Gustav Klimt's 1907 portrait of Adele Bloch-Bauer...is now aptly installed like a trophy head above the mantelpiece in Mr. Lauder’s Neue Galerie for German and Austrian art. Jon Stewart was joking on “The Daily Show” the other night about what that little green patch in the corner of the picture must be worth. You can’t buy publicity like that.Well, maybe Mr. Lauder could. The portrait cost him the equivalent of the combined gross domestic products of Kiribati and São Tomé and Principe. It’s a large, hallucinatory square of spectacular gold filigree. Adele looks almost as if she has inserted her head into one of those carnival cutouts, her thin face partly cast in shadow, obscured by the glare. Her lips are parted, eyelids heavy, cheeks pink. The eyes are two big, brown almonds. The overstuffed headrest of her chair makes a halo of beetle-wing delicacy. Monogrammed, her gown undulates with gently raised letters. And that green patch Mr. Stewart likes so much is a glimpse of emerald floor, thrusting the picture into depth. The coup de grâce is a spider web of hands, a classic Klimt touch of decadence, clasped so that one wrist bends at a rakish right angle.She’s half queen, half Vegas showgirl. The perfect New Yorker. It would be churlish of art lovers in the city not to thank Mr. Lauder for the portrait that for decades was a Viennese civic symbol. Its passage, there to here, is quite a saga. Ferdinand Bloch-Bauer, a wealthy Jewish industrialist, commissioned Klimt to paint his wife, twice. Klimt obliged, so the story goes, by making her his mistress. Public-spirited, she willed her art to Austria. Then she died of meningitis, at 43, in 1925. Ferdinand had to flee the Nazis 13 years later. They seized the family’s paintings; the family castle in Bohemia went to Reinhard Heydrich, the murderer of Wannsee; the family home in Vienna went to the Austrian national railway, which shipped Jews to the camps; and the diamond choker that Adele is wearing in the portrait went to Hermann Goering for his wife. Hitler apparently balked at acquiring the family porcelain. Too expensive, he said. And then, for more than 60 years, the Austrian government refused to return the paintings to the family, although Ferdinand had redone Adele’s will. Led by his niece, Maria Altmann, now 90 and living in Los Angeles, the Bloch-Bauer heirs finally won a court battle in January. In a nod to the city where she settled (her lawyer, by the way, is the grandson of another exile in Hollywood, Arnold Schoenberg), Mrs. Altmann lent the pictures to the Los Angeles County Museum of Art in April. Meanwhile, Mr. Lauder was negotiating the purchase of Adele, and arranging for this show to stop here. It includes the second Adele, painted in 1912. No longer gold and Byzantine with Egyptian flourishes, instead flowery, sketchier and brightly colored, like a Japanese print, she wears a halo made out of the brim of a huge black hat. Her dress is high-collared, not off the shoulder, her body face-forward and erect, a slender, sinuous Coke bottle shape, more chaste than carnal. This older Adele gazes at some spot just over our heads — she’s still regal but less Vegas. More Aubrey Beardsley via Edith Wharton.The other Bloch-Bauer pictures are landscapes; the earliest one, from 1903, of a birch forest, is exquisite: an archetypal Klimt mix of uncanny naturalism and geometric abstraction. Its forest floor makes a mosaic of Pointillist dots, broken up by irregular vertical stripes of perfectly real trees receding into idyllic space. For Klimt, bodies were erotic, nervous subjects, ripe for pornography; landscapes were Edenic. The Bloch-Bauers also acquired a picture he painted of an apple tree and an unfinished jigsaw-puzzle view of houses on the shore of the Attersee, where he spent summer vacations. Neither is great. But like the two Adele portraits, they raise the question whether, had he not died at 55, in 1918, Klimt would have ended up a pure abstractionist like Mondrian. The four pictures are on the market, Mrs. Altmann has said. She and her relatives are cashing in, which is their right. They offered the Austrian government a chance to buy the whole collection for about the money that Mr. Lauder reportedly spent on Adele. The Austrians balked. Too expensive, they said.When the Metropolitan spent $5.5 million on Velazquez’s portrait of Juan de Pareja in 1970, it was a scandal; now it seems cheap for one of the great paintings in the country. The sums that places like the Museum of Modern Art squander on mediocre buildings, which become obsolete the moment they open, are scandalous. The art market operates according to its own logic, which may have nothing to do with the quality of the art. Value is not price — whether the issue is a Klimt, or a ballplayer, or a chief executive paid millions of dollars, who runs his company into the ground. But Oscar Wilde had it right about cynics, price and value. It’s only natural to play the skeptic when the art world is a circus of profligacy, drunk with cash, and when dimwitted speculators make headlines, wasting fortunes on bad art. Who knows what the most money paid in private for a painting really is: maybe $135 million. For that amount, assuming it is what Mr. Lauder paid, his portrait of Adele, a hedonistic masterpiece, will be talked about in terms of how many lives might have been saved or how many lifted from poverty for this sum. As for the border separating public interest from private enterprise, it has never been fixed. The Neue Galerie is Christie’s annex now, exhibiting paintings for sale ($15 general admission, no children under 12 allowed), whose display is also a public service.Someday Adele will be seen for just what she is: beautiful, a gift to the city. And $135 million may even come to look like a bargain. Besides paintings and drawings, the exhibition contains rare vintage documentary material, ranging from letters, photographs, and personal effects, such as the artist’s cufflinks and seal (both designed by the architect Josef Hoffmann), to the only known surviving example of the painting smock that Klimt wore. As a special addition to the exhibition, the Neue Galerie is presenting the re-created interior—based on original floor plans and a 1912 photograph—of the receiving room from Klimt’s studio at Josefstädter Strasse 21, Vienna, which was occupied by the artist from 1892 until the summer of 1912. The display includes the original furnishings designed by Josef Hoffmann, executed by the Wiener Werkstätte. On the lower level of the museum is a display of children’s drawings created by students in Vienna, ages 10 to 14. The drawings are based on the departure from Austria of the Klimt painting Adele Bloch-Bauer I. They are presented at the Neue Galerie under the title “Adele Comes to America.”