The following apology was printed in the Guardian's Corrections and Clarifications column, Friday May 14 2004  The article below should have acknowledged reference to a piece by Marcus Fairs that appeared in Icon magazine. Apologies.  Zaha Hadid offers a moist, limp hand to shake. She's coming down with flu. This is a disappointment. Where is the vibrant monster I'd been promised from previous interviews? Where's the ball-breaking harridan barking abuse in Arabic into her mobile as she wafts into her north-London studio in vertiginous heels, before snarling unpleasant things to her staff in terrifyingly idiomatic Anglo-Saxon?  "It's all the flying I do," says Hadid, glancing at me with sad brown eyes. "I don't know what they put in the air on those planes, but it is really affecting my health." Since she won the Pritzker prize last month - effectively the Nobel Prize for architecture - Hadid, 53, hasn't stopped travelling. She's just back from Vienna, where she teaches, and will be jetting off again soon to oversee her many projects. To Rome, perhaps, where her extraordinary National Centre of Contemporary Arts (less a spaghetti junction than a tangle of chopped-up tagliatelli freeways) is under construction. Or to Leipzig, where her offices and technical spaces for BMW's HQ will mingle white and blue collars in a hearteningly egalitarian manner. Or to Wolfburg, also in Germany, where she's building a science centre. Or to Italy, where her Salerno ferry terminal is being thrown up. It's conceived like an oyster: hard on the outside, soft and fluid on the inside, and rather gorgeous all over. "The aquatic topography will offer insistently differentiated spaces, and experience, whilst providing clear orientation," explains Hadid's website. Love that "insistently".  These days Hadid needs more in her luggage than her trademark black Issey Mayake suits. She needs a hard hat - because people around the world are finally building her designs. Before the end of the year, she says, it is very likely that 10,000 workers will descend on a 35.2 hectare site in Beijing to work on something called Soho City. This development will, incidentally, give the lie to the notion that this woman doesn't do macho phalluses in glass and steel: before the decade is out there will be a forest of them in the south-east corner of Beijing's Fourth Ring.  For years, though, Zaha Hadid was known as the paper architect. Her genius lived in paintings and digital mock-ups, but died when exposed to the grizzly business of competitions and planning bids. She won awards, sometimes as many as four a year, but made a negligible contribution to the world's built environment. For many years her only substantial realised project was a fire station at a furniture works near Basel, but even that mutated into a millstone around her reputation. It was soon turned into a visitors' centre - and rumours spread claiming that her beautiful buildings might be rubbish at doing the jobs for which they were intended.  Then there was the C-word, one that only the boldest use in Hadid's presence. Cardiff - the city that nixed her opera house project in 1994 in favour of a rugby stadium, leaving Britain's global reputation for architectural conservatism intact. She seethed against the rejection of her scheme by politicians, some of whom had worried - she claims - about giving the project to a "foreigner". For the record, Hadid is a British citizen, an Arab, a Sunni Muslim, an Iraqi brought up in pre-Saddam Baghdad and educated by Catholic nuns and, since 2002, a Commander of the British Empire. "Maybe they're scared of me. I'm very outspoken," says Hadid. "I'm speculating here. I don't really know."  Since the late-1990s she says, things have improved - at least in terms of winning overseas commissions. "The prejudice is lifting," she says. But which one? Prejudice against women? Prejudice against someone who is outspoken? Or prejudice against Arabs? "Mostly the last one. Maybe now it's OK to be an Iraqi. It certainly wasn't."  The prejudices have lifted so much that Hadid won the Pritzker prize. She was the first woman to do so. "I never use the issue about being a woman architect, but if it helps younger people to know they can break through the glass ceiling I don't mind that. One thing that's exciting for me is that there's no stereotype of what I should do. It's very liberating."  Hadid was born in Baghdad in 1950. Her father was a Baghdad industrialist and a leading politician in the doomed Iraqi democracy that followed the end of the British mandate in 1958. She hasn't been back for 30 years, resolutely declines to comment on the current occupation (perhaps unsurprisingly, given that many of her most lucrative commissions are American), but recalls the Iraqi capital as a progressive place - especially for women. "When the men went to war, which Iraq did repeatedly against Iran, women ran the place. Most of my girlfriends wanted to be professionals. I wanted to be an architect. It didn't seem strange."  Nor did it seem strange for her to come to London to study at the Architectural Association in the early 1970s. It was a heady time: teachers, including Rem Koolhaas, Nigel Coates, Bernard Tschumi and Daniel Libeskind, challenged students to cast off their enthusiasms for modernist and postmodernist architects and develop a more radically experimental architecture. For Hadid, steeped as she was in the works of Mies van der Rohe, Le Corbusier and Russian constructivists (she's still looking forward to the Pritzker award ceremony in St Petersburg next month, chiefly because it is the home-town of her beloved Malevich), this was chastening stuff.  "The normative orthodoxy was overwhelming - you could only do buildings in one particular way. But my iconoclastic teachers helped us rebel against all that." And how. Hadid has, since graduation in 1977, developed radical new ways of arranging space and structure. Her buildings are not accumulations of stacked planes, but rather non-repeating layers that respond to patterns of use. For example, those twists of pasta at the Rome museum are flexible exhibition spaces that can be locked into each other depending on what is going on display.  Her designs are distinguished by sharp angles, flowing lines and dramatic juxtapositions. Critics suggested that there was something almost geological in her jagged and extruded forms, as if her buildings had been created not by woman but by the force of nature. But Hadid regards her works as responding to the site's landscape.  She likes talking about porosity, about estuarial flows. In Leipzig, for instance: "The idea was to create areas where everything is accessible and everybody can flow everywhere - to move away from the normative notion of the perimeter block as a fortified space." A political architecture then? "It is political because it is about openness. I baulk at using the term democratic."  She shows me photographs of her largest built project so far, the Rosenthal Centre for Contemporary Art in Cincinnati, which opened last year. "Look at this urban carpet," she says, pointing at the concrete path that is the floor of the transparent foyer. It then curves upwards to form the back of a central well in which a huge steel staircase (made by a local manufacturer of roller coasters) rises to provide access to six floors of gallery and office space. "The idea is to be open, to whisk people into the building and make them feel it is theirs."  Other more minor but no less beautiful constructions have been built - a ski jump near Innsbruck, a fire station in Vitra, a railway station in Strasbourg. It's a fat file of architectural achievement, though with one big exception. There's nothing in London. Indeed, the only British project Zaha Hadid Architects have on the go at the moment is a cancer care drop-in centre called Maggie's Centre in Kirkcaldy, Fife.  "They should really take advantage of us because we are here, and we are very imaginative. We have to be because the projects we work on have little money and little space." But nothing is happening: her Holloway Road bridge was never built, her redevelopment of Bishopsgate was stymied, and don't even ask why she didn't win the competition for the new BBC Music Centre at White City. "I guess you go into competitions and somebody wins. We were very disappointed. It was a tremendous scheme."  For the time being, Hadid can console herself with some more looming projects - a new Guggenheim for Taichung in Taiwan, a science hub in Singapore, a museum extension in Copenhagen, even another opera house (this one in Guangzhou, China).  "Zaha Hadid is an architect who consistently pushes the boundaries of architecture and urban design," says her website. Love that "consistently", I say, but it does sound tiring. "It is," she tells me. "We're working all hours." Workaholic and single, Hadid seems destined to have only one longtime companion - galloping influenza, the kind brought on by jetting to foreign climes to see dreams become real.
Zaha Hadid was once famous for not getting anything built. Now she has won the equivalent of a Nobel prize. By Stuart Jeffries.