The debate went on for most of the 20th century: was its greatest artist Matisse or Picasso? This was perhaps the only century of the millennium in which the championship was a two-horse race – and a very close race, so that there may never be a consensus lasting more than fifty years as to which of them was the winner. Nevertheless, there is a clear distinction in their greatness, one relating purely to its nature, not its degree. It’s that Matisse did not possess or need to possess genius.

The definition of genius is implicit in the platitude about its affinity to madness. Reynolds sought to deflate this dramatic notion with down-to-earth talk of an infinite capacity for taking pains. But surely that capacity is more relevant to greatness than specifically to genius; when it accompanies genius that is probably because genius breeds extreme obsession. Being extreme is one of the attributes of genius. Another is that its operation entails lateral thinking. Another is that it means being a medium rather than a maker: the inventiveness of those who have genius does not seem to come from them but through them.

An artist can be touched with genius without becoming a great artist. And the artist of genius can be a hedgehog or a fox. When a hedgehog of genius alters the course of art, it is through a crucial strategic discovery that changes the rules: the prototype is William Webb Ellis of Rugby School, who playing football one afternoon picked up the ball and ran with it. A fox of genius surprises again and again by the speed and wonder of his inventiveness.

These speculations have come in the wake of seeing an exhibition at the Tate Liverpool of a British sculptor in mid-career who is surely an artist of genius, Tony Cragg. If there’s another among that generation in Britain, it must be Gilbert and George, a pair of classic hedgehogs: everything they’ve done depends from that marvellous wheeze they had as students that a couple of artists could be living sculptures. Cragg is a fox, with a flow of invention that is dazzling and frightening in its prodigality and dottiness.

‘A picture, an image or a form,’ Cragg once wrote, ‘cannot be expressed with a thousand words – not even with a million.’ I use this as an excuse for having abandoned an attempt to evoke a number of the shapes, the surfaces, the configurations that occur in his work – if only in the hope of suggesting their sheer diversity. Even in the hands of a much better writer the attempt would be bound to fall short of summoning up the impact of his artefacts: half of their point is the immediacy with which their surprises surge up – surprises such as a set of tables and chairs with vicious little metal hooks dotted across them like chickenpox, surprises that set the nervous system jangling.

A list of the materials he has used does hint at the diversity of the work. Bricks, wooden sticks, rubble, found plastic bottles, found plastic fragments, found painted lengths of wood, wooden boxes, wardrobes, lava, clay, sandstone, rubber, found pieces of metal, wooden boards, plastic piping, glass bottles (clear, coloured or frosted), electric wires, slabs of granite, cast-iron, hardboard, fibreglass, plaster, steel, bronze, aluminium, limestone, lapis lazuli, serpentine, ceramic, a bicycle, marble, sandblasted porcelain, cement, polyester, polystyrene, tufa, wax, volcanic ash and a mosaic of plastic dice used as an epidermis. Cragg’s sculptures are responses to these materials. They seem to investigate the materials’ natural possibilities in the way that those of chosen musical instruments are investigated by composers such as Berlioz, Stravinsky and Boulez.

The exhibition in Liverpool, Cragg’s birthplace, is beautiful in every way: the individual sculptures; the relationships between them created by their placing and the virtual absence of distracting drawings; the rooms themselves, which are those on the building’s top floor, only recently opened and by far the best rooms there for their proportions, their design, their daylight and their views of the Mersey. Only one thing about the presentation is jarring. There’s a tiny room with a TV and chairs and a good video about Cragg which disrupts the quiet of the adjacent rooms, a quiet that is needed as a background to the imagined sounds of Cragg’s sculptures, which can range from a lunar silence to a pastoral murmur to an electrical hum to a mechanical splutter. The disturbance created by the video even when that room is empty suggests that it should have been placed downstairs in the sizable, uncrowded lobby.

For all the exhibition’s beauty, the choice of the works has made it less satisfying and exciting than it could have been. The gallery’s director, Lewis Biggs, begins his catalogue preface with the staggering information that for the last twenty years Cragg has produced ‘at least one exhibition every other month, and in many years one exhibition each month’, and goes on to regret how few of these have been in Britain. Indeed, the present exhibition, with its thirty-seven sculptures in seven rooms and two giant pieces on a lawn, seems to be the biggest Cragg has ever had here. In the circumstances, I can see no real reason why it is confined to recent work, with half of the sculptures completed in the last 15 months. I am not for a moment suggesting that it should have been a retrospective: a valid Cragg retrospective, representing his output since 1975, would have to be at least twice the size of this exhibition – and, if the Tate Modern at Bankside knows its business, one will be staged there within the next three or four years. Nevertheless, the present show should have been a bit more retrospective. Public galleries ought to be concerned with displaying the best rather than the newest, and this exhibition would have been greatly strengthened by the presence of a few of the outstanding pieces Cragg has shown in the last two or three years.

