Marina Ratner, an influential mathematician and Russian-Jewish émigré who defied the notion that the best and the brightest in her field do their finest work when they are young, died on July 7 at her home in El Cerrito, Calif. She was 78.

The cause was cardiac arrest, said her daughter, Anna Ratner.

Friends and colleagues have said that Dr. Ratner started as a good but unexceptional mathematician. “The beginning of her career was not particularly promising,” said Anatole Katok, of Pennsylvania State University, who met her in the early 1960s when both lived in the Soviet Union.

A common belief is that a mathematician who does not do great work by age 40 never will. But Dr. Ratner was about that age when she set off on an ambitious effort to connect the physics of the motion of objects with more abstract ideas of number theory.

She proved her most influential theorem after she turned 50.

“She struggled and went unrecognized for a long time,” said Artur Avila, a mathematician at the French National Center for Scientific Research in Paris and the Institute for Pure and Applied Mathematics in Rio de Janeiro. “She is also one of the main examples to counter the myth that mathematics is a young person’s game.”