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As a mathematician and an author, he specialized in “ergodic theory, Lie groups and differential geometry,” according to a university biography.

In seminal papers in the 1960s and 1970s, Furstenberg used ergodic ideas to show how even the most random sets of infinitely many whole numbers had to conceal some kind of regular structure.

The general idea of using the trajectory of an object to reveal information about the space it is moving through is called ergodic theory.

Furstenberg’s ideas had an impact across fields seemingly distant from ergodic theory, including geometry and algebra.

In addition, he was known for work in ergodic theory, and for mastering and influencing all aspects of dynamical-systems problems and approaches.