THE NICEST show in town, in this season of the flowers, is not hanging in a gallery but blooming in the streets. It will not last.

This spring, too, will pass, and its flowers die; but less transitory blossoms - those pictured by the painters - can be seen here the year round.

Every art museum shows them. The happy ladies lunching in the Renoir at the Phillips wear flowers on their hats. Austere "Miss Van Buren," in Thomas Eakins' portrait at the same museum, has blossoms on their dress. When Jimmy Carter recently visited the Corcoran, Severin Roesen's flower-laden still life caught the presidential eye.

There are blossoms in the pictures of Andy Warhol, Ellsworth Kelly and Georgia O'Keeffe. Even abstract painters paint them. The Washington color paintings by the late Morris Louis hanging at the Hirshhorn are called "florals" for good reason. The temple columns of the early Greeks were carved to look like flowers. Matisse cut his flat, bright blooms out of colored paper. Many masters whose works hang at the National Gallery of Art - Raphael, Rembrandt, Durer, Manet and Monet, Van Gogh and Gauguin - show us flowers in their paintings. Flowers blossom everywhere throughout Western art.

And not just Western art. The Oriental masters whose works are at the Freer put flowers of all sorts on their bowls, their screens and scrolls. There are blossoms in the Persian rugs at the Textile Museum. There were bouquets in the Tut show. "The Giver of Life writes with flowers," says the Aztec poem.

Flowers are a staple of high symbolic speech - and of simple-minded decoration. In the dime stores of my youth you could hardly buy a drinking glass that did not have flowers on it. We exchange flowers when we marry, when we worship, when we mourn.

And we are not the first. Next time you see blossoms on a summer dress or teapot, in a painting or a garden, consider for a moment this old, this very old, item from art history: Man was using flowers before man was modern man.

Sixty thousand years ago people went collecting bouquets on the hillside near the cave called Shanidar in what is now Iraq. The inhabitants of Shanidar were not just like us; they had different bodies, perhaps different brains. They were Neanderthals - extinct now. Some 30,000 years would pass before man would begin painting on the walls of caves - yet we know that those Neanderthals went out to gather flowers for presentation to their dead.

A cache of partial skeletons, all of them pre-human, has been unearthed in Shanidar by excavators digging deep into the cave. Since those bones were buried there, tons of dust have settled, and the scientists who dug them up found the ancient burial more than 20 feet beneath the level of the floor.

There are two good ways of measuring the age of such remains: carbon-14 dating, and pollen counting. Both were used at Shanidar.

Wild flowers grew there ice ages ago. The blooms themselves have vanished, but their pollen grains survive. By looking at a pollen grain (a microscope is required), scientists can tell what sort of plant it came from; and by statiscal analysis of pollen distribution, one can measure time. As the glaciers of the ice ages expanded and retreated, the pollen-generating plants growing in Iraq responded to the slow changes in the climate. Cold weather species prospered there awhile; later they retreated, leaving, as they did so, a changing microscophic record in the dust that filled the cave.

In a recent Science Magazine, Ralph S. Solecki, a Columbia University anthropologist, reported he had scraped small soil samples from the bones of Shanidar, had sent the samples off to Paris and had asked A. Leroi-Gourhan there to analyze their pollen grains and thereby gauge their age.

Such pollen counts are routine now; but "much to her surprise," Leroi-Gourhan found that those from Shanidar confounded her predictions. She eventually discovered why. Eight different sorts of flowers - blue bonnets, daisies, thistles, varrow, mallow, ragwort and hollyhocks, among them - had been put into the grave.

Seven of the flowers from the Shanidar flower burial are still picked in Iraq today for use as herbal medicines. One of them, yarrow, derives its English name from the Anglo-Saxon word for "healer." Another, known as "groundsel," means "swallower of pus." The mallow named "Althaea," which is Greek for "healer," also left its pollen on the bones of Shanidar. "One thing is certain," writes Solecki. "These flower pollens were not accidentally introduced into the cave, and hence must represent bouquets . . . Some person or persons once ranged the mountainside, collecting those flowers one by one."

That ancient flower burial suggests to Solecki that Neanderthals had "soul."

Flowers can be medicine (even sick cats comprehend that), but most city dwellers buying flowers at the corner know nothing of their propereties, myths or magic names. Much flower lore is lost, now, but the flower - as symbol - never seems to die.

Morris Louis, Leonardo and the Neanderthals of Shanidar did not all think the same thoughts. But while the motives that move painters are infinitely varied, their images remain peculiarly the same. For that which pleases us in life - and that which pleases us in art - are not unrelated.

With inexplicable consensus, we recognize the lovely as soon as we detect it - in a melody, a flavor, a fragrance or a face. When small children learn to talk, their societies determine whether they speak Japanese or French, but teachers do not give the young vocal cords or brains. Our capacity for speech - or for responding to the beautiful - is not gained anew with each generation. It seems, in part, built-in.

You need not be a perfumer to know that flowers smell good. You need not be a botanist to know that flowers matter. T.S. Eliot writes of "music heard so deeply that it is not heard at all, but you are the music while the music lasts." The joy evoked by flowers seems similar visceral. Flowers - and those friends of flowers, butterflies and birds - seem to draw from each of us a physical response.

Enjoy them while they're here. Fragility and hope, the certainty of death, innocence and healing, sexual propogation, love and resurrection - their messages are variable, but flowers area constant in the history of art.