Furstenberg was born to German JewsinNazi Germany, in 1935 (originally named "Fürstenberg"). In 1939, shortly after Kristallnacht, his family escaped to the United States and settled in the Washington Heights neighborhood of New York City, escaping the Holocaust.[1] 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" (1953) and "On the infinitude of primes" (1955). 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 pursued his doctorate at Princeton University under the supervision of Salomon Bochner. In 1958 he received his PhD for his thesis, Prediction Theory.[2]
In 2003, Hebrew University and Ben-Gurion University held a joint conference to celebrate Furstenberg's retirement. The four-day Conference on Probability in Mathematics was subtitled Furstenfest 2003 and included four days of lectures.[5]
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.[4]
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 1977, he gave an ergodic theory reformulation, and subsequently proof, of Szemerédi's theorem. This is described 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 then led to later important results, such as the proof by Ben Green and Terence Tao that the sequence of prime numbers includes arbitrary large arithmetic progressions.
2006 – He delivered the Paul Turán Memorial Lectures.[14]
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".[15]
Furstenberg, Harry, Stationary processes and prediction theory, Princeton, N.J., Princeton University Press, 1960.[16][17]
Furstenberg, Harry (March 1963). "A Poisson Formula for Semi-Simple Lie Groups". Annals of Mathematics. Second Series. 77 (2): 335–386. doi:10.2307/1970220. JSTOR1970220.
Furstenberg, Harry (1967). "Disjointness in ergodic theory, minimal sets, and a problem in diophantine approximation". Mathematical Systems Theory. 1: 1–49. doi:10.1007/BF01692494. S2CID206801948.