Furstenberg was born in Germany, in 1935. In 1939, Shortly after Kristallnacht, his family escaped to the United States and settled in the Washington Heights neighborhood of New York City, shortly before the outbreak of the Second World War. He attended Marsha Stern Talmudical Academy and then Yeshiva University, where he concluded his BA and MSc studies at the age of 20 in 1955. Furstenberg published several papers as an undergraduate, including "Note on one type of indeterminate form" and "On the infinitude of primes". Both appeared in the "American Mathematical Monthly, the latter provided a topological proof of Euclid's famous theorem that there are infinitely many primes.
Furstenberg gained attention at an early stage in his career for producing an innovative topological proof of the infinitude of prime numbers in 1955. In a series of articles beginning in 1963 with A Poisson Formula for Semi-Simple Lie Groups, he continued to establish himself as a ground-breaking thinker. His work showing that the behavior of random walks on a group is intricately related to the structure of the group - which led to what is now called the Furstenberg boundary – has been hugely influential in the study of lattices and Lie groups. In his 1967 paper, Disjointness in ergodic theory, minimal sets, and a problem in Diophantine approximation, Furstenberg introduced the notion of ‘disjointness,’ a notion in ergodic systems that is analogous to coprimality for integers. The notion turned out to have applications in areas such as number theory, fractals, signal processing and electrical engineering. In his 1977 paper, Ergodic behavior of diagonal measures and a theorem of Szemerédi on arithmetic progressions, Furstenberg used methods from ergodic theory to prove a celebrated result by Endre Szemerédi, which states that any subset of integers with positive upper density contains arbitrarily large arithmetic progressions. His insights led to important results, such as the proof by Ben Green and Terence Tao that the sequence of prime numbers includes arbitrary large arithmetic progressions. He proved unique ergodicity of horocycle flows on compact hyperbolic Riemann surfaces in the early 1970s. In 1977, he gave an ergodic theory reformulation, and subsequently proof, of Szemerédi's theorem. The Furstenberg boundary and Furstenberg compactification of a locally symmetric space are named after him, as is the Furstenberg–Sárközy theorem in additive number theory.
Personal life
In 1958, Furstenberg married Rochelle Cohen, a journalist and literary critic. Together they have five children and sixteen grandchildren.
1993 – Furstenberg received the Israel Prize, for exact sciences.
1993 – Furstenberg received the Harvey Prize from Technion.
2006/7 – He received the Wolf Prize in Mathematics.
2006 He delivered the Paul Turán Memorial Lectures.
2020 - He received the Abel Prize with Gregory Margulis "for pioneering the use of methods from probability and dynamics in group theory, number theory and combinatorics".
Selected publications
Furstenberg, Harry, Stationary processes and prediction theory, Princeton, N.J., Princeton University Press, 1960.
