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.