Time is on his side Alex Katz, pre-eminent painter of modern life, challenges the camera by showing painting's ability to freeze the moment "Eleuthera" (1984) American painting is about surface, European painting is about depth. Pioneering postwar figures - Pollock and Warhol, Bacon and Freud - confirmed the truth of that cliché. But the two most interesting American painters of the end of the 20th century, who survived into the 21st to make radical, exhilarating late work, each built a unique oeuvre by collapsing that difference. Both Cy Twombly, who died last year aged 83, and 84-year-old Alex Katz, whose new show at Tate St Ives in south-west England includes daring, monumental paintings made between 2007 and 2011, combine the language of American abstraction with a European inflection: in Twombly's case the influence of history, myth, lyric poetry, in Katz's the impulse of plein air painting of light and sea, and an engagement with society at play, alluding to Monet, Bonnard and Matisse. "Black Hat (Bettina) " (2010) Superbly installed in bright, sea-facing galleries, Alex Katz: Give Me Tomorrow is this summer's most optimistic, pleasure-charged UK exhibition. For half a century, Katz has delighted audiences with his consistent, lucid, condensed depictions of beautiful people and beautiful places: from "Ives Field" (1956), a near-monochrome in brilliant orange that owes as much to Rothko as to the landscape tradition, to the parade of stylised, long-limbed bathers in DayGlo swim-caps, constructed like a classical frieze in "Eleuthera" (1984) and the magnificently simplified "Black Hat (Bettina) " (2010) - scarlet lips; cool shades; the slight incline of a head under a wide-brimmed hat; a brilliant, sunburst-yellow ground. Defiantly flat, closely cropped, hard-edged, precisely deliberated, each image has just enough depth to insist - with a touch of irony - on the illusion of reality. Each, too, is in dialogue with various epochs and media of art history, including the commercial, but Katz's concern from the start was to be a painter of modern life. That was an audacious, ill-received idea in the 1950s; Katz stuck to it doggedly: "What I wanted to do felt right. There wasn't a reason in the world why there couldn't be a contemporary representational painting. It just seemed to me that there should be a way to see a representational world in our time. An array of 1950s-1960s portraits of Ada, his wife and lifelong muse, demonstrates how rapidly, wittily and inventively Katz evolved his depictive vocabulary. "Ada on Red Diamond" riffs on abstract geometric forms. "Red Blouse (Big Ada) " anticipates, at bold scale, pop art's clean lines and graphic stylisation. On a saturated fiery red surface, "Reclining Bather" casts Ada as an odalisque updated, with her dark bob and lemon swimsuit, to the 1960s. Nonchalant, inscrutable, she is portrayed six times in varying cocktail-party poses in "The Black Dress," with an economy of gesture and detail, as well as a joke on the idea of identikit series, that makes the work an emblem of the times. Katz has likened Ada to Dora Maar, Picasso's lover, in her malleability. Her high cheekbones, Roman nose and expression of inner composure lend her the air of a goddess, yet it is really the detachment and force of Katz's formal compositions that make her an icon. In "Beach" (1965), she is a model from the milieu of advertising, her profile enlarged and turned horizontal, blending with a clichéd idyll of sand and sunbathers. This was a breakthrough piece, where Katz appropriated devices from film and commercial photography into a painterly idiom; he wanted, he said, "to make paintings you could hang up in Times Square." Yet, unlike pop artists, he was never interested in redeploying media symbols or in the commodification of culture: it is hard to think of a less political painter. Nor did he overtly, like his contemporaries Warhol or Gerhard Richter, challenge photography by co-opting its mechanised repetitions or aestheticising its blur. Instead, he challenged the camera by demonstrating painting's ability to freeze the moment, and remain fresh and direct, in contrast to the nostalgic datedness of a photograph. Time is his greatest theme. That is clear enough in the five-metre seascape called "4.30pm": with spare marks, a simplified construction and a reduced palette - just three bands of colour and a few tiny white block-like boats - Katz fixes the eternity of an instant of clear, late afternoon light on the Maine coast. The abstracting tendency is emphasised by the work's juxtaposition here with two other marines that are almost pure monochromes: "Beige Ocean," whose lively strokes suggest dynamic, breaking waves, and the quieter "Green Reflections 3," where the white lights sparkling on the water's surface recall Monet's water lilies. But time is as pertinently the subject of the large-scale Manet-like society beach scenes of the 1970s. "Isleboro Ferry Slip" (1975), depicting Katz's 15-year-old son Vincent walking on a jetty in Maine, also captures that late afternoon crystalline light on a deep blue sea. The presence of Vincent - a long-haired, dreamy, poignant, 1970s adolescent pin-up calling to mind Tadzio in Visconti's 1971 film Death in Venice - makes the work a meditation on beauty, youth, time passing yet preserved for ever through the vividness of paint, the fall of light. "Round Hill" (1977) "It's the instantaneous light, if you get it right then you get it in the total present tense, that's what you're going for, that's eternity," Katz says. In "Round Hill" (1977), the light is a harsh glare, enveloping five languid bathers in the Caribbean in a self-contained, enclosed moment of time and place. The figure in the foreground turns away from us, so we see only the back of his head; the others are self-absorbed, expressions hidden behind sunglasses. One is lost in reading - Shakespeare's Troilus and Cressida. Why that play? Perhaps because it is so cynical about human relationships - the reference underlines the unease, the feeling of dislocation, between Katz's figures. More likely, though, it is because Troilus contains Ulysses" famous speech, "Time hath my lord a wallet at his back," about time and fashion. "For time is like a fashionable host/ That slightly shakes his parting guest by the hand,/ And with his arm outstretch'd, as he would fly,/ Grasps in the comer," Ulysses tells the sulking Achilles. But Katz seeks to defy time by fashion: Ada's 1960s little black dress; Vincent's 1970s big coiffed hair rippling in the wind; the 21st-century extravagant spectacle of Bettina's floppy hat. I think style is the content of my painting, and style belongs to fashion. Fashion is the immediate present and that's what I'm really after ... to maintain that present tense feeling," Katz says. In an overly conceptual era, he has become our pre-eminent painter of modern life by acknowledging that surface has depths, and "painting must try to get to the most mysterious thing, which is appearance." "Alex Katz: Give Me Tomorrow," Tate St Ives to September 23, www.tate.org.uk , then Turner Contemporary, Margate, from October