For most of us, life in three dimensions is difficult enough. But not for Tony Robbin. For Robbin, an acclaimed artist and geometry enthusiast, the real challenge comes in visualizing the fourth dimension.

Ever since his debut at the Whitney Museum of American Art in 1974, Robbin has been bent on creating artistic depictions of space in the fourth dimension. In addition to the 25 solo exhibitions of his painting and sculpture, Robbin holds the patent for the application of quasicrystal geometry to architecture and is well-known as a pioneer in the computer visualization of four-dimensional geometry.

In his insightful new book, Shadows of Reality: The Fourth Dimension in Relativity, Cubism, and Modern Thought, Robbin investigates different models of the fourth dimension and how these are applied in art and physics. The book, which Science calls “a fascinating flythrough of the diverse, intellectually rigorous climes in which Robbin finds tracks and traces in hyperspace,” breaks much new ground: It is a revisionist math history as well as a revisionist art history. Robbin argues that Picasso used the projection, or shadow, model of the fourth dimension to invent cubism, and that Minkowski had four-dimensional projective geometry in mind when he structured special relativity. The argument is brought to the present with a discussion of the most creative ideas about space in contemporary mathematics, including twisters, quasicrystals, and quantum typology. Helpfully, Robbin clarifies these esoteric concepts with readily comprehensible drawings and diagrams.

An exhibition of Robbin’s latest work is also currently on display at the gallery of the American Association for the Advancement of Science in Washington, D.C. It is Robbin’s first solo exhibition since 1992.