Art and Geometry: A Study in Space Intuitions

by William Ivins Jr.

One of Western civilization's jealously guarded myths is that of Greek cultural supremacy. In this controversial study, William Ivins shows that the limitations of the Greek worldview actually hampered the development of the arts and sciences and gives a stimulating history of the new ideas of the Renaissance, especially in painting and geometry, that freed us from ancient misconceptions. Beginning with the Greeks, the author explains for the general reader the differences between ancient and Renaissance painting and sculpture, proving that the curiously static quality of Greek art arose from a misunderstanding of the laws of perspective. He then shows how this misunderstanding was corrected by Alberti, Pelerin, Durer, and other Renaissance artists who provided the first fruitful investigations of perspective. From there to projective geometry was but a step, and the author covers this major advance in our knowledge through the work of Nicholas of Cusa, Kepler, and Desargues. This book is perhaps the only concise history in English of the development of mathematical perspective and projective geometry. But the author's ability to relate styles in art to advances in geometry and his ingenious theory of the modern "visual" worldview and the Greek "tactile" worldview mean that his book will be provocative not only to mathematical historians but also to art historians and to anyone concerned with the history of thought, from philosopher to layman.

Genres: Art, Mathematics, Nonfiction, Science

128 pages, Paperback

First published June 1, 1964

About the author

William Mills Ivins Jr. (1881 – 1961) was curator of the department of prints at the Metropolitan Museum of Art, New York, from its founding in 1916 until 1946, when he was succeeded by A. Hyatt Mayor.

The son of William Mills Ivins Sr. (1851 – 1915), a public utility lawyer who had been the 1905 Republican candidate for Mayor of New York City, Ivins studied at Harvard College and the University of Munich before graduating in law from Columbia University in 1907.

After nine years' legal practice, he was asked to take on the conservation and interpretation of the Met's print collection. He built up the remarkable collections that can be seen there today, and he wrote many prefaces to exhibition catalogues, as well as other, occasional pieces which were later collected and published. His best-known book is Prints and Visual Communication (MIT Press, 1969, ISBN 0-262-59002-6 (first published 1953 by Harvard University Press)), and his How Prints Look (1943, revised edition 1987) remains in print.

Reviews

[Kevin Bjorke · Rating 4 out of 5]

A quick read from 1946 -- this one might be a disappointment to those who wanted books full of images, but full of intriguing ideas for those who are interested in how geometry developed and glimpses into just what the geometers of the past might have been aiming to accomplish. Ivins book seems aimed more at how art drove advances in geometry, rather than the reverse. I found the sections involving Alberti and the final chapter of Ivins musings about change the best (almost a century later, Ivins himself has become history, describing the a-bombs dropped during the writing of this book as a having momentous import both in society writ large and in geometry's purpose).

[Hooper Bring]

McLuhan cites this in “The Garbage Apocalypse” as demonstrating that print reduced the kinetic aspects of geometry and emphasized the visual.

[Charles · Rating 4 out of 5]

The ancient Greeks were in many ways intellectual powerhouses in the sense that they advanced many aspects of geometry, developing many concepts of the formal proof based on the abstraction of the pure figure. Yet, they were also weak in many areas, which is the major thesis Ivins puts forward. His arguments are based on the development of the geometrical ideas that led to a usable understanding of mathematical perspective.
This book is a short history of the development of the understanding of perspective by Alberti and other Renaissance artists and how it led to an understanding of projective geometry. It also led to much more realistic artwork, where the depictions of humans and nature were more lifelike. Much of the content is contructed from lengthy footnotes that are used to list sources as well as bolster and further explain the content.
It is a book that can be read with understanding by people with both art and math backgrounds. While some of the positions are a bit controversial, that is natural when ancient history is being interpreted.

[Kendra]

amazing, and a lot of struggle, so.....u have to read i this