I am thinking, for example, of one of the sculptures monstrously spotted with hooks in the 1997 Whitechapel show – the work with several chairs and a piano dating from 1993. And then I’m thinking of the finest piece in glass by Cragg I’ve ever seen: the orgiastic, cataclysmic version of Pacific (1998), that was shown at the Lisson Gallery in 1998-99. I’m also thinking of two of the dice-coated sculptures with a white ground and black spots, the bipartite Secretions of 1997 seen at the Whitechapel and the Secretions of 1998 at the Lisson. The Liverpool show includes the first piece, dated 2000, to have dice with a black ground and white spots. The effect is intriguingly different: so for those who know the black-on-white pieces, it’s frustrating not to see the two sorts side by side, while for those who don’t, the white-on-black piece is deprived of some of its meaning. The going-for-newness strategy is a loser in two ways. It lowers the quality of the exhibition and it makes for repetitiveness. Too high a proportion of the pieces are in black bronze, so that an audience unfamiliar with the work as a whole gets no inkling of the diversity of material and consequent diversity of form as well as surface that is one of its prime glories.

In fact, more than half the exhibits are black bronzes, almost all of them members of two series, one of which Cragg calls ‘Early Forms’, the other ‘Envelopes’: in the second a bronze shell is perforated by numerous holes through which we usually see a second similar form within. What the ‘Early Forms’ and the ‘Envelopes’ have in common, besides being in cast metal, is that their shapes recapitulate the biomorphic abstract vocabulary of typical sculptures of the 1930s by artists such as Henry Moore.

Obviously, one of the qualities most urgently needed in an artist of Cragg’s relentless originality is a readiness to be taken for a madman or a fool. Ironically, the biggest risk of that kind Cragg has ever chanced has probably been that of being thought unoriginal in using a language resembling Moore’s. Unoriginal and corny. The point de départ of Late Modernist sculpture in Britain was Anthony Caro’s rejection c.1960 of the great panjandrum whose assistant he had been. Ironically again, some of Caro’s early pieces in painted welded steel contained involuntary echoes of Moore’s reclining figures. But that is by the way. The polemics of the new movement which took sculpture off the pedestal and placed it on the floor forcefully removed Moore from his pedestal and left him on the floor. So visitors to Cragg’s acclaimed show at the Venice Biennale in 1988 were surprised to find themselves admiring sculptures which blatantly looked back to Moore. We were surprised because there had been not the slightest sign of such an interest in his big exhibition at the Hayward only a year before. And it was still more surprising that Cragg of all people could be so corny.

And Cragg has persisted with this biomorphic language: the Liverpool show, indeed, includes several examples in materials other than bronze. One is Tourist (2000), in polystyrene and fibreglass: a large baroque undulating ring of ovular shapes which calls to mind the old fairground canopied ride called the Caterpillar; the surface is smooth and white with meandering coloured areas as on a globe. So Cragg has become involved with a range of forms that go back to prehistoric fertility statuettes, forms suggestive of pregnant bellies and the breasts and buttocks that go with them. Moore is not necessarily the main reference for these maternal shapes. Cragg’s biomorphs are often more redolent of Hans Arp’s, largely because these are less anthropomorphic. Moore’s, which are essentially offsprings of Picasso’s Metamorphosis I and II of 1928, are usually variations on a whole human figure or head and shoulders. Cragg’s evocations of the human body tend to relate to its parts, external or internal. In any event, the human references have been diminishing. There is no intimation of the human body in St Gallen (1997), one of the earlier pieces shown in Liverpool, with its elegant horizontal spiral movement, while in Rod (2000), which follows clearly from it, there is little intimation of organic life of any kind: it evokes machinery – turbines or radiators – as do other recent bronzes such as Stephenson, affirming Cragg’s perennial attachment to man-made models.

That attachment is at its most explicit in the works that are actual assemblages of found industrial products. These include the group which moves me above all others: those in glass. Some are plain glass, some coloured glass, some sandblasted glass. All sorts of glass containers are incorporated, but the most favoured is a claret bottle – a rewarding shape in that its cylindricality makes it a phallic image while its hollowness makes it an uterine image with a passage leading into and out of it. The containers, which usually seem countless, can be standing up or lying down or placed over spikes issuing in all directions from a tubular metal construction; plate glass is sometimes used horizontally or vertically as a divider. Often a few things are cracked or broken.

There are three glass assemblages at Liverpool, of which the biggest and finest is Cistern (1999), in coloured frosted glass and steel. Seen across the room, it doesn’t suggest the violent inner movement conveyed by the version of Pacific shown at the Lisson. It is only when one closes in that it starts to become animated, with the action growing frantic and furious when one is near enough to feel oneself into the midst of it. All the works in glass accentuate a feeling often induced by Cragg’s most typical sculptures – a feeling of danger. The danger is two-edged. There is a threat to the body of the person looking at the thing. And there’s a threat contained within the thing itself – a nasty suspicion that it could self-destruct. These fears arise from Cragg’s ways of relating the elements of a work so that he seems to be keeping the lid on a potential explosion. And the threats to the spectator and the work alike are heightened in the glass sculptures because of a peculiarity of the material: a glass object can readily get broken and is thus in danger; once it does get broken it gets dangerous. The sense of danger is enhanced when there are already cracks or breaks somewhere. The sculpture becomes a paradigm of reality: death and destruction happen among shimmering reflections of benign light.

I was walking with a stick at the time of my stay in Liverpool. Again and again I had to stop myself from using it on Cistern in order to pre-empt a disaster.