In May 1965, two months after the Los Angeles County Museum of Art opened its doors, Yook Young-soo, the wife of Park Chung-hee, president of the Republic of Korea, paid a visit. She was so disappointed with the paltry display of Korean art that she gave the fledgling institution 23 ceramic works. The collection now spans 500 paintings, sculptures, ceramics and textiles, and an 850-piece trove of historic pottery shards. On view now are cutting-edge contemporary artists...