I once had an art teacher who taught me how to cheat by smudging. I was working in charcoal at the time, producing frighteningly obvious black lines that highlighted all my artistic shortcomings. If I smudged their edges, however, the faults in my bold outlines disappeared. I arrived instantly at a more subtle effect. Smudging helped because it hid.

For some reason, I kept remembering this lesson as I trooped around the seemingly impressive Vilhelm Hammershoi exhibition that has arrived at the Royal Academy accompanied by a chorus of reverential whispers. Hammershoi isn’t an obvious smudger - his pictures appear startlingly clear and precise. With its endless silences and anally exact bipolar moods, Hammershoi’s art fires an arrow of instant recognition at your own sense of despair. Yet this constant repetition of the same depressive mood that you get here, the habitual reaching for the tube of wrist-cutter grey, the showy framing of the intense Scandinavian emptiness, kept reminding me of my art teacher’s lesson. The outlines weren’t being smudged, but the creativity was.

Hammershoi was born in Copenhagen in 1864 and died there in 1916. So, his life in the Danish outback coincided exactly with one of the most adventurous epochs art has seen. The year before he was born, Manet’s notorious Le Déjeuner sur l’herbe was rejected by the Paris salon and modern art entered the world, kicking and screaming. By the time he died, Picasso had painted Les Demoiselles d’Avignon, and cubism, futurism and vorticism had arrived and left. None of which had any impact whatsoever on any of the paintings you see here, all of which appear to skip a couple of centuries in their genealogy as they trudge morosely back to the 17th century and endlessly circle the room, looking for old-masterish moods.

Hammershoi was the same age as Toulouse-Lautrec, 11 years younger than Van Gogh, 25 years younger than Cézanne. But all he seems to have wanted is to become Vermeer again. His art exists in a parallel world with a different chronology. If you have not heard of him before, that is because his reputation spent most of the 20th century in a coma. It didn’t fit any of the existing stories of progress, so, for the entire modernist epoch, he was ignored. It was only when a couple of world wars caused the hunger for the new to wear off, and enough distance separated our times from his, that his aggressive regressiveness ceased to matter, or to appear obvious, and he came back into the reckoning. Nowadays, the gravest danger threatening his reputation is not underestimation, but its opposite.

His life was another symphony in grey. Nothing distinctive ever happened. He studied. Got married. Moved into an apartment. Painted it. Moved into another apartment. Painted that, too. And that’s it. No children. No wars. No adventures. No actual reason for all this sucking gloom that funnels his creativity into a narrow trickle and turns him into a one-trick pony. Hammershoi didn’t earn his misery. He inherited it. Like so many Scandinavian creatives of his epoch, he seems utterly insensitive to any of the colours or possibilities of the new century. Addicted to bleakness, he just sits staring glumly at his four Danish walls, endlessly repositioning his props - the settee, the piano, the vase, the wife. The resulting emptinesses are too mannered and elegant to be real. If art deco had done depression, it would probably have done it his way.

The show begins rather magically, however, with a triptych of tiny farmyard views painted in his early twenties. Everything that was to harden into cold mannerism by the next room is initially in evidence as a warm, gentle inclination, as Hammershoi stares squintily at an old barn and gets carried away with the abstract throb of the broken light dappling the thatch and the big summer sunbeams bleaching the whitewashed walls. He was good outdoors: responsive, happy and enraptured. It was when he went indoors that the agoraphobia set in, and here the show turns miserable.

In 1890, he got engaged to Ida Ilsted, the sister of a fellow student - of course - whom he paints in the same year in a black dress with a grey top, sitting in a grey room, looking glum. When I got engaged, I couldn’t stop smiling for most of the year, and bored everyone I met with tales of my sweetheart’s beauty and sexiness. Hammershoi chooses to emphasise his fiancée’s gloominess instead, by painting a sad wooden doll of indeterminate age who stares intensely into the distance, as if her best years are already behind her and she has just learnt that the life-insurance premiums were never paid.

Ida was to appear frequently in Hammershoi’s art, but only rarely did he look her in the face again. Most of the time, all you get is a back view, a lonely silhouette against a window, a sad outline in the room beyond, as this most dutiful of wives takes up her rightful position in her husband’s art as a reliable studio prop. The fact is, Hammershoi couldn’t do faces very well. A strange double portrait from 1898 of the artist and his spouse gives us an Ida so stiff and generalised, she might have been carved by a maker of ships’ figureheads. Instead of smudging his figures to make them convincing, Hammershoi turns them around and paints their backs. And it has the immediate effect of increasing the whispery sense of mystery in his art.

The apartment into which they moved in 1897 was to become the background for the bare, moody interiors on which his modern reputation chiefly rests. This show home of loneliness, with its minimal furnishings, doomy shadows and ghostly female dreamers, is a clear steal from Vermeer. But where Vermeer manages to suggest all sorts of complex emotional possibilities in the light-touched faces of his caged women, Hammershoi hams up their loneliness something awful, with melodramatic thrusts of light, threateningly open doors and soul-squashing vistas of emptiness. Before every painting was begun, a maid with a powerful vacuum cleaner seems to have been sent in to remove all traces of proper human habitation.

In a clever bit of exhibition-making, the organisers have pinned up a layout of the apartment next to the relevant paintings, so you can see what was painted in which room. After a few minutes of trying to match the spaces to their theoretical geography, you begin to realise that the aura of intense realism Hammershoi brings to his art is entirely false in its origins. The details never add up. That window could not have been over there if it was also over here. The settee is in three places at once. What seems to be a record of an actual location and an actual relationship turns out to be a carefully controlled fantasy of fin-de-siècle Copenhagen gloom. Thus the difference between Vermeer and Hammershoi is the difference between a Bergman film and Home Alone 3.

Vilhelm Hammershoi, Royal Academy, W1, until September 7

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