Born to actress Fanny Brice and her second husband, professional gambler Julius W. "Nicky" Arnstein, April 23, 1921, he spent his early years living with his mother and his sister, Frances (later the wife of producer Ray Stark), while their father was in prison on a variety of charges stemming from a history of thefts, swindles, and confidence schemes.
Important influences included then-active artists Henri Matisse and Pablo Picasso (one of whose works Brice acquired at the age of fourteen).
A 1950 L.A. Times review of his solo exhibition at the Frank Perls Gallery (Beverly Hills) praises the still lifes "that stress the geometrical aspects of common objects."
He is particularly remembered for the "classic modernism" of his late work, in which masses reminiscent of ancient ruins figure prominently, inspired in part by an important trip to Greece in 1970.
From 1948 until 1952, he taught at the Jepson Art Institute in Los Angeles, and the following year began his long tenure at UCLA, continuing until his retirement in 1991, where he was a beloved teacher, and mentored generations of artists, for whom he "offered a connection to European Modernism."