Despite its name, Minimal art makes big claims on time, space, and a viewer’s patience. One of its stalwarts, the sculptor Carl Andre, once complained about seeing his floor-hugging work in galleries hung conventionally with paintings. “If you have anything on the walls you can’t see anything on the floor. It’s impossible,” he said. The comment is a sculpture-friendly rewording of the classic jibe, attributed to Baudelaire, that sculpture is what you trip on when you step back to look at a painting. In the case of Mr. Andre, however, chances are you will neither hurt yourself nor anger the custodian, as Mr. Andre’s most familiar work consists of metal plates arranged on the ground in grids. The audience is actually encouraged to walk over the pieces.

His latest exhibition at Paula Cooper, with whom he first took part in a group show in 1968, is true to form: It consists of 10 mostly copper tile configurations which form a neat grid around the two galleries, along with two groupings of timber segments of identical length. As regards process and means, Mr. Andre is an artist who has stuck to his guns — or is stuck in a rut, depending on your degree of sympathy with his enterprise.

By his own criteria, Mr. Andre has at the Paula Cooper the optimum viewing conditions for this work. The artist’s tiles are either one-quarter or one-eighth of an inch thick; Ms. Cooper’s walls are 17 feet high, rising in their sumptuously rafted, skylit ceiling to 27 feet. There is a rich associative consonance between the work and the space, particularly for an artist who, at the outset of his career, boasted of an ambition to make work free of human association. Ms. Cooper, once a pioneer gallerist in SoHo, was the first dealer to forsake that area for west Chelsea in the 1990s to escape the mainstream commercialization of SoHo, attracted to the remoteness and purity of Chelsea.

In contrast to fellow Minimalists such as Dan Flavin or Donald Judd, who were attracted to modern industrial materials in their pristine state — fluorescent light strips, meticulously fabricated aluminum boxes — Mr. Andre has always been attracted to industrial components in a more raw, “natural” condition. His beams are split and weathered, his tiles worn and slightly oxidized. It is ironic, then, that while both dealer and artist are devotees of purity, their combined effect is steeped in nostalgia for a manufacturing past.

But heavy industry has often featured in Mr. Andre’s aesthetic roots. His family worked in shipbuilding, and he supported himself as a young artist by working as a freight train brakeman. The sensation of railroad lines inspired the observation that sculpture can derive greater power from clinging to the ground over an expanse than it can from verticality, despite Mr. Andre’s early love for the Romanian sculptor Constantin Brancusi, whose pedestals are the source for Mr. Andre’s timber pieces.

It is this odd mix of brutalism and nostalgia, the prosaic and the poetic, that differentiates Mr. Andre from his Minimalist peers, prompting the critic David Sylvester to once describe him as a Romantic among Neo-Classicists.

By those old-fashioned standards, however, the current show finds the artist in classical mode: His arrangements stick to strict grids in neat numerical variations, recalling the simplistic math, the “ABC art” as it was once dubbed, of the early days of Minimalism. In this installation, he works with a ready-made grid incised into the cement floor of the main gallery at Cooper’s. In the northern corners of this room are grids of, respectively, three and five square tiles. In the corners of the central incised square are grids of four, five, six, and seven tiles square. In the southern corners of the room, in vertically stepped gradations of 9:1 and 8:1, respectively, are stacks of timber titled, “9th Cedar Corner” (all from 2007) and “8th Old Eastern Pine Corner.” The layout is essentially symmetrical, and where it is irregular in the detail of its configurations, it seems so according to simple rules.

The meaning, in other words, is not allowed to rest for too long with math, but the math is insistent enough to be a present, material fact.

This is work of a quality that can certainly inspire indignation or tedium, but whatever your taste threshold for the minimal, Mr. Andre achieves incredible poise. When you think about what more or less could have been done within the terms of the artist’s vocabulary, this installation is at the tipping point between demure and forceful presence.

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With spare, reductive art, location is all, as Mr. Andre’s show amply proves. Willard Boepple is a sculptor who possesses a comparable sense in his work of the power of economy, yet he is willing to brave exhibiting conditions that could hardly eschew purity more forcibly. Two of his “Room” sculptures of the late 1990s are on view in the lobby of an office building in the Wall Street vicinity — 125 Maiden Lane, one of a number of buildings owned by the arts patron Francis J. Greenburger that participates in an ambitious exhibitions program.

There are two pieces on view: a smaller model in poplar wood and a commanding 8-foot-square cube, “Room” (1999), in brushed aluminum. While Mr. Boepple comes out of the formalist tradition of abstract sculpture dominated by David Smith and Anthony Caro, he shares with the Minimalists a fascination with commonplace functional forms: ladders, cogs, shelves, house frames. In his case, however, these are fabricated with aesthetic deliberation, rather than appropriated ready-made, and abstracted. The appeal of these forms is that while connected with the body they avoid figuration. They are things to which bodies relate, though, on their own, the body is absent.

“Room” relates to the convention of a drawing in space, and entices the eye to explore both its flatness and its volume. The body, however, is denied entry, and must circle this object that seems a bit big to be sculpture but too self-contained to count as installation. Inserted in this open structure are planar sheets, often on the horizontal, that read like shutters or shelves. Also detaining the eye is the irregularity of openings and placements.

Further distracting, or intriguing, are the alien surroundings of a nondescript 1970s lobby with its low ceilings, granite tiled floor, and busy green marble walls. Within such a space, however, the work takes on new meanings of alienation, crampedness, and dislocation. The placement feels like either a test for formalist resolve or a riposte to any idea of aesthetic purity.

Andre until December 15 (534 W. 21st St., between Tenth and Eleventh avenues, 212-255-1105).

Boepple until February 16 (125 Maiden Lane, between Water and Pearl streets, 212-206-6061).