“Curious that in every city I hear the lions roaring,” Max Beckmann noted in his diary in 1947, a few days after reaching New York from Amsterdam, where he had spent the war years in exile from his native Germany. Whatever the remark means, it reminds us that Beckmann loved the circus and identified with the big cats. In his 1940 painting In the Circus Wagon, two soulful tigers cower in a cage while a stern Beckmann, centered in the blaze of a lamp, reads the paper and hunkers over his own prey, an odalisque in pink resembling his wife. He dares the tigers to interrupt him, but he wouldn’t be half so macho without that nearby tamer keeping guard in his impressive uniform. It’s Beckmann’s classic persona, growling and grimacing and mocking himself all the while.

Beckmann is back at MoMA after almost forty years, and this time it took a team of curators to tame him: Robert Storr of NYU and formerly of MoMA, Sean Rainbird of Tate Modern, and Didier Ottinger of the Centre Pompidou. The exhibition, wisely reduced from its Paris size and hung generously and simply (though without much in the way of storytelling or even simple divisions), presents nearly seventy paintings in twelve rooms, a good sampling of graphic work, and a few sculptures. It is content to sample Beckmann’s various modes (except still life, virtually absent) without exhausting any of them, or us.

Seeing this artist in retrospect raises a question: How could a painter who started out and ended up so very bad—and I don’t mean good, avant-garde bad, I mean bad bad—get so very good? Beckmann crafted some of the most memorable visual conundrums of the past century and a string of masterful self-portraits, but getting to them can be heavy weather.

The exhibition starts with The Sinking of the Titanic, 1912, the biggest canvas in the show and a real disaster. About one hundred figures flounder in a greasy green soup, clinging to lifeboats and to a total misunderstanding of the marine paintings of Manet and Delacroix. It got mixed reviews at the 1913 Berlin Secession, but it was Beckmann’s pride and joy. Elsewhere in the room the shades of Vuillard, van Gogh, Hodler, and Corinth (Beckmann was borrowing right and left) try to swim as far from the wreckage as possible. Only The Street, 1914, oddly absent from the catalogue, offers a hint of greatness to come. Probably painted on the eve of war, it shows the bowler-hatted artist rising from a vertically compressed crowd that includes his wife, his son, and a horse. And the only reason it works is that, in 1928, Beckmann cut it down from a much larger canvas.

The war nearly destroyed Beckmann the man, who saw the worst of it as a volunteer nurse and orderly, but it saved Beckmann the artist, giving focus to his ungainly mix of avant-garde ambition and academic training. “My art can gorge itself here,” he wrote to his wife, Minna, from the front lines in April 1915. By July he’d had something like a nervous breakdown. With a leave of absence in October, he settled in Frankfurt, where he recovered and started a new life away from his family in Berlin.

Now he focused on making prints of war scenes and deformed veterans à la Grosz; the few paintings from this time depict religious subjects and mix the hysterically twisted figures of Grünewald with (to my eye anyway) the rambling structure of Kandinsky’s then-new Compositions. Three of these strange works are included here, but a fourth, Resurrection, 1916, is regrettably absent. True, it wouldn’t have been easy to include such a huge picture (bigger than The Sinking of the Titanic). But it’s intriguing that Beckmann, who seldom had finishing anxiety, kept this incomplete work on view in his studio for years, as if to warn against the pitfalls of the multifigure allegory that would become his grail.

Having got the explicitness of both world war and Christianity out of his system, Beckmann hit his stride with a single work, The Night, 1918–19. A powerfully impacted scene of domestic violence (think A Clockwork Orange), The Night employs a restrained palette and a coarse-grained cubist space whose large fragments create surface tension without sacrificing legibility. Here Beckmann invented several things that stuck: a way of building the composition from the figures themselves, who, like the beams and struts of an old mine, support the rectangle of the canvas; an elusive kind of storytelling that adds up visually but not quite narratively; and a vocabulary of obsessional objects—candles, horns, jutting elbows, soles of feet, theater stages, and mullioned windows, to be joined in later works by cigarettes, newspapers, flying fish, crystal balls, stringed instruments, succulent plants, ladders, swords, and dinner jackets. The problem with hitting one’s stride so early (Beckmann was not yet thirty-five) is that there is nowhere left to go. While Beckmann’s space contracted and expanded after The Night, his compositional and narrative formulas never really changed again.

