Bronze is the most extraordinary material. It works big; it works small, cast into details literally as fine as a hair. It can be marvellously ornamented, or pared down to a Giacometti or Brancusi-like stillness. Both sculptors have works in this show; in fact it is hard to think of a major name in international sculpture from the late Middle Ages to today who does not. It survives being buried under volcanic ash, or immersed in sea-water, for centuries – the latter giving it a marvellously seaweedy green patina, beautifully displayed (and lit) on the 4th-century BC Dancing Faun, who greets the visitor entering the show. It can look like a jewel, or like piled dung, or tidal mud, as in Willem de Kooning's Clamdigger of 1972. Impossible to look at this blackened, windswept, life-size figure, and not imagine that somewhere beneath his feet there might lurk the twin to the Faun, which was indeed rescued from the coastal ooze off Sicily in 1998.

This show – wisely casting off the chronological arrangement of the previous Royal Academy sculpture exhibition, which only served to highlight its lacklustre ending – is all about encouraging the visitor to look and compare, across centuries and across civilisations. It leads the visitor from Africa, India, and the Holy Land to China and the Far East, and across six millennia; and the thematic grouping of the show ('Animals', for example – a room I went back to over and over again) helps enormously in appreciating and understanding a medium and a great many exhibits that will, I imagine, be completely unknown to most of the show's visitors. A wonderfully startled-looking Chinese elephant, a mere stripling at just 3000 years old, sits one room away from a joyously placid Hindu 'Ganesh'. An Egyptian cat watches a Brancusi bird. A Bourgeois spider both climbs and seems somehow extruded by the gallery wall. Frederic Remington's Coming through the Rye (1902 – imagine the opening shot of Bonanza, cast in bronze), which gloriously ignores that boring old art-historical dictate about never showing horses with all four hooves off the ground at once, sits catty-corner to the exquisite attenuated Danish Chariot of the Sun (14th century BC), which is itself sharing a case with the Strettweg Chariot, piled with eager-looking little figures that to London eyes may look like nothing so much as a caravan of 'Gorms', on tour. It was created 2,700 years ago.

Which makes the point: how incredibly modern, how unsullied by time so many of these pieces appear. Even when they quite clearly bear the patina of centuries, they still seem extraordinarily untouched, as appealing and as beautiful to us today as to their first owners – if not more so. There is scarcely a piece here (other than the odd overblown, over life-size figure) that you wouldn't make off with in a wheelbarrow, if you could, and many that are tiny enough to be held and marvelled at in the hand, and were designed in the round to be so admired. Perhaps casting in bronze encourages simplification and refinement, and sheer, pure artistic worth. Perhaps those glowing green or gold-speckled surfaces in fact hide immense sophistication of creative thought. Something to ponder on, perhaps, when in Room 2, which in keeping with the exhibition's title, (Bronze, note, not 'Bronzes') is devoted to the techniques of casting bronzes, explained here with exemplary clarity and great enthusiasm – this is certainly the first such show I have ever been to that at this point exhorts the visitor 'Please Touch!' Once you know how it's done, go back and peer again at some of your favourites. That bronze bust of Catherine de' Medici, for example, in the 'Portraits' section with which the show ends. All those bang-on details of the most fashionable Renaissance dress – the thick ruff, the jewels, the tightly curled hair – why don't they work? Bronze is a substance that lasts; in fact time seems only to improve it. To preserve such quotidian details as the most a la mode mounts for your jewels in this epoch-defying medium seems faintly ridiculous, especially next to the Benin bronzes displayed alongside them. Those might be portraits too – but they are sculptures, first.

The show comes with extremely informative wall-panels and very discreet, well-positioned little labels – also a plus – and a catalogue that is almost as lovely as that for the RA's famous Aztecs show. It is blessedly or sadly uncrowded, depending on your point of view. Go crowd it up a little – this is a show that enlarges knowledge and changes understanding. It is not one to miss.

Bronze, at Royal Academy of ArtsErato reviews Bronze at the Royal Academy.4