Man Ray, “Endgame,” 1946. Oil on canvas. (Copyright Man Ray Trust / Artists Rights Society (ARS), NY / ADAGP, Paris)

In the mid-1930s, the American expat photographer, painter and surrealist Man Ray was introduced by his friend Max Ernst to a curious collection of dust-covered objects at an elite school for higher mathematics in Paris. Made of plaster, wood, wire, paper and other materials, they were three-dimensional models of complex trigonometric equations. To Man Ray, they had an appealing weirdness, suggesting biomorphic and human forms, curious saddles and declivities, bulging cones and at least one shape distinctly like an amply proportioned human posterior.

Ernst had already incorporated drawings of these forms into his own surrealist collages. Man Ray would photograph them, sometimes individually, sometimes juxtaposed with other models. What for Ernst were merely data points in images that also combined references to nature and art, were for Man Ray seductive objects to be celebrated in their own right. What the photographer Edward Weston did for peppers, Man Ray did for these strange models, dramatizing them, and rendering them with a strange, monumental glamour.

But that wasn’t the end of it. With the approach of World War II, Man Ray fled France for his homeland and migrated to Hollywood, where he returned to these enigmatic forms, using them as inspiration for a series of paintings he called “Shakespeare Equations.”

An intriguing exhibition at the Phillips Collection has gathered 14 of the 23 “Shakespearean Equations” and, for the first time, reunited them both with the photographs made in the 1930s, and many of the original models themselves, borrowed from the Institut Henri Poincare. While there is much in this show that will appeal to science nerds who fancy all art as somehow derivative of natural or scientific forms, the real interest lies in the complicated visual process of moving from idea to form to permutations of form. It is a concentrated introduction to the intellectual habits of surrealism, and though not a comprehensive overview of Man Ray’s career, a revealing snapshot of his artistry.

Man Ray’s celebration of the models wasn’t without controversy, especially from fellow surrealists such as Andre Breton. Surrealism celebrated the dreamlike, the unconscious and libidinal, and the chance meanings that emerged from juxtaposition and dialogue of radically different things. Man Ray’s mathematical models, Breton feared, belonged to the world of rationality. Breton worried that presenting mathematical objects as “surreal objects” ran the danger that art itself could be “outclassed.”

Man Ray, Still life composition for “Minotaure,” 1933. Three-color carbon transfer print. (Copyright Man Ray Trust / Artists Rights Society (ARS), NY / ADAGP, Paris)

Man Ray clearly felt otherwise, and much of the fascination of this exhibition is tracing how what one might call the “value added” of art changed the meaning of models he represented. Framing, lighting, the choice of background material, and the positioning of objects were the essential photographic tools for finessing the models into new photographic forms. With painting, Man Ray had at his disposal color and texture, and endless opportunities to play games with shading, outline and subtle gradations of tonality. He also infused many of them with erotic suggestions, accentuating their fleshiness, organic curves and anatomical analogies.

And by adding Shakespearean references, he moved his paintings even further from their original mathematical origins, into the world of familiar narrative, with allusions to the half-remembered speeches of “Hamlet” and “Lear,” the bewildering complexities of “Twelfth Night,” the frenetic whimsy of “Merry Wives of Windsor,” and the bloody-minded murders of “Macbeth” and “Julius Caesar.” And yet many of the references are hermetic, and perhaps entirely arbitrary. The two breastlike forms joined by a saddle-shaped fin in “Romeo and Juliet” may give one the sense of young lovers clasped together under a dark and moonless sky. The lumpy sphere in a trompe-l’oeil frame of “As You Like It” is more enigmatic, as is the watermelon-like form that seems to be holding down an open book in “Much Ado About Nothing.”

Man Ray professed himself as indifferent to whether or not these paintings would live up to their Shakespearean titles as he was indifferent to the mathematical formula that generated the models he had photographed more than a decade earlier.

“We would play games trying to get people to guess what play belonged to which picture,” he remembered. “Sometimes they got it right; sometimes of course, they didn’t, and it was just as well!”

