Hyperbolic Surfaces

The Mathematical Precision of Maldonado’s Concrete Vision

Tomas Maldonado’s Hyperbolic Surfaces (1959) stands as a defining work of Concrete Art, a movement that rejected representation in favor of pure abstraction rooted in geometric rigor. Created during Maldonado’s tenure at the Ulm School of Design—where he later became rector—this composition embodies the artist’s fusion of mathematical logic with visual harmony. The interlocking black and white planes appear to warp and recede, a visual manifestation of hyperbolic geometry where parallel lines diverge. Unlike the organic abstraction of contemporaries like Arp or Miró, Maldonado’s approach was architectural, treating the canvas as a space for intellectual rather than emotional exploration.

The painting emerged at a pivotal moment when Concrete Art was transitioning from its Swiss and Dutch origins into a broader international dialogue. Maldonado, an Argentine-Italian artist, became one of its most articulate proponents, arguing that art should be “concrete” in the sense of being self-referential—existing solely through its own formal properties. Hyperbolic Surfaces exemplifies this philosophy: the title itself directs attention to the work’s structural principles rather than any external narrative. As MoMA’s archives highlight, Maldonado’s contributions to the Ulm School helped cement Concrete Art’s influence on mid-century design education, bridging fine art and industrial aesthetics.

Concrete Art and the Ulm School: Maldonado’s Intellectual Framework

By 1959, when Maldonado painted Hyperbolic Surfaces, he had already spent nearly a decade at the Ulm School of Design (HfG Ulm), an institution founded by Inge Aicher-Scholl and Otl Aicher as a counterpoint to the Bauhaus. The school’s curriculum emphasized a synthesis of art, science, and technology—a philosophy that permeates this work. Maldonado’s compositions from this period often explored optical phenomena, but Hyperbolic Surfaces stands apart for its explicit engagement with non-Euclidean geometry. The warping grids defy classical perspective, inviting viewers to experience spatial ambiguity without resorting to figurative illusionism.

This painting also reflects Maldonado’s dialogue with the Arte Concreto-Invención movement, which he co-founded in Argentina in 1945. While earlier works from that group emphasized vibrant color fields, his European period marked a shift toward achromatic palettes and structural complexity. The Art Story’s overview of Concrete Art notes how artists like Maldonado used geometric abstraction to “create a universal visual language,” a goal that aligns with the Ulm School’s mission to design for a post-war, globally connected world. In Hyperbolic Surfaces, the absence of color focuses attention on the interplay of form and void, a reductionist approach that would later influence minimalist and op-art practitioners.

Maldonado’s genius lies in his ability to make mathematical concepts visually palpable. Hyperbolic Surfaces doesn’t just depict geometric principles—it enacts them, turning the canvas into a field of perceptual experimentation.

The Engineering of Optical Illusion

Composition: Defying Euclidean Logic

The painting’s structure relies on a grid of black rectangles that appear to curve inward, creating the illusion of concave surfaces. Maldonado achieves this by subtly varying the width of the white intervals between forms—a technique that exploits the brain’s tendency to perceive depth where none exists. The composition’s symmetry is deceptive: while the left and right halves mirror each other, the central axis introduces a slight distortion that disrupts perfect balance, reinforcing the “hyperbolic” effect suggested by the title.

Surface and Execution: Precision as Principle

Maldonado’s methodical approach extended to his materials. The edges of the black forms in Hyperbolic Surfaces are razor-sharp, with no visible brushstrokes—a result of his use of masking tape and multiple layers of paint. This meticulousness was not merely aesthetic but ideological: for Concrete artists, technical perfection reflected the work’s conceptual purity. The matte finish of the black planes further enhances the optical vibration, as the absence of glare allows the forms to appear as pure geometric entities rather than painted surfaces.

Where to Display Hyperbolic Surfaces

This print’s monochromatic palette and geometric rigor make it remarkably versatile. In modern interiors, it serves as a focal point against neutral walls—particularly in spaces with clean lines and minimalist furnishings. The 30×40 cm (12×16") dimensions suit a study, home office, or gallery wall arrangement, where its optical intricacy invites prolonged viewing. For maximal impact, position it at eye level in a well-lit area; the interplay of light and shadow across the matte surface enhances the illusion of depth. Avoid overly busy backgrounds: the work’s power lies in its contrast with simplicity, making it an ideal counterpart to contemporary architecture or mid-century modern décor.

More Works by Tomas Maldonado

Discover additional framed prints by this pioneer of Concrete Art, each reflecting his rigorous approach to form and space.

Tomas Maldonado

Desde Un Sector

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