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 disciplin

FOREWORD by Neil deGrasse Tyson IX PREFACE XI 1 Arithmetic and Geometry 1 2 Proportion 73 3 Infinity 109 4 Formalism 151 5 Logic 197 6 Intuitionism 225 7 Symmetry 249 8 Utopian Visions after World War I 277 9 The Incompleteness of Mathematics 321 10 Computation 355 1 1 Geometric Abstraction after World War II 385 12 Computers in Mathematics and Art 455 13 Platonism in the Postmodern Era 499 NOTES 512 ACKNOWLEDGMENTS 547 CREDITS 548 INDEX 549

"This is a marvelous coffee table book ... very well researched and documented. It touches upon so many fundamental questions that philosophers, scientists, mathematicians and artists have asked since antiquity. But yet it guides the reader smoothly through all these competing visions and theories without becoming dull or getting lost in abstraction. This is the history of Western civilization with particular interest in art and mathematics, illuminating and instructive, and all wrapped up in a rich, colorful, and fancy book."--Adhemar Bultheel, European Mathematical Society "This is the beauty and power of this book: [Mathematics and Art] is an intellectual tour de force of art history and its interaction with mathematics that will draw most readers, including me, back for further reading and study."--Frank Swetz, MAA Reviews "Excellent new book... Overall this is a comprehensive, valuable and detailed book. It is written in an accessible style, with enough mathematics to interest the technical reader without overwhelming one with an arts background... Its rich anthology is particularly relevant today, given the explosion of interest in the digital arts and the need for digital artists to use maths creatively. I will definitely be keeping it close at hand."--William Latham, New Scientist "The author does an artful job in creating a wide-ranging and beautifully illustrated survey that mathematicians and art historians will enjoy."--John Barrow, The Art Newspaper "This sumptuously illustrated book chronicles the history of mathematics through its intersection with the development of visual art... Gamwell articulates the compelling, far-reaching connections within these fields in a way that is rewarding for scholars yet accessible to non-specialists."--Choice "Beautiful books that display the beauty of art are fine additions to many coffee tables; beautiful books that display the beauty of mathematics are fine additions to few coffee tables. Gamwell's impressive work integrates the beauty of these two disciplines to create a work larger than their sum... A book for all ages and of all ages: truly a brilliant 'millennial' composition!"--Sandra L. Arlinghaus, Mathematical Reviews "This splendidly produced volume will appeal to everybody interested in mathematics and art and offers room for agreement and disagreement with the author... This volume stands out by its richness in contents, its wealth of colour reproductions and, last but not least, its very affordable price."--Dirk Werner, Zentralblatt MATH "This wonderful book gives a very thorough overview of the impact of mathematics (and science) of the visual arts (and architecture) over the centuries."--Eos "An interesting read, filled with paradigm-shifting history and art, the book still posits a linear perspective of the relationship of art and mathematics, specifically recounting the ways math has influenced art."--Karie Brown, Mathematics Teacher "A monumental volume... Excellently illustrated by 523 images... Many highlighted quotations from writings of outstanding personalities of the sciences and the arts make the volume more colourful."--Gyorgy Darvas, Symmetry "Mathematics and Art is an enjoyable read accessible to anyone interested in the history of mathematics and art."--Andre Michael Hahn, British Journal for the History of Science

"Mathematics and Art describes mankind's search for patterns and the expression of these numbers and forms by artists. This book will enrich the reader's understanding of mathematics and the arts throughout history, and their deep interconnections in today's global culture of high technology and contemporary art."—Tatsuo Miyajima, artist"Lynn Gamwell is a singular intellect and this is a singular book. Her text weaves together philosophy, art, science, and mathematics in their historical settings. The illustrations are absolutely stunning. Her eye for the juxtaposition of art images, math diagrams, text, and marginal quotations makes turning every page a delight. Each chapter leaves the reader with a sense of beauty, insight, and truth."—Eric Heller, Harvard University"Often artists understand how to make art but not what to make, and for centuries, artists have looked toward nature for subject matter and inspiration. Leonardo advised, ‘Don't copy nature. Follow the ways of nature.' Everything in nature, from plants and atoms to crystals and cosmology, can be predicted through mathematics, and a visual study of the intersection between mathematics and art history has long been needed. This book beautifully satisfies that need."—Dorothea Rockburne, artist"Handsomely illustrated and containing a wealth of information, this book is a must for anyone interested in the relations between science, nature, mathematics, and art. It is destined to become a classic on par with E. H. Gombrich's landmark work The Sense of Order."—Eli Maor, author of e: The Story of a Number"This impressive work is a must for anyone interested in the interactions between mathematical ideas and art, and in particular the ways in which, throughout history, mathematical ideas have inspired painters, sculptors, and architects. Few books dealing with this complex topic achieve such a degree of accomplishment and clarity as Gamwell's handsome volume does."—Leo Corry, author of A Brief History of Numbers"Many contemporary artists feel a deep connection to mathematics and computer science. In this book, Lynn Gamwell traces the origin of this connection and describes why it is particularly strong in artists, like myself, who are from a European culture."—Manfred Mohr, artist"Having spent many decades putting mathematics into visual form for a new understanding of it in my art, I recommend this thoroughly researched and well-written book for students to immerse themselves in mathematics' intricacies, rich history, precision, and yes, wonders."—Agnes Denes, artist"In this book, Lynn Gamwell provides a marvelous exploration of the development of symbols and diagrams, and shows how this helps us to better understand the rich connections between art and mathematics."—Dick Termes, internationally acclaimed artist"This book stands alone in describing how art has been inspired by mathematics. With its lavish illustrations, it has a stunning visual impact and Lynn Gamwell does a masterful job of providing a history of mathematics and art, and how they are intertwined. From ancient works to modern abstract expressionism, the book's many colorful artworks are mesmerizing. This is an important reference for anyone interested in mathematics or art."—Edward Belbruno, Princeton University"With intelligent writing and abundant illustrations, Lynn Gamwell's book presents a kaleidoscope of art related to math and physics. The global breadth of the work discussed spans from antiquity to modernity and reflects a courageous vision, resulting in a tremendous resource for scientists and artists alike."—Claire and Helaman Ferguson, coauthors of Helaman Ferguson: Mathematics in Stone and Bronze"Delving into this remarkable and profusely illustrated book is akin to slipping into a seminar on two areas—art and mathematics—that are often thought of as being at odds. Instead, Lynn Gamwell eloquently links the artist and the mathematician, as she traces the cultural history of their interconnected disciplines. You will find yourself coming back to these pages, again and again, to reread part of a chapter or to savor certain passages and images."—Richard Waller, executive director of the University of Richmond Museums"There is increasing interest in the intersection of mathematics and art, and this wonderful book shows that mathematicians and artists have been inspiring each other for a long time. All who are interested in these two fields—as well as many who believe they are interested in one but not the other—will be enthralled."—Robert Bosch, Oberlin College"This well-written and interesting book links the philosophical views of different periods to trends in mathematics, philosophy of mathematics, and cutting-edge art. Filled with wonderful illustrations and delightfully insightful and inspiring connections, this book can be enjoyed by scholars, general readers, and all who are interested in mathematics, philosophy, and art history."—Eve Torrence, coauthor of The Student's Introduction to Mathematica