During his short life — he died in 1848, at the age of 47 — Thomas Cole became something of a national culture hero: a young one for a young nation. He was esteemed as the founder of national landscape painting in the U.S. — the so-called Hudson River School. At his death, the wild places of the Catskills mourned him. “We might dream,” declaimed William Cullen Bryant in his funeral oration on Cole, “that the conscious valleys miss his accustomed visits and that the autumnal glories of the woods are paler because of his departure.” His death, opined a newspaper editorial, was “a public and national calamity.” Even allowing for the high rhetorical tint required of such exequies 150 years ago, it’s hard to think of an American artist whose death, tomorrow, would inspire such sentiments. Why did Cole’s do so? For answers, consult “Thomas Cole: Landscape into History,” a show of more than 75 paintings curated by art historians William H. Truettner and Alan Wallach on view at the National Museum of American Art in Washington through Aug. 7. It is highly engaging, not least because the curators — without imposing a modern agenda on Cole’s work — have done such an intelligent job of ferreting out what ideas of American identity he satisfied, including political ideas. Cole was the first boy wonder of American painting to prove himself entirely on native ground. Earlier prodigies, like Benjamin West, had had to do it in Europe, and it mattered greatly to John Singleton Copley’s clients in Boston that Sir Joshua Reynolds praised Copley’s early work. But neither Europe nor England paid attention to Cole. From across the Atlantic he would have seemed a mere provincial, fluctuating between derivative Claudian pastorals and apocalyptic religious allegory in the manner of John Martin. Cole had no formal training. He learned about landscape painting from theoretical tracts and the early-19th century equivalent of how-to manuals, backed up by a great deal of attentive looking. He couldn’t draw the human figure — but then neither could his hero, Claude Lorrain. His efforts in that direction, as in a huge painting of Prometheus chained to his rock with the eagle flying in for lunch, were risible. Wisely, he kept his Indians and woodsmen and saints in the far distance. The outline of his life seems a fable of what emigration could inspire. The young artist — Cole was the son of a small trader from Lancashire — arrives in the aesthetically uncharted wilderness, where, self-taught, by dint of “natural vision,” he begins to create a new, true and specifically American picturesqueness out of rocks, gorges, sunsets, trees and distant Indians. He is taken up by the plutocrats of his day, some with long patrician roots, like Stephen van Rensselaer III, America’s biggest landlord, and others more recently arrived, like the grocery millionaire Luman Reed. Old money wanted to show that taste was not a monopoly of Europeans. New money hoped to prove that it too had refinement and a stake in forming the national image.