Mathematical forms rendered visually can give aesthetic pleasure; certain works of art -- Max Bill's Moebius band sculpture, for example -- can seem to be mathematics made visible. This collection of essays by artists and mathematicians continues the discussion of the connections between art and mathematics begun in the widely read first volume of The Visual Mind in 1993.

Mathematicians throughout history have created shapes, forms, and relationships, and some of these can be expressed visually. Computer technology allows us to visualize mathematical forms and relationships in new detail using, among other techniques, 3D modeling and animation. The Visual Mind proposes to compare the visual ideas of artists and mathematicians -- not to collect abstract thoughts on a general theme, but to allow one point of view to encounter another. The contributors, who include art historian Linda Dalrymple Henderson and filmmaker Peter Greenaway, examine mathematics and aesthetics; geometry and art; mathematics and art; geometry, computer graphics, and art; and visualization and cinema. They discuss such topics as aesthetics for computers, the Guggenheim Museum in Bilbao, cubism and relativity in twentieth-century art, the aesthetic value of optimal geometry, and mathematics and cinema.

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Summary: A Feast for the Eye, Mind and Spirit

Rating: 5

This splendid book is a feast for the eye, mind, and spirit. It is a sequel to the 1993 book, The Visual Mind: Art and Mathematics, also edited by Michelle Emmer, an Italian professor of mathematics. It uses visual examples and thoughtful essays to explore the intersection of the disciplines of mathematics and art.

Here are some highlights of this fascinating collection: There are several articles on mathematically-themed sculptures that display unusual concavities, knots, interlacements, and Mobius-style twists, with detailed analyses by their creators. There is an essay relating Picasso's cubism to Einstein's Theory of Relativity; another uses computer simulation to generate approximations of Paul Klee's art; a third illustrates explains the importance of circle packings in Japanese art and culture. There is a beautifully- photographed description of architect Frank Gehry's computer-assisted development of models for the Guggenheim Museum in Bilbao, Spain. Also outstanding are essays on the depiction of mathematics and mathematicians in relatively recent movies and another on the role of beauty in the evolution of mathematical proofs.

My one complaint is that these articles are very uneven in terms of overall quality and accessibility by non-mathematicians; some are scholarly papers that require the knowledge of college-level mathematics.

This book is excellent; however Emmer's first book, mentioned above, is even better. It's out of print but well worth searching for.