Alice Neel was born with the century in 1900. Her mother didn’t encourage her in a career because she was a girl. Nevetheless, Neel knew what she wanted—to paint—and she went for it. Even when she had to be hospitalized for a nervous breakdown—in 1930, her husband took their small daughter and left for Cuba—the doctors went against the trend and let her draw and paint during her stay. Now, almost 40 years after her death in 1984, Barbican is presenting Neel’s largest U.K. retrospective yet. —Jensen Davis