There was still something missing—something called painting. Up to 1925 Beckmann betrays very little flair for putting paint on canvas. In the first half of the ’20s he uses small, soft brushes, blending and scrubbing his paint so the canvas texture shows through in patches, like bad skin. But in 1926 he revolutionizes his paint handling and as a result “enters for the first time into the actual discourse of the Modern,” as Reinhard Spieler notes in his 1994 monograph. (The first newstyle painting here is a nifty little portrait from ’26 of Beckmann’s second, very young wife, Quappi, in a blue dress, looking, as always—maybe she had a good side—to her left.) The fact that this watershed goes unremarked in both the show and its catalogue is stunning. If MoMA won’t announce the Modern, who will? Spieler writes of an “abstract planarity of color” that gives the paint a “certain life of its own.” To put it simply, Beckmann had taken up big brushes and started whacking at the canvas, pulling light colors over dark and dark over light. Furthermore, he had remarried in 1925, so perhaps an erotic renewal inspired the painterly one. If that sounds like Picasso, it should. But the portrait of Quappi, for all it owes to Picasso’s contemporaneous chunky classicism, has a surface all its own. Even with the big brush, Beckmann kept his paint thin to let undercoats show through, and the result is a paradox of rough-hewn facture and careful layering—a tough, carved look and an inner light at the same time.

Beckmann remained a modeler at heart, in love with the play of light and dark, which he endowed with ethical meaning. “All these things come to me in black and white like virtue and crime,” he wrote in 1938. “But I cannot help realizing both because only in the two . . . can I see God as a unity.” And by “God,” Beckmann meant artists, above all himself. In 1927’s Self-Portrait in Tuxedo, black and white mix electrically on his triangular shirtfront, which in turn serves as a plinth for a heroic head lit from one side by direct light and from the other by reflected light. It’s a breathtaking demonstration of how flat, jagged shadow, properly seen, can make the world go round. And it plays to Beckmann’s strength. He was a portrait painter; his bodies are boneless puppets and his faces and hands exquisite.

For my money, this kind of painting is Beckmann’s great achievement. The show includes a number of gems from this period, but I kept thinking of the absences, too, like Large Still Life with Telescope, 1927—a wild synthesis of Surrealism, Léger, and Matisse done up in a dissonance of orange and yellow. Beckmann considered color secondary to light and dark, and maybe for that reason he felt free to play with it like nobody else—as in The Harbor of Genoa (also 1927), which is, happily, included. Here Beckmann returned to the problem of sea green and got it glaringly right.

The year 1933 brought another turning point. Immediately targeted by the Nazis, Beckmann was dismissed from his Frankfurt teaching post. He moved to Berlin, and, as if reflecting his “inner emigration,” the paintings become urgent and packed. So begins the long era of the triptychs, those impossibly ambitious modern mythic narratives. Here I’m glad Mr. Storr was selective, including only four of Beckmann’s nine. Departure (started in Frankfurt in 1932 and completed in Berlin) is first and best, largely for its hallucinatory middle panel. Actors, 1941–42, is second-best, but it looks stiff by comparison, more medieval miracle play than Surrealist vision. Generally more powerful are the single paintings of triptych ambition, like Death, 1938, which features an upside-down male chorus line and a hairy horn-blowing angel with an erection. (Don’t miss William Kentridge’s appreciation of it in the catalogue.)

When, in 1937, he was made a star of the “Degenerate Art” exhibition, Beckmann and Quappi fled to Amsterdam, and he fled into his work. The high point in this part of the show comes early, with the moody, late-Titianesque Self-Portrait with Horn, 1938, in which Beckmann squints toward the apocalypse, and, facing it, the arch Self-Portrait in Tails, 1937, which sets his matte black tux against a Kirchneresque flurry of green and blue boas and orange wallpaper: Ah, for the Berlin of the old days!

When Beckmann finally made it to the US in 1947, accepting a teaching job at Washington University Art School in Saint Louis, his art strained and fell apart. His colors got more colorful, his black outlines blacker, his arabesques arabesquier (late Matisse is lurking). He started to texture his color areas, creating an unhappy effect of woodblock or of Bernard Buffet. Beckmann’s health was failing, but I prefer to blame America, especially New York, where he moved in 1949 to live out the last year and a half of his life. Unlike Mondrian, who really loved popular culture and experienced a late rebirth in Manhattan, Beckmann was an ambivalent slummer in nightclubs, an evangelist against movies and newspapers. I think the pop surfeit of the city made him soulsick. Or perhaps he couldn’t deal with a cityscape even denser than his paintings. Maybe the lions were too loud. In any case, Beckmann had predicted America’s effect on him. “It will be your ruin,” he wrote in 1947 before sailing. His Falling Man of 1950 is a sad end to the show, a stiff Icarus of the skyscrapers.

Harry Cooper is curator of modern art at the Fogg Art Museum, Harvard University.