This is the kind of exhibition Tate Modern should put on all the time – a serious, sensitive and eye-opening encounter with a great modern artist.  Arshile Gorky was one of a generation of artists in 1930s New York who were fed by Roosevelt's New Deal while they studied the works of the European modern movement in Manhattan's Museum of Modern Art. By the 1940s, these painters were opening themselves to a Jungian unconscious of mythic forms; by around 1950, they were becoming famous for abstract, wall-filling visions of sublime mystery.  But by the time Jackson Pollock and the other abstract expressionists broke the ice, Gorky was dead. He killed himself in 1948, with his painting still in the movement's intermediate phase of development, not yet purely abstract; his tearpools of paintings swim with psychic metaphors and spectral shapes, shards of figures, washes of landscape.  The achievement of this exhibition is to reveal that – far from being unresolved – these are among the monuments of American art. They flow and burst with life, evoking waterfalls in drips of thin green and orange paint. The talent that enabled Gorky to perfectly ape Cézanne in an early still life makes his poetic dreams of the 1940s formidably sharp. These are not vague shimmers, like Rothko's Slow Swirl at the Edge of the Sea, but scarily real encounters with monsters and memories, made real in jagged black lines that stab through swirls of colour. These colours are by turns harshly hot and mercifully cool, and flow with a captivating freedom.  In the two versions of his portrait The Artist and His Mother, Gorky himself faces you: a boy lost in time with his mother, who died in Turkey's Armenian genocide at the end of the first world war. His canvases return obsessively to his childhood by Lake Van, as they strive manfully to create a place for a displaced heart.
Both serious and surprising, this new retrospective looks at the work of an artist famous for his swirls of colour and spectral shapes