In 1983, a groundbreaking book on the history of modern art was published: The Fourth Dimension And Non-Euclidean Geometry In Modern Art, by Linda Dalrymple Henderson, now a professor at the University of Texas, Austin. In that meticulously researched volume, Henderson unravelled the deep connections between early 20th century art (cubism, futurism, dadaism, surrealism, and related movements) with the mathematics of the 19th century, particularly the emergence of the fourth dimension and the idea of non-Euclidean spaces. Her book, though out of print for many years, was highly influential, inspiring a rethinking of the origins of those artistic movements. For example, she showed how the popular idea of connecting cubism with Einstein is simply a myth. Given that Einstein wasn't well-known by the public until after the eclipse experiments of 1919, cubists such as Picasso and Braque certainly weren't aware of Einstein's writings on higher dimensions. In fact, Cubism started in 1907, when Einstein himself did not yet believe in a fourth dimension. Rather, the cubists were familiar with the mathematical idea of the fourth dimension--a spatial (rather than temporal) idea popularized by numerous 19th century thinkers. Similarly Duchamp, as Henderson pointed out, was influenced by Poincaré, not Einstein.
Finally, Henderson's masterful book is back in print, issued by MIT Press in a brand new edition. The new edition begins with a magnificent "reintroduction" spanning the latter half of the 20th century (1950s - 2000), and including vital cultural connections between the fourth dimension and the visual arts (along with other media). As Henderson demonstrates, interest in higher dimensions has grown in recent decades through the emergence of string theory and other scientific ideas. This rebirth of interest has been reflected in artistic ventures of the period.
The Fourth Dimension And Non-Euclidean Geometry In Modern Art is an essential book for anyone interested in the intersection between science, mathematics and culture. It offers a riveting chronicle of the emergence of the idea of the fourth dimension in math, its popularization in literature and its adoption by the world of art that has persisted until the present day. Highly recommended!