This year is the 150th anniversary of the American architect’s birth, and there is a great deal of activity to mark the occasion: a blockbuster show at the Museum of Modern Art in New York (12 June–1 October), and a bundle of hefty new books from his leading biographers. More than half a century after his death, Wright’s reputation looks in fine health.

The words ‘American architect’ feel a little bare when applied to Wright – convention pushes for the addition of a superlative, such as ‘greatest’ or ‘best loved’. He is routinely described as America’s ‘favourite’ architect, generating among the public the kind of affection that most 20th-century architects could only fantasise about. This pre-eminence was hard won, and never inevitable – in fact a snapshot of Wright’s career makes failure appear the recurring theme. And it’s a lonely sort of achievement: triumph for Wright, obscurity for his ideas.

The buildings that secured Wright his lasting fame came very late. Wright was born in Wisconsin in 1867. Fallingwater, the Pennsylvania house that brought him global fame, was completed in 1937, when he was 70. The Solomon R. Guggenheim Museum in New York, the masterwork that crowned his career, opened in 1959, six months after his death at the age of 91. Though he built far more than his image as a prickly visionary might suggest – hundreds of works, mostly individual houses – those two bought him the lease on immortality, and he knew it.

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Wright would use biological metaphors in his buildings throughout his career, such as the tree-like columns at the Johnson Wax Headquarters building, a major commission completed in 1939. But in speaking of ‘organic’ architecture, Wright did not mean straightforward biomorphism of the sort that too often serves as a substitute for inspiration among ‘visionary’ architects. ‘Be warned this word “organic” is like the word “nature”,’ Wright wrote in his book The Living City (1958). “If taken in a sense too biological, it would not be what it is: light in darkness; it would be a stumbling block.’ Instead Wright intended a broader and more sophisticated connection to the landscape, both physical and human, ‘a daily working concept of the great altogether’. He imagined architecture and planning as playing roles in forging an American identity, one that united land, people, and democracy – Usonia.

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Wright’s advocacy for Broadacre was accompanied by polemics against the modern city, in particular New York. ‘Tier above tier rises the soulless habitation of the shelf,’ he wrote in The Living City, adopting the apocalyptic cadence common among urban critiques of the time:

‘Interminable empty crevices run up and down the winding ways of windy unhealthy canyons. Heartless, this now universal grip of grasping, unending stricture. Box to box on box-boxing, glassed-in boxing looking into other glass-boxing. Black shadows falling on glass fronts with artificial lights burning behind them all day long. Millions upon millions of little cavities, cells squared by the acre, acreage spread by the mile. This a vast prison with glass fronts. […] Incongruous mantrap of monstrous dimensions! Enormity devouring manhood, confusing personality by frustration of individuality? Is this not Anti-Christ? The Moloch that knows no God but more?’

Diatribes like this have given rise to the impression that Wright was an anti-urban architect, a view Levine sets out to disprove. The Urbanism of Frank Lloyd Wright is a companion to Levine’s landmark study The Architecture of Frank Lloyd Wright, published in 1997, and it is as monumental as might be inferred from the 20-year wait. To make his case, Levine teases out an urban thread from Wright’s earliest projects, including a plan for a residential subdivision of Chicago, and a 1928 scheme for three small towers at St Mark’s-in-the-Bouwerie in New York. The St Mark’s scheme, often overlooked among Wright’s unbuilt projects in favour of flashier fare like his mile-high skyscraper brainwave, was clearly important to the architect – although squashed by the Depression, he continually returned to and recycled its plans and drawings. It was the seed of later urban schemes proposed for Washington, D.C. and Pittsburgh, consisting of towers sprouting from a part-buried slab that takes the form of a sculptural landscape. The organic principle of union with the landscape might seem to have lost some of its subtlety, but the ideas are spectacular: at Pittsburgh, the spiral ramp of the Strong Automobile Objective is inflated to megastructural scale, and an aquarium is sunk into the confluence of the city’s rivers, achieving something close to perfect union with the water. Levine concludes with one of Wright’s final projects, again unrealised, a masterplan for Baghdad.

Models of Wright’s St Mark’s towers are an important feature of the exhibition at MoMA, as is his original model of the Guggenheim Museum, and the catalogue contains a detailed examination of the immense effort that went into their restoration. As well as celebrating Wright’s 150th anniversary, the exhibition marks the transfer of the architect’s copious archives – 55,000 drawings, 125,000 photographs, 300,000 sheets of correspondence, dozens of models – from Taliesin and Taliesin West to the museum and Columbia University. This archive is the evidence of Wright’s decades of thought, writing, striving and designing – a body of architectural work of unique originality and vitality. It is the secret of why there is still much to learn about Wright, and why he rewards study. Fallingwater and the Guggenheim are the tip – the archive is the iceberg.