The competition was launched in 1955 by Premier Joseph Cahill, prompted by conductor Eugene Goossens, who insisted the dramatic harbour promontory of Bennelong Point was the only proper site. Two hundred and thirty-three entries arrived from thirty-two countries. The winner, announced in January 1957, was Jørn Utzon, a 38-year-old who had won seven design competitions before but had never seen a single one of his buildings constructed. His drawings of soaring white shells, inspired by bird wings, clouds and the segments of an orange, were almost universally admired as groundbreaking. The jury, which included the great Finnish-American architect Eero Saarinen, recognised something extraordinary. What no one yet understood was how fiendishly difficult those poetic curves would be to actually build.

The shells were the problem that nearly sank everything. As first drawn they had no defined geometry at all, and the engineers at Ove Arup and Partners spent years failing to find a way to construct them economically. Between 1957 and 1963 the team worked through at least twelve different schemes, trying parabolas, ellipsoids and circular ribs, leaning on some of the earliest uses of computers in structural analysis. The breakthrough came around 1961 with an idea of disarming elegance: every shell would be cut from the surface of a single imaginary sphere, 75.2 metres in radius. Suddenly the curves could be cast from common moulds. The roof was finally clad in over a million tiles in glossy white and matte cream, made in Sweden, arranged in a subtle chevron pattern that looks pure white only from a distance.

For the first stage Utzon and the engineers worked in genuine harmony, but the politics curdled around them. The government had demanded construction begin in 1959, before the design was finished, fearing public opinion might turn. Costs and delays piled up. After the 1965 election brought in a new government, the incoming Minister for Public Works, Davis Hughes, proved openly hostile, and payments to Utzon were withheld. In February 1966 the architect told Hughes that if his fees were not paid he would resign. Hughes accepted the resignation on the spot. Utzon left, and an Australian team led by Peter Hall took over the interiors, scrapping much of his original work. The main hall became a concert hall whose famously high roof left it acoustically troubled, and the smaller theatre was left unable to stage large-scale opera.

The numbers tell the scale of the saga. The 1957 estimate put the cost at seven million dollars and promised completion by Australia Day 1963. The building was finally finished in 1973 at a cost of 102 million dollars, roughly fourteen times the original figure, funded largely by a state lottery. Yet history has been kind to Utzon. In 2003 he received the Pritzker Prize, architecture's highest honour, and in his final years he was quietly reconciled with the Opera House Trust and consulted on its refurbishment. In 2007 the building was inscribed as a UNESCO World Heritage Site, an honour rarely granted to a work by a living architect. Today it hosts more than 1,800 performances a year and draws over ten million visitors, a monument to a vision that triumphed despite everything done to compromise it.