The invention of infinity : mathematics and art in the Renaissance

As any student of art will tell you, one of the chief accomplishments of the Renaissance was the development of perspective in painting—the introduction of spatial perception that led to the legendary beauty and majesty of works by Giotto, Botticelli, and da Vinci. In The Invention of Infinity, Dr. J. V. Field, a noted historian on math and the arts, tells the remarkable story of how the "practical" mathematics of Renaissance artists actually influenced the development of "proper" mathematics—a true story of life imitating art. Here is the fascinating history of the emergence of modern mathematics during the Renaissance, and its intimate relationship with the artisan and artistic traditions of the time. The book covers the period from 1300 to 1650, when craftsmen were educated in "practical mathematics," and when the field of mathematics was gradually taking up a more significant place on the intellectual landscape. Field traces the influence of the mathematics of perspective in the arts, and shows how this led to the invention of a new kind of geometry in the 17th century—the new projective geometry of Desargues—which proved to be a highly significant contribution to the development of modern mathematics. Additionally, the author explores the 14th and 15th-century "abacus" schools popular among merchants and craftsmen, and the contrast between these practical, widely used tools and the abstract arithmetic and geometry taught in the universities of the time, and their application in the theory of music and elementary astronomy. Extensively illustrated with superb color and black and white plates, and including selected extracts from the original mathematical texts, this clear and entertaining account will delight anyone interested in the history of mathematics and art, as well as in the multi-layered social history of the Renaissance. From Giotto to Michelangelo and beyond, the period from about 1300 to 1650 saw an extraordinary flowering in the visual arts in Western Europe. The works produced were sometimes of astonishing quality and their history has been well documented and much discussed. The scientific endeavour of the time has received considerably less attention. The history of science is a newer discipline than history of art, and no topic is newer than the history of mathematics in the period that saw the beginning of the Renaissance in the arts. This book tells us about the everyday worlds of art and mathematics in a time when artists were merely 'craftsmen' and their practical mathematics was separate from the mathematics of scholars. The story brings together the histories of art and mathematics and shows how the craftsmen's discoveries changed learned mathematics, taking it beyond the admired achievements of the Ancient Greeks. Infinity at last acquired a precise mathematical meaning. The journey takes us through consideration of some of the world's most renowned paintings, and lively accounts of the mathematical techniques and discoveries of the time. We are in a world where art and the sciences have not yet pulled apart from one another, and it becomes clear that the mathematical nature of what we now call Science may well owe something to the tradition of what is now called Art. xii, 250 p. : 25 cm Includes bibliographical references and index Medieval mathematics and optics and the Renaissance style in art -- Building, drawing and 'artificial perspective' -- Through the wall: Masaccio's Trinity fresco (c.1426) -- Piero della Francesca's mathematics -- Piero della Francesca's perspective treatise -- Practitioners and patricians -- The professionals move in -- Beyond the ancients -- Fragmented perspectives