So who did what in Greenwich? I see the hand of Mather everywhere, particularly in the details such as the fat timber handrails and steel-mesh balustrades. The big, "clear-span" roof - the largest in Europe - is to some extent shopping-mall architecture, so one might tentatively chalk that up to his colleagues at BDP. The objects that visitors look at are arranged, and to some extent devised, by the exhibition designer, Jasper Jacob. But in the end, attribution doesn't matter. The extraordinary complex of buildings comprising historic Greenwich has always been made by many hands. Wren and Hawksmoor are notoriously difficult to disentangle; many others were involved over the years on what was to become the Royal Naval College, and many more on the other buildings around it. The original architect of the National Maritime Museum, Daniel Asher Alexander, also designed Dartmoor jail. Others extended it. The achievement of Greenwich is the magnificent ensemble effect: every individual piece is subservient to the whole, and the open spaces are as important as the buildings.

The NMM now sits much more happily in all this. Its entrance is at last where it should be - through the grand entrance portico facing the Royal Naval College. Before, it used to be round the side, at the back. You can see that something interesting is happening as you approach, since the previously open spaces either side of the portico are now glazed in, with a huge, slowly rotating ship's propellor just inside on one side, and a flashing lighthouse lantern on the other. You enter through a low lobby and get a glimpse of the soaring roof above through a circular light-well, before finally emerging into the big space.

To appreciate it fully, you have to be up on the podium. Sensibly, this is not cluttered with myriad little objects, instead having a few very large ones - a cube, a globe and a tower, each containing exhibits or screens. Greenpeace's famous protest pod, at present helping Norwegian police with their inquiries, will also take its place here. The stern of a Trafalgar-era ship, HMS Implacable, is pinned on the facade of the surrounding courtyard like a giant brooch - the past overlooking the future. The sails of a 1960s round-the-world yacht rise from the "street" below, that defines the edge of the courtyard. Down there you will also find a graceful 1930s speedboat and a prosaic stack of shipping containers.

They're playing the same game here as at the Louvre in Paris or the British Museum, or - eventually - the Victoria and Albert Museum: in each case the central courtyard, overlooked for years, becomes, in one way or another, the orientation point for the whole museum. A lot of the clever work at Greenwich, for instance, is in the corners, where new stairs and bridges allow people to disperse logically from the centre into the existing galleries. There are also a lot of new galleries, as the space beneath the podium is packed with displays - some traditional "black boxes", others expressed as glazed frontages onto the "street". And overlooking all this, in what looks to me like a very Matherish new building behind the entrance facade, is the mandatory but welcome cafe-with-a-view.

It all makes a great deal more sense than it used to. Some time before the British Museum rebuild is finished (where Mather, incidentally, came second to Norman Foster in the architectural competition), you can see the benefits of making a great big glazed space at the heart of a previously cluttered and confusing museum. It works - sunlight is filtered just enough to avoid glare and overheating.

All the new showmanship is to do with sweetening the pill. The new spaces and their displays are intended to get people into what is still a very object-rich collection, despite all the changes of recent years. Computers will allow you to search through the 2m artefacts in store. It would have been inconceivable, a few years back, for the NMM to go to the Arts Council for a grant to commission contemporary artists to work within the museum - including a coastal "sound sculpture" by Bill Fontana involving loudspeakers buried in the approach path. Some may see this as dangerously over-trendy. But never fear: uniform fetishists are still well catered for. And real fundamentalists can still find Nelson's bloodstained coat.