But the surrealist project wasn’t about definite meaning, it was about creating conditions in which explosions of diverse meanings were possible. If mathematical equations produced a definite shape in three-dimensional space, human equations were more about bringing variables and unknowns into volatile proximity. Which might, in a way, be a decent description of what a dramatist such as Shakespeare is all about: Setting up the field, or the chess board, so that an unknown number of variables can interact.

All of this was happening in Hollywood, at a time when many of the greatest artists and intellectuals of Europe were languishing there in spectacularly productive pools of ennui. The opening party for Man Ray’s first Shakespearean Equations exhibition included among its guests Igor Stravinsky, Aldous Huxley, Luis Bunuel and Jean Renoir, plus assorted Americans of significant stature.

It’s hard not to detect some irony in the Shakespeare paintings, the kind of irony one might expect from a man who once said “there was more Surrealism rampant in Hollywood than all the Surrealists could invent in a lifetime.” The great boon of this exhibition is the presence of the mathematical models that energized Man Ray’s decades-long fixation on these forms. The interplay between the models and the images feels a bit like the cult of celebrity, like the interplay between the glossy black-and-white studio head shot, the lurid color poster that teases the film, and the star or starlet in the flesh. Man Ray’s photographs and paintings have, in a curious way, made the models “famous.”

Hiroshi Sugimoto, “Kuen’s Surface: A Surface with C onstant Negative Curvature (Conceptual Form 0006),” 2004. (Courtesy Hiroshi Sugimoto)

By extending its focus to other chapters of Man Ray’s career, the exhibition also calls attention to his fundamental concern with surfaces. The mathematical models, though solid, are all about the surfaces described by the equations they represent. But the exhibition also includes examples of Man Ray’s “Rayographs” from the 1920s, images made by placing objects directly on photosensitive material, then exposing them to light from various angles. The Rayographs play with a sense of two-dimensional and three-dimensional space, mixing a sense of objects that have body, weight and extension with mere outlines and inverse silhouettes. A self-portrait, painted in 1941, also plays with the idea of surfaces by reproducing in paint the distortions of a 1938 photograph that captured his image in a fun-house mirror.

We have a long intellectual inheritance in which surface is equated with superficiality, with triviality and lack of serious meaning; this exhibition celebrates the great productivity of surface, its generative power, its ability to generate yet more surface, more variations, more potential for new meaning.

‘Hiroshi Sugimoto: Conceptual Forms and Mathematical Models’

The Man Ray exhibition is paired with another, smaller show devoted to a similar interplay of images and objects by the Japanese photographer and artist Hiroshi Sugimoto. Very much in the tradition of Man Ray, Sugimoto has also studied and photographed 19th-century mathematical and mechanical models. But he has, in a sense, pushed his fascination into precisely the direction that Breton worried about when Man Ray was pursuing similar themes in the 1930s. Not only has Sugimoto photographed old models, he has used precision electronic milling machines to manufacture his own achingly beautiful aluminum models, of which this show includes three. What they lack in Man Ray’s Hollywood glamour they more than make up for with a hard, brilliant and impenetrable perfection.

Throughout both exhibitions, one will feel haunted by the vexatious problem of what is real, and what isn’t. These are echoes of one of the oldest arguments in human history, whether we know the truth of things through some abstract form that covers all particulars or arrive slowly at truth by building up knowledge of the things as found in the real world. Sugimoto’s models may seem to represent the former, perfect objects that might be floating in the ether, while Man Ray consistently moved his mathematical forms toward the earthy, the cluttered, the organic and the sexual. After spending time with both artists, however, it is the mathematical formulas that begin to seem thin, intangible and lacking in reality. Like a piece of music, they are lifeless until given form by human beings. They may be pure, and perfect, but it’s not a purity or perfection we have any access to.

Man Ray — Human Equations: A Journey From Mathematics to Shakespeare and Hiroshi Sugimoto: Conceptual Forms and Mathematical Models are on view at the Phillips Collection through May 10. 1600 21st St. NW. 202-387-2151. www.phillipscollection.org.