What is beauty?

A mushy question, that one. It has too many answers.

Small is beautiful. Black is beautiful. Sunsets, Cindy Crawford and the Pythagorean theorem are beautiful as well.

Defining it is difficult, perhaps impossible, yet beauty is a real force that stabs us when we see it. In one way or another, artists and their audiences--and the public institutions that introduce them to each other--pursue beauty all the time.

But what is it? "Regarding Beauty: A View of the Late 20th Century," which opens the fall season at the Hirshhorn Museum and Sculpture Garden, retrieves that knotty question and addresses it head-on.

Sex, thought D.H. Lawrence, was beauty's key component, and all the nudes in art--from the 30,000-year-old Venuses of the Ice Age to the present--contribute to his argument. Numbers have their own chillier sort of beauty. When the poet Edna St. Vincent Millay wrote that "Euclid alone has looked on beauty bare," she spoke of mathematics, not of unclothed women, though she tipped her hat to Lawrence in the last word of her line.

Curvaceous bodies are beautiful; so is linear geometry. In 18th-century London, the artist William Hogarth combined these two contentions when he decided that The Beautiful had the S-curve at its core.

He was sure he knew what beauty was. The artists in the Hirshhorn show--there are 36 in all, most of them still living--tend not to be so sure.

Most of them believe, as Charles Baudelaire insisted 150 years ago, that what humans see as beautiful is not permanent and ageless, but changes with the times. Can a gross-out be thought beautiful? Can a disordered mess? Many modern artists have happily rejected traditional views of beauty, agreeing that to label something beautiful is to pretty much condemn it as trivial and false.

The painter Barnett Newman was agreeing with that point of view when he wrote in 1948 that "the impulse of modern art is the desire to destroy beauty." Whether modern artists have destroyed beauty or succumbed to it, or both, ought to be apparent when "Regarding Beauty" opens Oct. 7.

The collector Duncan Phillips did not seek the beautiful in either human bodies or Euclidean geometries. What moved him most was color. To commemorate his vision, the Phillips Collection will be offering "Renoir to Rothko: The Eye of Duncan Phillips," which opens Sept. 25. The exhibition, which the Phillips calls "the most comprehensive and ambitious" in its history, will fill the whole museum, which is being extensively refurbished for the 350-object show.

Another art collector crucial to this city also will be honored with an exhibition of his gifts. "An Enduring Legacy: Masterpieces From the Collection of Mr. and Mrs. Paul Mellon" opens Nov. 7 at the National Gallery of Art.

Phillips and Mellon both acquired fine examples of 19th-century French art, and both admired the abstractions painted by Mark Rothko. Less familiar forms of beauty, or at least much older ones, will be presented when the National Gallery opens "The Golden Age of Chinese Archaeology: Celebrated Discoveries From the People's Republic of China" on Sept. 19.

Other shows of ancient art will also be on view. "Treasures From the Royal Tombs of Ur" opens at the Arthur M. Sackler Gallery on Oct. 17. "Gold of the Nomads: Scythian Treasures From Ancient Ukraine" goes on view at the Walters Art Gallery in Baltimore on March 3, and "Music in the Age of Confucius," a display of 2,500-year-old Chinese instruments, some of them still playable, opens at the Sackler on April 30. Not so old, but far from new, are the objects to be seen in "Palace of Gold and Light: Treasures From the Topkapi, Istanbul," which opens March 1 at the Corcoran Gallery of Art.

The National Gallery will host two exhibitions of master drawings. The first of these, "The Drawings of Annibale Carracci" (1560-1609), opens Sept. 26. The second, "From Schongauer to Holbein: Master Drawings from Basel and Berlin," which opens Oct. 24, will focus on the art of Northern Europe. So will "Tilman Riemenschneider: Master Sculptor of the Late Middle Ages," a display that brings together more than 50 of his Late Gothic carvings; it opens Oct. 3.

Last season Washington's museums stressed portraits by painters--Chuck Close, John Singer Sargent, Ingres. Most of the portraitists exhibiting this season will be photographers instead.

"A Durable Memento: Portraits by Augustus Washington, African American Daguerreotypist" opens Sept. 24 at the National Portrait Gallery. "Brassai: The Eye of Paris" opens Oct. 17 at the National Gallery; "Women" by Annie Leibovitz goes on view Oct. 27 at the Corcoran Gallery of Art; "Tete a Tete: Portraits by Henri Cartier-Bresson" opens two days later at the Portrait Gallery; "Arnold Newman: Sixty Years" goes on view March 15 at the Corcoran; and "Nadar/Warhol: Paris/New York" opens March 12 at the Baltimore Museum of Art. Additional portrait photographs will be included in "Defining Eye: Women Photographers of the 20th Century," which opens Oct. 7 at the National Museum of Women in the Arts.

African conceptions of beauty, African American conceptions of beauty and the links between them will be explored by a pair of exhibitions. "Wrapped in Pride: Ghanaian Kente and African American Identity," a collaboration among the Smithsonian Institution's National Museum of African Art, the Anacostia Museum and the Center for African American History and Culture, will open Sept. 12. "To Conserve a Legacy: American Art from Historically Black Colleges and Universities" will go on view at the Corcoran on Nov. 19.

Though monographic painting shows will be less numerous this season, a number have been scheduled. These include "Edward Hopper: The Watercolors," opening Oct. 22 at the National Museum of American Art; "Martin Johnson Heade," which goes on view Feb. 13 at the National Gallery; and "Gerrit Dou"--he was Rembrandt's first pupil--which opens at the National Gallery on April 16.

For something completely different, the Hirshhorn will present "Dali's Optical Illusions," a show of his "paranoidal-critical" oils, opening April 19.