# Hillel Furstenberg

**Hillel (Harry) Furstenberg** (Hebrew: הלל (הארי) פורסטנברג) (born September 29, 1935) is an American-Israeli mathematician, a member of the Israel Academy of Sciences and Humanities and U.S. National Academy of Sciences and a laureate of the Wolf Prize in Mathematics. He is known for his application of probability theory and ergodic theory methods to other areas of mathematics, including number theory and Lie groups.

Harry Furstenberg | |
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Hillel Furstenberg in 1992 | |

Born | |

Nationality | Israel American |

Alma mater | Princeton University |

Known for | Proof of Szemerédi's theorem IP set Evenly spaced integer topology Furstenberg–Sárközy theorem Furstenberg boundary Furstenberg's proof |

Awards | Israel Prize Harvey Prize Wolf Prize |

Scientific career | |

Fields | Mathematics |

Doctoral advisor | Salomon Bochner |

Doctoral students | Alexander Lubotzky Vitaly Bergelson Shahar Mozes Yuval Peres Tamar Ziegler |

## Biography

Hillel Furstenberg was born in Germany, in 1935, and the family emigrated to the United States in 1939, 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 in 1955. He obtained his Ph.D. under Salomon Bochner at Princeton University in 1958. After several years at the University of Minnesota he became a Professor of Mathematics at the Hebrew University of Jerusalem in 1965.

He gained attention at an early stage in his career for producing an innovative topological proof of the infinitude of prime numbers in 1955. 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.

## Awards

- 1993 – Furstenberg received the Israel Prize, for exact sciences.[1]
- 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.[2]

## Selected publications

## See also

## References

- "Israel Prize Official Site – Recipients in 1993 (in Hebrew)". Archived from the original on 2014-10-12.
- "Turán Memorial Lectures".
- Furstenberg, Harry; Furstenberg, Hillel (1960-08-21).
*Stationary Processes and Prediction Theory*. ISBN 0691080410. - Masani, P. (1963). "Review:
*Stationary processes and prediction theory*, by H. Furstenberg".*Bull. Amer. Math. Soc*.**69**(2): 195–207. doi:10.1090/s0002-9904-1963-10910-6. - Furstenberg, Harry; Furstenberg, Hillel (1981).
*Recurrence in Ergodic Theory and Combinatorial Number Theory*. ISBN 9780691082691. - Petersen, Karl (1986). "Review:
*Recurrence in ergodic theory and combinatorial number theory*, by H. Furstenberg".*Bull. Amer. Math. Soc. (N.S.)*.**14**(2): 305–309. doi:10.1090/s0273-0979-1986-15451-0.