Leonard Hayflick, a biomedical researcher who discovered that normal cells can divide only a certain number of times — setting a limit on the human life span and frustrating would-be-immortalists everywhere — died on Aug. 1 at his home in Sea Ranch, Calif. He was 96.

His son, Joel Hayflick, said the cause was pancreatic cancer.

Like many great scientific findings, Dr. Hayflick’s came somewhat by accident. As a young scientist in the early 1960s at the Wistar Institute, a research organization at the University of Pennsylvania, he was trying to develop healthy embryonic cell lines in order to study whether viruses can cause certain types of cancer.

He and a colleague, Paul Moorhead, soon noticed that somatic — that is, nonreproductive — cells went through a phase of division, splitting between 40 and 60 times, before lapsing into what he called senescence.

As senescent cells accumulate, he posited, the body itself begins to age and decline. The only cells that do not go into senescence, he added, are cancer cells.

As a result of this cellular clock, he said, no amount of diet or exercise or genetic tweaking will push the human species past a life span of about 125 years.

This finding, which the Nobel-winning virologist Macfarlane Burnet later called the Hayflick limit, ran counter to everything scientists believed about cells and aging — especially the thesis that cells themselves are immortal, and that aging is a result of external causes, like disease, diet and solar radiation.