At a time when America is struggling in its relationship with Europe, a new show at the Portland Museum of Art offers a reminder that dialogue, whether in art or politics, can increase understanding. The underlying thesis of “Monet to Matisse, Homer to Hartley: American Masters and Their European Muses” is that such conversations also can increase beauty. Given the caliber of the works in this show, which runs through Oct. 17, it’s a convincing, if already well-known, position.

Consider the all-star cast. Here’s a partial listing: Bellows, Picasso, Braque, Bouguereau, Calder, Cassatt, Cezanne, Dali, Degas, Homer, Magritte, Leger, Picabia, Motherwell, Steichen, Toulouse-Lautrec, Renoir, Pollock and Whistler. Even Gertrude Stein could not convene that many artists in one room, much less in a room due north of Boston.

With her famous salon on Rue de Fleurus in Paris, Stein is a well-known historical host to a mix of American and European artists. She provided a kind of intellectual dating service, one that encouraged and measurably altered the art world. Look back to Europe, she seemed to say to the varied artists who passed through her door, so that you may look forward as Americans. Her advice was heeded in a big way.

Though she is not referred to in the literature of this show, Stein, like the photographer Alfred Stieglitz, looms in the background of this collection. Stieglitz, however, figures prominently because the exhibitions at his “291” Gallery in New York City and his encouragement and largesse to many American artists helped spearhead the 20th century exchanges between both sides of the Atlantic. Some of the artists in this show arrived on the American scene through his gallery.

Carrie Haslett Bodzioney, curator for this show, retroactively joins Stein and Stieglitz to assert the well-documented exchange between the two continents by placing formally related works of art side by side. Thus, Picasso’s “Femme lisant” of 1935 introduces Will Barnet’s “Awakening” of 1949. Monet’s “The Custom House” of 1882 illuminates Frederick Childe Hassam’s “Isles of Shoals” in 1915. Braque and Max Weber, Fernand Leger and Stuart Davis, Degas and Cassatt, Renoir and Theodore Robinson seem to sit down to tea with each other here.

Of course, Cezanne speaks to the largest group, especially the Maine painters John Marin, Marsden Hartley and Marquerite Zorach. Cezanne’s deep interest in rich colors and thick brush strokes, as well as his thematic appreciation of local life, influenced each of these painters, and the parallels, if not homages, emerge in this show. Was there something inherently simpatico between Maine and Europe, something about the landscape and light? It’s possible to answer yes after seeing the way these works mingle and mesh in topic and technique.

In one of his scholarly essays, referenced in the exhibition’s fine catalog, Hamilton Easter Field, the critic and teacher who organized the Ogunquit School of Painting and Sculpture early in the 20th century, wrote: “There’s as much right here in Maine as there is in Monet’s Normandy.” A truism, after all, for which all lovers of American art are grateful.

In one of the more revealing pairings, Renoir’s 1869 portrait “Woman in a Chantilly Lace Blouse” hangs next to George Bellows’ 1919 “Emma in the Black Print.” No two pieces in the show create quite as much synergy and tension. Renoir’s is richly patterned, with his subject’s lace dress finely depicted in the foreground and a lace tablecloth and dining scene in the background. The smiling woman in the portrait is old Europe in all its elegance, certainty and pride.

While the lace of the dress in Bellows’ portrait is every bit as ornate, Emma, its wearer, is surrounded by an eerie darkness. The white light on her face and chest, and the shadows that surround her might have come from another master, such as Vermeer. But in fact, the qualities of this portrait say something about an American identity, indebted to but breaking from earlier traditions. Emma is not matronly like Renoir’s subject. She does not smile. Instead, Bellows, another painter drawn to Maine, endows her with an early “rebel without a cause” detachment, an aloof self-absorption.

In subject matter more than style, Frederic Bazille’s “Summer Scene” (1869) and Thomas Eakins’ “Swimming” (1885) require some explication, which is given in the catalog, but only suggested by the museum’s gallery notes. Both works depict nude men, standard topics for the Greeks, but considerably less common than female nudes between 1870 and 1950, the time period this show spans. Eakins was dismissed from his teaching post for the homoeroticism of this work (as well as for his questionable teaching tactics in figure drawing classes). The oil painting, which depicts six nude men (including Eakins) and no full frontals, is a pastoral story of male frolic, with elegant forms and careful, if not caring, details of nature. Bazille’s work, with its bold colors and playful males, is more energetic though less edenic.

For all its instructive ideals, the side-by-side approach may be overly intrusive for viewers who like to make their own connections. What’s extraordinary by the end is the number of works worth pausing over. At its best, any art exhibition does something to stretch the imagination, form a new opinion or amend an old one. The Portland show offers several opportunities but its central one has been a bedrock of art history classes: America and Europe, as artistic centers, have been united, provoked and made more beautiful by each other for years.

The Portland Museum of Art will present “Monet to Matisse, Homer to Hartley: American Masters and Their European Muses” through Oct. 17. For information, call 775-6148 or visit www.portlandmuseumof art.org. Alicia Anstead can be reached at 990-8266 and aanstead@bangordailynews.net.