Alfred G. Knudson Jr., a medical researcher who helped decode a mystery of cancer — using genetics, mathematics and intuition to explain how and why certain forms of the disease attack — died July 10 at his home in Philadelphia. He was 93.

His death was announced by the Fox Chase Cancer Center in Philadelphia, where Dr. Knudson had served as president, scientific director and in other capacities since joining the institution in 1976. He had heart ailments and dementia, said his wife, Anna Meadows, a pediatric oncologist.

Dr. Knudson was among the most renowned researchers in his field, with honors including a 1998 Lasker Award, commonly known as the American Nobel, and a 2004 Kyoto Prize recognizing him for a discovery that “opened a new horizon in modern cancer genetics and played a pivotal role in the major developments” in cancer research.

Dr. Knudson first published that discovery, known as the “two-hit” theory, in a 1971 paper that became a classic of medical literature.

By that time, scientists had observed that certain types of cancer appeared to be hereditary. They could not fully explain, however, why particular people escaped the disease despite its prevalence in their families, and why other people developed cancer with no family history of it.

Alfred G Knudson Jr., a medical researcher who helped decode a mystery of cancer, died July 10 at his home in Philadelphia. (Fox Chase Cancer Center)

Seeking an explanation, Dr. Knudson studied dozens of cases of retinoblastoma, a rare form of cancer often suffered in childhood that affects the lining of the eye. He chose to study a pediatric cancer because young patients, who are unlikely to have undergone the genetic mutations that may affect an adult over the course of his or her life, present a relatively pure form of the disease.

There are two types of retinoblastoma — a hereditary form and a non-hereditary, also known as sporadic, form.

Dr. Knudson observed that in hereditary cases, patients became sick at an early age, with multiple tumors in both eyes. In non-hereditary cases, cancer developed when the child was older, and in a single eye.

Dr. Knudson subjected his data to statistical analysis, which indicated to him that retinoblastoma might result from the coincidence of two genetic events, or “hits,” as they became known.

He theorized that in hereditary cases, the patient inherits from at least one parent a damaged gene. That gene alone is not enough to produce cancer. But when the patient absorbs a second hit, such as radiation or a defect in DNA replication, cancer may develop. In the non-hereditary form of the disease, a patient inherits healthy genes from both parents and must be stricken by two genetic hits.

The two-hit theory led Dr. Knudson to infer the existence of antioncogenes, later called tumor suppressor genes, which act as brakes to stop cells from turning cancerous.

More than a decade later, advances in molecular genetics validated that theory, Alfonso Bellacosa, a professor of cancer epigenetics at the Fox Chase Cancer Center, said in an interview. Dr. Knudson’s insight was “amazing,” said another colleague, Fox Chase chief scientific officer Jonathan Chernoff, for its “prescience.”

Dr. Knudson’s work came to inform the study of all hereditary cancers, including cancers of the breast, ovary, colon and kidney. He was credited with opening the field of medicine in which individuals with known predispositions to cancer are monitored for cancer prevention and early detection.

Alfred George Knudson Jr. was born in Los Angeles on Aug. 9, 1922.

He received a bachelor of science degree from the California Institute of Technology in 1944 and a medical degree from Columbia University in 1947, then returned to Caltech to earn a PhD in biochemistry and genetics in 1956. He was a Navy and Army veteran.

Dr. Knudson spent part of his early career in Houston at the MD Anderson Cancer Center and the University of Texas Graduate School of Biomedical Sciences, where he was dean. He was drawn to genetics, he told the Lasker Foundation, because it “was unique at that time among the biological sciences because it had a precision about it that wasn’t customary in biology.”

“He had ideal training,” said Joseph Testa, a scholar of human genetics at Fox Chase. “He was perfectly suited to make such a discovery that was over the head of just about any other person who was thinking about cancer at that time.”

Dr. Knudson’s marriage to Paula Knudson ended in divorce.

Survivors include his wife of 39 years, Anna Meadows, of Philadelphia; three daughters from his first marriage, Linda Gaul of Austin and Nancy Knudson and Dorene Knudson, both of Houston; three stepchildren, Brian Meadows of Centerville, Tenn., Adam Meadows of Wyndmoor, Pa., and Elizabeth Meadows of Philadelphia; 10 grandchildren; and two great-grandchildren.

Interviewed for the book “The Emperor of All Maladies: A Biography of Cancer” by Siddhartha Mukherjee, Dr. Knudson reflected on the knowledge of the disease that he divined. It was, he said, like inferring “the wind from the movement of the trees.”