The only thing missing from Martin Gottfried's sturdy biography of Danny Kaye is its subject. He's there somewhere, but always blurred and elusive. In Nobody's Fool: The Lives of Danny Kaye, Gottfried repeatedly tells us that as a performer, Kaye, who died in 1987 at age 74, was indefinable. In private he was, well, intensely private. His stage performances, which by all accounts surpassed his familiar movie roles (The Secret Life of Walter Mitty and Hans Christian Andersen, among others) and galvanized international audiences during the '40s and '50s, were exercises in comic, vocal, balletic virtuosity, a series of whimsical masks. Behind the masks, the man who evolved out of David Daniel Kaminski, a Brooklyn childhood, and a Catskills resort apprenticeship could be charming, but also abruptly cold, tenaciously depressed, or simply opaque. Kaye's ''black moods'' extended, Gottfried notes, even to innocent autograph-seekers. The author tells of a time when, at the height of his career, Kaye was asked by a fan to sign his name: ''Kaye...snatched the paper out of the fellow's hand. Then, turning scarlet with rage, he rose, rolled the paper into a ball, and threw it at the man.''
Gottfried finds no evidence to back up the rumor that Kaye was secretly gay and had an affair with Laurence Olivier (a theory that's elaborated in Donald Spoto's biography of Olivier). Kaye did have a wrenching affair with Eve Arden, and several flirtations that distracted him from a troubled marriage to Sylvia Fine, who helped to invent his stage persona. But sex seemed to matter less to him than work and his three Walter Mittyish private passions: flying his own plane, watching operations in hospitals, and cooking gourmet Chinese dinners. If there was an essential Danny Kaye, he remains, in Gottfried's phrase, an ''eternal question mark.'' B