Dr. Marina Evseevna Ratner

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, Private .

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.”

Amie Wilkinson, of the University of Chicago, pointed to the classic video game “Asteroids” to explain Dr. Ratner’s work.

“When an object crosses the right edge of the screen, it instantaneously appears on the left edge of the screen moving in the same direction,” Dr. Wilkinson said in an email. “The simplest case of Ratner’s Theorem applies to the motion of objects in the ‘Asteroids’ game. If an object moves in a straight line indefinitely without turning, there are only two possibilities: Either it will return to its initial position and repeat its path indefinitely, or it will never return to its initial position and instead will visit every possible region of the space.”

Dr. Ratner showed that for a higher dimensional, more complicated video game, an equivalent statement was true.

Her dynamics research helped unravel mathematical problems that had resisted more direct, traditional approaches of attack.

Dr. Avila said Dr. Ratner’s work had been the basis for that of younger mathematicians like Elon Lindenstrauss and Maryam Mirzakhani, two winners of the Fields Medal, the most prestigious honor in mathematics. Dr. Mirzakhani, the first woman to win a Fields, also died this month.

“What is remarkable about these results of Ratner is how many unexpected applications they had,” Dr. Lindenstrauss said in an email. “It is almost as if this dynamical fact was a philosopher’s stone that allowed many mathematicians to show quite remarkable things, in remarkably diverse situations.”

Marina Ratner was born on Oct. 30, 1938, in Moscow, the daughter of scientists. She graduated from Moscow State University in 1961. She then worked for four years as an assistant for Andrey Kolmogorov, a prominent Russian mathematician, before attending graduate school at Moscow State. She completed her doctorate in 1969.

When she applied for a visa to leave the Soviet Union for Israel, Dr. Ratner was pressured to leave a teaching job at the High Technical Engineering School in Moscow, Anna Ratner said.

“She had a very hard time in Russia,” said Alexandre Chorin, a colleague at the University of California, Berkeley. “The Russians took a variety of steps to penalize her.”

Dr. Ratner and her daughter immigrated to Israel in 1971, where she was a lecturer at the Hebrew University of Jerusalem. She was able to pursue her mathematical research but was unable to find a permanent position.

Her work caught the attention of Rufus Bowen, however, at Berkeley, and he lobbied the university to hire her. It did, in 1975, initially for a temporary position, and even that, given her relatively meager record, was controversial in the department. She eventually became a tenured professor.

Dr. Ratner was a member of the American Academy of Arts and Sciences and the National Academy of Sciences.

In addition to her daughter, she is survived by two grandchildren.

A marriage to Private ended in divorce.

Dr. Ratner’s style of working may have contributed to her not receiving as much acclaim as some thought she deserved. She always worked alone. At Berkeley, she earned high marks as a teacher of undergraduates but taught only one doctoral student.

She also did not always do the best job of promoting her achievements.

Étienne Ghys, a mathematician at École Normale Supérieure de Lyon in France, recalled spending six months trying to understand the results of her dynamics research to present them at a seminar. When he discussed the papers with her, he told her that he had the feeling that she had written the papers not for other mathematicians to understand but mainly to convince herself that the theorems were correct.

Dr. Ghys said Dr. Ratner replied: “Yes! Exactly! You understood why and how I write mathematics.”