I don't quite know how I'd managed to avoid the Ashmolean Museum all my life, but until just the other day I had. "Avoiding" isn't quite the right word of course; it wasn't that I crossed the road to steer clear every time I visited Oxford and at all other times the chances of falling through the front door was non-existent. A museum doesn't follow you around, pleading for a relationship, after all, and the Ashmolean could have been said to have been shyer than most in some respects, an institution that kept itself to itself. In fact, a dim sense of it as a dusty and superannuated place may have been one of the reasons I never went, though I'm ashamed to say (it's a formulaic phrase but it's actually true in this case) that I never really thought about it that clearly. Anyway, I've broken my duck now - visiting to see what the architect Rick Mather has done to the building for its £61 million refit and departing a bit startled to see what treasures I'd unwittingly ignored.

The Mather reinvention of what lies behind Cockerell's 1845 building is simultaneously spectacular and unobtrusive. It was one of the conditions of the project that the doubling of the museum's display space should not be achieved by breaking the existing roofline of the site, so Mather's extension is effectively a building without an outside, occupying a space that used to be filled by a series of grand Victorian sheds and which is bound on all sides by other buildings. The spectacular bit comes from the central atrium space - flanked by a rather lovely ziggurat of staircases and pulling natural light all the way down to a sunken lower floor - and from the rooftop restaurant that allows visitors to get a novel perspective on the dreaming spires. And this sudden expansion of space hasn't just meant that the museum can show objects that used to lie unseen by all but specialist scholars, but that it can also rethink the way they're shown from scratch. The current motto appears to have been borrowed from E M Forster - "Only connect" -with an architecture and a curatorial programme that stresses the links between separate geographical areas and periods.

Like the Victoria and Albert's new Ceramics Gallery it offers an unstuffy, engaging way of looking at the objects on show, as a kind of cultural game of Chinese whispers, with a technique or an artistic style being passed from hand to hand, adapting and altering as it goes. It's a way of looking at the historical record that is congenial to one-world multiculturalism - with no particular culture privileged over any other - and as such quite alien, I would have thought, to the classicist Victorian supremacy which is still just detectable in the older building. It is, to me, a highly appealing approach - one that blends scholarship about the provenance and origin of the objects with a sense of how important miscegenation and interchange are to the vitality of any civilisation. It's not an approach the BNP could much care for, with its implicit acknowledgement that cultural impurity is at the heart of any vigorous society.

And it is, of course, as historically determined as any of the objects on show. Suddenly, the Ashmolean has become the very model of a modern museum, with its expansive white walls, it's lovely minimalist vitrines, it's inviting admission that the experts don't know everything and sometimes guess at what they can't prove. But there will inevitably come a day when this begins to look outdated, and a future curator frets at the orthodoxies he or she has inherited, and the whole thing - money permitting - is turned over again. I'd urge you to go and see it in its fresh-paint glory. But I find myself wondering whether we need a museum for display styles as well - to preserve these revealing accounts of the intellectual stories we tell ourselves.

Thomas Sutcliffe