WASHINGTON — It's said that there are many types of intelligence, other than the bookish kind.

Wayne Gretzky had what you could call athletic intelligence. He had a genius for understanding how bodies and objects move through space.

An investor such as Warren Buffett has a brain that does the same with dollars.

The great American painter Jasper Johns had what you could call pictorial intelligence — a rare genius for grasping how pictures work, and for doing things with them that no one else had done before.

"Jasper Johns: An Allegory of Painting, 1955-1965," a major new exhibition at the National Gallery of Art through April 29, makes it clear that Johns has an artistic mind up there with only a few other geniuses in Western art. If Titian is the Galileo of painting, and Cezanne its Darwin, then Johns is, if not Einstein (that would have to be Picasso) then at the very least its Francis Crick.

Coming out of nowhere — Johns had barely practiced as an artist when he made his first crucial works in 1954 — the 24-year-old established the DNA that a great deal of later art is built on.

It's almost as though Johns' work rethought pictures from scratch, questioning everything we think we know about them.

Can a picture represent a thing — a flag, a target — and be a concrete example of that thing at the same time?

For a picture to be about color, one of art's classic aims, do its colors have to be in color, or can they be replaced by the words for them, rendered in shades of gray? Or maybe, if you want to go for real color, you should go all the way and include it in your picture only as plain, foursquare blocks of red, blue and yellow, floating among all the other things your picture tries to show. And if you do that, are you working in abstraction — or are you in fact making a picture that points beyond itself to things out in the world, such as color charts and paint chips?

Say you do take that radical step away from the safety of abstraction. What, then, are all the different ways a picture can evoke the world beyond its edges, without ever rendering an image in the conventional sense?

Johns covered objects in paint — a skull, his hands, the side of a house-painter's brush — then pushed them up against his canvases. He heated the base of an erotic sculpture by Marcel Duchamp and used it to melt a cryptic shape into a wax-covered canvas. He actually bit into another wax surface, leaving a "picture" of his scraping teeth. He covered his face with oil, rolled it like a cylinder-seal across some paper, then lightly rubbed the sheet with charcoal to reveal the strange imprint.

Or say you stick with abstraction for a moment. (Johns is all about assembled moments and sudden changes of mind.) Can an abstract artist leave a hand-painted trace — as expressionist painters such as Jackson Pollock and Willem de Kooning had been so keen to do, in the moment just before Johns — without it pointing back to him and his big artistic ego? You could, maybe, use a mechanical device to make your mark — a stick pushed around a pivot, in Johns' case, used to smear paint in a circle — instead of your own brush-wielding hands. Or you could splash paint on with a brush, but in such a random way that it can't speak a word about the kind of man you are.

Maybe it's a good thing that Johns had so little background in fine art — what he learned at college in South Carolina, two semesters at Parsons School of Design in New York, one whole day at Hunter College in the Bronx.

He had no investment in old ways of doing things to keep him from discovering new ones.

Take Johns' famous target pictures. The picture is clearly of something — the target that you see in it — but it is also the thing itself, right in front of you.

A modest work on paper shows a classic Johns target set askew inside a larger field of mottled orange paint.

Here, because of the most subtle shift in composition, we're back to the Old Master model for artmaking: The picture isn't simply the target itself, filling Johns' surface from edge to edge, as almost all his other targets do.

Now it's truly a picture of a target once again against some particular background, as it might appear at one particular place and time.