Hillel Furstenberg

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Hillel Fürstenberg (2020)

Hillel Fürstenberg , also Harry Furstenberg ( Hebrew הלל פורסטנברג; *  September 29, 1935 in Berlin ) is an Israeli mathematician who deals with probability theory , ergodic theory , topological dynamics and number theory. On March 18, 2020, he was awarded the Abel Prize , one of the highest international awards in the field of mathematics.


Fürstenberg was born in Berlin in 1935 into a German-Jewish family. His family managed to emigrate from Nazi Germany to the United States in 1939, just a few months before the outbreak of World War II . His father died on the trip, and Hillel was raised by his mother and older sister in an Orthodox Jewish community in New York City . He studied at Yeshiva University in New York, where he received his BA and MS degrees in 1955 . During his studies, he published mathematical works in well-known specialist journals. In 1958 he received his doctorate under Salomon Bochner at Princeton University ( Prediction Theory ). In 1959 he was a Moore Instructor at the Massachusetts Institute of Technology . He then went to the University of Minnesota before becoming a professor at the Hebrew University in Jerusalem in 1965 . In 1964 he received a research grant from the Alfred P. Sloan Foundation ( Sloan Research Fellowship ).

His doctoral students include Alexander Lubotzky , Vitaly Bergelson and Yuval Peres .


Hillel Fürstenberg in Jerusalem (1975)
Hillel Fürstenberg in Berkeley (1992)

Fürstenberg applied methods of probability theory and ergodic theory in number theory and the theory of Lie groups . In 1955 he gave a new proof of the infinity of prime numbers using topological methods . This was already proven by Euclid , but the methods used were important. In 1977 he gave a new, ergodic proof of Szemerédi's theorem about arithmetic progressions in subsets of positive density of natural numbers, in 1972 he proved the unambiguous ergodicity of rivers along horocycles on compact hyperbolic Riemannian surfaces. Ergodicity for geodetic flows on compact manifolds of negative curvature was already proven in the work of Gustav Hedlund and Eberhard Hopf at the end of the 1930s, but these are not clearly ergodic. Fürstenberg is also known for his structural theorem for minimal, distal flows in topological dynamics. He delivered early fundamental studies on random matrices (whose asymptotic behavior it with structural movements of the underlying Lie groups in connection sat) and studied stochastic processes in homogeneous spaces and the asymptotic behavior of random walks on groups.

Honors and memberships

In 1993 he received the Israel Prize and the Harvey Prize of the Technion in Haifa . In 2007 he received the Wolf Prize in Mathematics (with Stephen Smale ) and in 2020 the Abel Prize (with Grigori Alexandrowitsch Margulis ). He is a member of the Israel Academy of Sciences, the US National Academy of Sciences, and the American Academy of Arts and Sciences .

In 2010 he gave a plenary lecture at the International Congress of Mathematicians (ICM) in Hyderabad ( Ergodic structures and non conventional ergodic theorems ), in 1990 he was invited speaker at the ICM in Kyōto ( Recurrent ergodic structures and Ramsey theory ), in 1962 in Stockholm ( A Poisson formula for semi-simple Lie groups ) and in 1970 at the ICM in Nice ( Boundaries of Lie groups and discrete subgroups ).


In 1958, Fürstenberg married his wife Rochelle, a magazine writer specializing in art and culture. He has five children with her.

Fonts (selection)

  • On the infinitude of primes . In: American Mathematical Monthly. Vol. 62, 1955, p. 353. doi : 10.2307 / 2307043 JSTOR 2307043
  • Ergodic behavior of diagonal measures and a theorem of Szemerédi on arithmetic progressions. Journal d'Analyse Math., Vol. 31, 1977, pp. 204-256. doi : 10.1007 / BF02813304
  • Recurrence in Ergodic Theory and Combinatorial Number Theory. Princeton University Press 1981. ISBN 9780691642840 .

See also

Web links

Commons : Hillel Fürstenberg  - Collection of images, videos and audio files

Individual evidence

  1. a b A biography of Hillel Fürstenberg. (pdf) Abel Foundation, accessed on March 22, 2020 (short biography in German).