By all accounts, William Steig (1907–2003) was in person the same contradictory individual we sensed for decades in his New Yorker cartoons and children’s books. He was wise but naïve, gruff but gentle, doubtful yet essentially optimistic. This Sunday, the Jewish Museum celebrates the centennial of Steig’s birth with an exhibition of some 200 works showing his astonishing diversity as a cartoonist, an illustrator, a writer, and even a sculptor. Although small in dimensions — as required for life-size publication — his drawings radiate an expansive curiosity about the world, an almost childlike delight further emphasized by the installation’s brightly colored walls, flower-painted sofas, and reading nook with beanbag chairs. Steig’s most memorable images, however, also show a sober side: a wistful bittersweetness about humankind’s lonely travails.

From his start at the New York Times in 1930, Steig brought to that paper’s pages the rough-and-tumble attitude of his Jewish working-class upbringing. The magazine’s writers had traditionally provided the cartoonists’ punch lines, but Steig conceived, drew, and captioned his own work. He apparently later discarded most of his earliest cartoons, but the upcoming exhibition includes a collaboration with cartoonist Helen Hokinson from 1935, which bears the caption, “Pardon me, young man, are you a member of this Study Group?” It depicts a prim museum doyen surrounded by well-dressed children, and — Steig’s contribution — a rumpled, scowling youth.

Steig’s early drawings related the city’s boisterous absurdities with the efficient, atmospheric ink washes familiar to any older New Yorker reader. “What a beautiful morning!” (1950) features a potbellied man, beaming in his underwear at a dingy apartment’s window. Nearly a dozen cartoons from the long-running “Small Fry” and “Dreams of Glory” series touch poignantly upon the escapades and dreams of youth. With wonderful understatement, a 1953 drawing relates the various pains of a minor accident: A boy lies crying next to his toppled bike, while five smaller kids silently watch, mindful of the boy’s wounded pride. Steig trusts us to fill in the raft of unspoken feelings.

Oddly enough, Steig never considered himself a natural illustrator. The exhibition includes a video, in which the artist describes his passion for “free drawing” — working without preconditions. From the late 1930s through the early 1950s, Steig produced “symbolic” drawings, which editor Harold Ross deemed inappropriate for the New Yorker. They strike a decidedly edgier, idiosyncratic note, reflecting his marital and medical difficulties at the time, as well as a budding enthusiasm for the peculiar theories of the psychoanalyst Wilhelm Reich. A handless man stares at the stumps of his arms in “Loss of a memory” (1939). “God is watching” (1950) features a vacant-eyed child, edging warily along a sidewalk. More appealing are the Picasso-esque faces, executed with the crisp linear verve, if not quite the plastic vigor, of the Cubist master. The folded mass of popping eyes, bushy eyebrows, and curling lips in “Kibitzer” (1945) becomes the perfect expression of heedless intrusion.

Adventures of a more conventional kind made their way — hilariously — into the New Yorker. In “Are we early?” (1956), a visiting couple stands in a doorway, perplexed, while the husband and wife wrestle furiously on the floor. In an untitled cartoon from 1976, another pair has resolved their differences, at least momentarily: The burly wife, with a formidable glare, wheels her cigar-chomping husband down the street in a baby carriage.

Steig’s drawing style evolved over the decades. By the 1960s, he had dispensed with preliminary sketches and adopted a looser, wirier line. In the 1970s, a new and happier marriage led Steig to more lighthearted imagery. An untitled drawing from 1971 shows newlyweds embracing rapturously in their little cabin, although the yard brims with hints of intimacy’s price: a caged bird, a chained dog, and even a shackled flower. In “News” (1982), a couple huddles to read a newspaper — and huddle they must, because their sanctuary is a small nest in a tree’s upper branches.

The exhibition includes much more: drawings for New Yorker covers in full, spirited color; three engrossing sculptures produced in the mid-1930s. And then there are the children’s books, a venture first undertaken by Steig in his early 60s. He ended up producing 39 of them, including the Caldecott Medal-winning “Sylvester and the Magic Pebble” and, of course, “Shrek!” The exhibition includes several dozen preliminary sketches and final drawings for many of the books, which can be perused (in their commercially printed form) in the exhibition’s reading room.

Fans of Steig’s books know that they resonate with the same offbeat observations of his cartoons. Their scenarios, however, more often have practical, moral resolutions. In “Doctor De Soto” (1982), a dentist mouse considers treating a fox waiting outside with a painful toothache. The dentist confers with his wife: Should we buzz him in? Is it right to deny him treatment just because he might eat us? Of course, together they outwit the fox while simultaneously rendering their professional services.

A mock-up for the book outlining its plot, along with a number of the original drawings, is on view in one of the galleries. Like so much else in the exhibition, these drawings speak of an avid curiosity and affection for the whole of life, with a good dose of skepticism about its particulars.

Until March 16 (1109 Fifth Ave. at 92nd Street, 212-423-3200).