She embarked on weeks of intensive study, a process little different, she later said, from preparing to write a doctoral dissertation. She made her first appearance on the show in late 1955, returning week after week until she had won the top prize, $64,000 — only the second person, and the first woman, to do so. She later won the same amount, also for boxing knowledge, on a spinoff show, “The $64,000 Challenge.”

In the late 1950s, amid the quiz-show scandals (which included revelations that contestants on some shows, “The $64,000 Question” among them, had been fed correct answers), Dr. Brothers was called before a grand jury. In an exercise that was curiously reminiscent of her appearances on the shows, she was peppered with arcane boxing questions to test her authentic knowledge of the subject. She passed handily, and no taint of the scandal attached to her.

In 1956, as a result of her performance on “The $64,000 Question,” Dr. Brothers was invited to be a commentator on “Sports Showcase,” a television show on Channel 13 in New York, which had not yet become a noncommercial station. One show led to another, and before the decade was out she was a television star.

If, in later, years, Dr. Brothers’s public image had acquired the faint aura of camp, it was leavened by her obvious awareness of that fact — and her corresponding ability to laugh at herself in public. (Who without such self-knowledge would have agreed, as she did, to appear on both “The David Frost Show” and “The $1.98 Beauty Show,” a late-’70s Chuck Barris game show-cum-parody?)

But for the most part, Dr. Brothers displayed a far more serious side: More than once, she dissuaded suicidal callers to her radio show from ending their lives, keeping them on the line with encouraging talk until their phone numbers could be traced and help dispatched.

In her book “Widowed” (1990), she wrote candidly of her own suicidal despair after her husband’s death from cancer, and her eventual resolve to go on with her life.