’Trinity: Pharmacology, Physiology, Pathology’, 2000

For 20 years, from shark to spot paintings to skull to Sotheby’s, what Damien did next has mesmerised the public and inspired and stifled his contemporaries in equal measure. Few artists have invented, as Hirst has, a new way of making art that is both a breakthrough in iconography and uses a whole new repertoire of materials: animals in formaldehyde, pharmaceutical cabinets, more diamonds than the market can easily supply. As a result, not only has Hirst towered over the Young British Art movement; the strength of his cold, clinical vision and impersonal tone has more or less crippled the evolution of any other sort of art by his generation in the UK. It is no coincidence that the two most original, brilliant British-born painters among his peers, Cecily Brown and Chris Ofili, long ago chose to live and work abroad.

How extraordinary, then, that the six-room exhibition at the Scottish National Gallery of Modern Art that launches Anthony d’Offay’s nationwide “Artist Rooms” series is the first Hirst solo show in a British museum. Including modern and contemporary work valued at £125m, Artist Rooms is the largest gift of art to the nation in a century. To open with Hirst is symbolic for the project, connecting it with the latest, sexiest living art, but is also significant for the artist. Combining wow-factor works such as the unnerving double-mirrored cabinets of fish and skeletons, “Something for Nothing”, with more modest pieces from the National Gallery of Scotland’s collection, such as an early spin painting, it allows us to grasp the arc of his oeuvre with a new clarity.

’Controlled Substances’, 1994

Recently, Hirst’s public love affair with money has obscured all but the commercial aspect of his career. In his past two exhibitions, White Cube’s “For the Love of God”, centred on the £50m diamond skull, in 2007, and Sotheby’s £95m auction show “Beautiful Inside My Head” in 2008, Hirst deliberately presented his work through a prism of pound signs. Crucially, Edinburgh sheds that Mayfair glitz. The sparsely arranged rooms at the bright, airy, neo-classical Modern Art Gallery invite calm, sober engagement with Hirst’s work in the light not of spiralling prices but of history.

Hirst holds his own within the grand setting, which underlines his rigour and how his clean, austere aesthetic throws into relief his brutish subject matter. In the opening room, three elegant, pared-down pieces emphasise the chemist’s shop and the morgue as key subjects: the painting “Grey Periodic Table”; an unusually uncluttered butterfly diptych, one black, one white canvas, “Monument to the Living and the Dead”; and “Trinity”, three tall pristine glass cabinets of coloured plastic mannequins and body parts. “Trinity”, with its opened-up sections of the body, a life-size torso sliced horizontally into slabs of butcher’s meat, giant models of teeth and eyeballs, hands stripped to bloody veins, foetuses, a snakish green intestine, places him in the classical tradition, as constructor and deconstructor of the human figure. The subtitle, “Pharmacology, Physiology, Pathology”, announces his theme of life and death as interpreted through a relationship to science, while the triptych form and death-haunted graphic realism of this serious work mark him as heir to Francis Bacon.

Hirst’s other lineages are, of course, the vitrines and stacks of minimalism and the lurid banality and detachment of pop. The blade-encrusted neon cancer paintings at White Cube and Sotheby’s kitsch formaldehyde zoo played up the latter. It is d’Offay’s achievement here to save Hirst from himself by a judicious selection, mostly of early work, which emphasises the former, and so lends gravitas to genres lately reduced to absurdity by repetition and self-parody.

’Away from the Flock’, 1995

The beleaguered, pinkish lamb, head tilted upwards, in “Away from the Flock” (1995), is urgent, affecting, simple, individual, exquisitely made: the real thing, rather than the decadent variations – gold-crowned calf, pig with dove’s wings, foal with unicorn horn, cows’ skulls with beachball – sold at Sotheby’s. “New York” (1989), a straightforward glass and MDF pharmaceutical cabinet, and the raw, strikingly hand-painted acrylic “Controlled Substances Key Painting (Spot 4a)” (1994) are similarly more arresting and authentic than their glossy, rapidly produced recent successors. And it is a masterstroke to juxtapose the spot painting with a monochrome quartet of lightbox close-ups of pills, “Painkillers”, and the 1981 photograph of a laughing 16-year-old Damien Hirst “With Dead Head”: a tragic-comic trio of melancholy and romance.

In quality, range and persuasive installation, these six rooms make up a landmark small retrospective that acknowledges Hirst’s importance but also, perhaps, will liberate younger artists from him by fixing him historically. To this end, I think, the other Artist Rooms surrounding the Hirst display are singularly well chosen to establish a continuum between modern and 21st-century art, between different media – painting, drawing, photography, sculpture – and between lesser-known and famous names. Here Hirst takes his place, but appears more classical, less sensational, by the context.

Each of the other rooms, enlightening on its own terms, showcases artists (one per room) who, like Hirst, play formal games of ironic distancing. The rippling surfaces of Vija Celmin’s luminous, blurry charcoal and graphite drawings of night skies, desert floors, spiders’ webs, have the cool serenity of minimalist reliefs. Alex Katz’s small landscapes of winter branches, flat seas, his wife at a window, are direct, decorative, pulsating with colour – yet their spare, controlled surfaces hold you at bay, denying intimacy. Francesca Woodman’s coolly experimental photographs take the artist’s own body as mannequin; draping herself against crumbling walls, framing herself by window panes, Woodman explores the contrast between the soft intimacy of the female nude and the unyielding, angularity of glass or plaster. Hers is an interpretation of femininity made possible by 1970s freedoms but dominated by a formal not feminist agenda: “Me and Francis Bacon and all those baroques are all concerned with making something wiggle and snake around a hard architectural outline,” Woodman said.

’With Dead Head’, 1981

In 1981 Woodman committed suicide, aged 22; her photographs and a gallery dedicated to Andy Warhol’s late photographic multiples hand-stitched together are especially poignant and prescient. Warhol’s six images in “Statue of Liberty” (1986) progressively darken, the shadows finally obscuring the message “liberty enlightening the world” as if predicting the Bush years. His “Dissection Class” and “Cadaver” point to Hirst’s “Trinity”; a skull-like self-portrait in his silvery fright-wig taken the year before he died is as ghoulishly charismatic as Hirst’s self-portrait laughing at death. Artist Rooms here more than fulfills its aim: by examining significant artists in depth, it dramatises too the threads and loops of the past 30 years of art-making, and shows that art history is not the sum of themes and schools but of individual imaginations.

‘Artist Rooms’, Scottish National Gallery of Modern Art, Edinburgh, until November 8. www.nationalgalleries.org tel: +44 (0)131 624 6336