The Guggenheim's Zaha Hadid exhibition illustrates, with equal clarity, the genius of the architect, the lack of a world-class venue in London and the problems of working in Wales

You have to go and see Zaha Hadid's retrospective at the Guggenheim museum in New York. There couldn't be a better space to show her work. For this is a building that, like much of Zaha's output, takes an idea and pursues it to its ultimate end at the expense of all else. Once any great structure is completed the trials, the fights and the overspend are forgotten. Well, perhaps not forgotten, but forgiven, and the stories themselves become part of the folklore about what a heady and frustrating experience it is to make a masterpiece.

At the base of the swirling ramp are paintings I remember from the Architectural Association. They were astonishing enough in their day, and demonstrate the influence of Rem Koolhaas, her then mentor. Walk the walk up the ramp and the oeuvre of Zaha's office is revealed in chronological sequence. The struggle, the experimentation, the relentless pursuit of ideas, the risk taking and the defiance of conventional architectural presentation techniques are displayed with an energy that gradually picks up pace - as the ramp spirals upwards so does the work, ending with a climax that is the manifestation of a unique and brilliant talent.

Yes, you will have to go to New York. There is no such space to show in London - and besides, it is hard to imagine being able to raise the money necessary to put on a tour de force of this scale. When a major retrospective of one of the world's greatest architects, Le Corbusier, has to be confined to the inhospitable surroundings of the Barbican, you realise the difference between patronage in the UK and the USA. It is perhaps for similar reasons of patronage that Zaha has not yet built in the country she has chosen to make her home in, although her design for the Architecture Foundation, modest as it is in scale, holds out much promise.

Of course, there can be a downside to such blatant corporate largesse. It was the sponsors who had the last word at the after-dinner speeches, although Zaha upstaged them with her ribbing of Thomas Krens, the director of the Guggenheim, whom she claims to have located, via her prodigious texting, in a lap-dancing club in Moscow - and the more he denied it the more she insisted. But it was a night of glamour and celebration. Circular tables sparkled in the candlelight and when viewed from above were the consummate architectural plan. The guests dressed for the occasion in extravagant attire, accessorised by geometrically challenging handbags and jewels. Zaha, stunning as ever, wore a stiff black silk dress with a fishtail-like train that created a plume behind her.

Only one other architect has been honoured with a retrospective at the Guggenheim: Frank Gehry. Now we have the work of an Arab woman who has defined a radical new aesthetic - I'm proud to be her friend.

At the Metropolitan Museum, which I visited the next day, there were rooms named after their patrons whose incoherent art collections are unfettered by curatorial intervention. But if this is the price you pay to get things to happen, I'll settle for the American way. And if you do go to the Met, spare some time for Anglomania, a display of British fashion, and one of the most cleverly conceived shows I have seen in an age.

Zaha, stunning as ever, wore a stiff black silk dress with a fishtail-like train that created a plume behind her

One nation under football

Long live football. While the populism of Zaha's show had thousands of visitors queuing round the block on the opening day, the World Cup has seen our ghastly shopping centres emptied of people who instead have gathered in town squares, parks, pubs and plazas. It is a fact that football has the power to bind a community more than any piece of urban planning, but of course the passion is fleeting and it is the public spaces, and their respite from commercialism, that are there for us at all time.

The Birmingham syndrome

So what is going on in Birmingham? Birmingham City has been relegated but not a lot else seems to be happening. There was so much optimism around the time we designed Selfridges. It was carried by a passionate and enthusiastic council and allowed us to fulfil ambitions beyond our station - after all, it was just a shop, built to a developer's budget.

Now there are just cancelled projects and endless reports, apparently designed to come to contrary conclusions, that smack of petty politics and the aroma of decay surrounding a hung council. It feels like Birmingham could become the new Wales, a land where architects and investors fear to tread (the exception being Richard Rogers' Welsh assembly, and even that almost didn't happen). Remember Zaha's unbuilt Cardiff opera house? The people of Birmingham deserve better than this. Vote back Labour!