Nobody was making art like Donald Judd in 1961. Quite out on his own, he began producing large, untitled paintings that rejected the prevailing movements of the period. In New York, where Judd had studied philosophy and art history at Columbia University a decade earlier, the splashiness of abstract expressionism was revered. But Judd had no intention of aping the loose, highly gestural mark-making of Jackson Pollock or Willem de Kooning. Nor did he share Roy Lichtenstein's fascination with the zany world of comic-strip imagery. Judd preferred the less exclamatory work of Barnett Newman, whom he considered the "best painter in the country". In his own 1961 work, Judd moved towards a harder, leaner vision.
In the first painting of Tate Modern's superb retrospective, executed on canvas, a thin white line meanders and ripples across a field of deep blue. But Judd soon jettisoned these undulations altogether. Working instead on masonite, he mixed sand with the paint to lend it a bulkier, more sculptural texture. The black lines drawn taut on the surface curve at either end, so that we recognise the form as a colossal hairpin. Yet the overall impact now centres on spareness and solidity, enriched by the intense red spread thickly across the picture surface.
With hindsight, we can sense Judd turning away from his earlier commitment to painting. He was searching for more palpable alternatives and, near the end of this decisive year, he became still more radical. Spreading an expanse of masonite and wood with sheer black paint, he lodged an aluminium baking pan at its heart. The entire work projects into space like a shallow relief, and the matt blackness surrounding the pan is an ideal foil for its gleaming gold lustre.
Even at his most severe and reductive, Judd never forsook the sensuous charge of colour. But he had to move further in the direction of sculptural form. He made more reliefs, mainly flat on the wall yet framed, at apex and base, by dark metal bands curving outwards. Judd must have relished the move into three-dimensional space. By 1963, he had decided to make a floor-based work, painting a rectangular wooden box with light cadmium red. Then, rather than leaving it whole, he inset a length of iron pipe at the top. An industrial ready-made, the pipe looks brazen and defiant, making the box seem almost opulent. Even so, it seems absolutely right in its shallow trough.
No wonder Judd attacked the critics' attempts to describe his work as minimal. "A simple box is really a complicated thing," he protested, echoing Constantin Brancusi's defence of his work. Both men, who can now be rewardingly compared in Tate Modern's two concurrent shows, shared a desire to purge sculpture of all unnecessary elaboration. But Judd went further than Brancusi by insisting that art "based on human bodies . . . has had its day". In an arresting phrase, he declared that his sculpture should look as if it had arrived "full-blown in the middle of the night".
Those stirring words are eloquent enough to remind us that Judd also worked for several years as a professional art critic. And his finest work certainly possesses a feeling of inevitability. Even when he started building units of form, either ranged along a wall or ascending in majestic stacks from floor to ceiling, Judd made sure that our eyes are not distracted by the parts. When encountering these often titanic aggregations of steel, iron, aluminium, copper or Plexiglas, we are conscious of wholeness. And we are beguiled by Judd's willingness to counter geometric severity with seductive delight. Leaning over the open top of a rich copper box, we realise that the glowing redness of the enamel within gives off a sensation of irresistible warmth.
Such works also make us aware of Judd's growing fascination with a dialogue between presence and absence. The four great cubes of galvanised iron in To Susan Buckwalter look weighty, and gain much of their power from Judd's refusal to pretend that they are anything other than abstract units made by fabricators. But the empty spaces between them play a vital role in the sculpture, and the square aluminium pipe running along the top is open at both ends. Standing at either side, we are able to peer all the way through the blue-lacquered pipe's interior. It opens up the sculpture, making us conscious of the outside/inside debate enlivening Judd's subsequent work.
In 1965, Judd denied the existence of any landscape references in his work. Five years later, however, he spent the summer travelling through the south-west of the US and began to consider work responding to a particular stretch of countryside. Although still based in New York, Judd had grown increasingly tired of big-city life. He had spent much of his childhood on his grandparents' farm in Missouri, and remote rural settings appealed to this shy man. In 1971, he discovered in the Chihuahuan Desert a quiet Texan town called Marfa. From that moment until his death in 1994, Judd's most ambitious sculpture was created for the buildings and outdoor locations he acquired at Marfa and the surrounding area.
In the latter stages of the Tate show, we grow more and more aware of the work's immensity - not only its size, but also its ability to evoke the vastness of a supremely elemental place. Judd's involvement with architecture and his fierce views about the best way to install his work reached their ultimate fruition at Marfa. No one can fully grasp this great sculptor without visiting the epic sequence of pieces made for the permanent settings he created there. But the Tate show offers a bracing summary of his achievements and, by the end, their single-minded unity is overwhelming.
"Donald Judd" is at Tate Modern, London SE1 (020 7887 8000) until 25 April. Earlier Judd shows are discussed in Richard Cork's four volumes on modern art, recently published by Yale