traditional mathematics, this comprehensive study of the anonymous "Manual of Mongolian Astrology and Divination" (published by A. Mostaert in 1969) takes on the fundamental problem of the post-enlightenment categorization of knowledge, in particular the inherently problematic realms of religion and science, as well as their subsets, medicine, ritual, and magic. In the process of elucidating the rhetoric and logic shaping this manual the author reveals not only the intertwined intellectual history of Eurasia from Greece to China but also dismantles many of the discourses that have shaped its modern interpretations.