Cy Twombly is the last great American artist

 "The life of Edgar Allan Poe - what a tragedy!" wrote the French 19th-century poet and critic Charles Baudelaire of the American essayist, failed journalist, author of verses and tales of mystery and imagination, who grew up in Richmond, Virginia, 80 miles from Twombly's Lexington, and who was found dying on the streets of Baltimore in 1849. "All the documents I have read have led me to the conclusion that the United States was nothing but a vast prison house for Poe," decided Baudelaire, "a gaslit desert of barbarism - and that his inner spiritual life as a poet, or even as a drunkard, was a constant struggle to escape from the influence of this hostile atmosphere." Poe obsessed the French poets and painters who invented modernism - not least because his life and art constitute a cruelly shadowed portrait of America - and Poe had his own idea of what modern art might look like. "For the paintings over which his elaborate fancy brooded, and which grew, touch by touch, into vaguenesses at which I shuddered the more thrillingly, because I shuddered knowing not why - from these paintings (vivid as their images now are before me) I would in vain endeavour to educe more than a small portion which should lie within the compass of merely written words." So says the narrator of Poe's story The Fall Of The House Of Usher of the abstract paintings that his nervous friend Roderick Usher creates as he goes insane in the troubled family home. "For me at least, in the circumstances then surrounding me, there arose out of the pure abstractions which the hypochondriac contrived to throw upon his canvas, an intensity of intolerable awe..." It is as if Poe prophesies the modern painting that appeared in New York in the 1940s. And Pollock, like Poe, was a prisoner in America. Both were killed by drink, Poe at 40, Pollock at 44. If any paintings resemble those executed by Roderick Usher, they are Pollock's arabesque phantasms. The critic Greenberg noticed at the time that the first real American artist had something "gothic" about him; Pollock even titled a painting Gothic. Twombly is the heir of this gothic Pollock. His paintings write an alternative history of American art, a pessimistic, southern story. It took a leap of imagination for anyone to find modernity in Pollock's romantic helixes. Twombly sees their tragic intensity. Even today, the abandon with which he smears roses and drips briars recalls Pollock. Twombly is a great painter not because he has "rebelled" against Pollock, but because he has understood him. His most disconcerting translation of Pollock has always been his writing, wildly scrawled, sometimes a stream of illegible consciousness, sometimes single words, sometimes lines of poetry coming out of the Poe vagueness: fragments of argument and recollection and expressions of longing. His art is full of words, which ache to express the totality of what he wants to say. Quoting poetry is ostentatious, and a defeat; after all, it is not Twombly's language. And yet to write down a piece of poetry is to feel it.

 "Fanatics have their dreams, wherewith they weave/A paradise for a sect," begins Keats's The Fall Of Hyperion. For Keats, this is an image of a dream that fails to be shared. But what does this same line mean when Twombly scribbles it among buttocks, breasts, penises and turds frolicking in space? The line becomes hysterical. Sexuality pervades the archaeology of ancient Rome; pornographic paintings, scabrous graffiti. All of this is in Twombly's scatological Roman paintings from the early 1960s that mingle his own sexuality with that of a ruinous hedonistic city - the city also of La Dolce Vita. Violence is as recurrent in his work as sex. In the 1975 drawing Mars And The Artist, the word Artist is juxtaposed with that of Mars, god of war, on a sheetrubbed and striated with troubled lines and erasures and two phallic shapes. Desire for Twombly is a battle. In this sense, he is exactly like Pollock. As a painter Twombly is as ritualistic and frenzied as his predecessor, but by accepting the discipline of classical literature and myth he acknowledges a tradition outside his raging self. This is not sublimation, not repression. It is simply the acknowledgment that art is a sharing, that even the most brutal painted mark assumes a system of meaning. So Twombly transposes his dilemmas, his inordinate sensuality, his insatiability, on to a luxurious territory sprawling over centuries and millennia. No European artist of the past 30 years, not even Joseph Beuys, has loved European history like Twombly. This is a painter who commemorates the 16th-century Battle of Lepanto, who invokes the Greco-Roman gods as living presences. The culture Twombly has chosen is classical in the largest sense, including the poets who have gone to Rome, the painters who have painted it - most of all, Poussin and Turner - and the history of the Mediterranean world. In the 1960s, US critics, steeled by minimalism, turned on Twombly's effulgent history paintings as the fatuous daubs of an émigré corrupted by old, old Europe. This pretty much describes his greatness, of course. The colours in this wonderful exhibition are those of overripe fruit, flowers squashed and about to fade, spilled wine. It is all impossibly heady. Cy Twombly is an American gone to the bad - a decadent exile who chose to live among the mouldering palaces and antiquities of Europe. A man who is dirty-minded, and history-minded. Somehow, the two go together for this genius of rot.

· Cy Twombly: Fifty Years Of Works On Paper is at the Serpentine Gallery, London W2, April 17-June 13. Call 020-7402 6075