But Michael Watson, the executive director of the American College of Medical Genetics, said medicine was already “rapidly moving” toward genetic screening in healthy patients, though there are “still gaps in our system to be able to do that effectively.”

Patients must have good counseling about the potential benefits and drawbacks of testing, and how to evaluate risks that are based on percentages, experts said. Many expressed concern about the costs and the potential harm of the tests, including psychological effects, stigma and discrimination.

Dr. King estimated that the first round of universal screening of all women 30 and older would identify 250,000 to 400,000 American women with harmful mutations in BRCA1 or a second gene, BRCA2.

Critics may object that “women aren’t ready for this,” she said. But she argued: “Why should women be protected from information that will empower them and allow them to control their lives? We don’t need that kind of protection.”

She added, though, that women should not be told about other rare mutations whose significance is unknown.

Dr. King became interested in genetics while doing graduate work in statistics at the University of California, Berkeley, in the late 1960s, She took a genetics course and realized that mathematics held a key to solving a number of biological puzzles. In 1974, when few scientists believed that inherited breast cancer could be linked to a single mutated gene, and years before other scientists developed high-speed automated techniques to analyze the molecular sequences now used to identify such mutations, Dr. King relied on her mathematical knowledge to hunt for a hypothetical breast cancer gene.

She analyzed data from more than 1,500 families in which women received new diagnoses of breast cancer at 55 or younger. She concluded that 4 percent of the families carried a single mutant gene that predisposes women and men to the cancer even without environmental exposures or lifestyle risk factors.