# Hillel Furstenberg

This biography of a living person needs additional citations for verification. (March 2020) (Learn how and when to remove this template message) |

Harry Furstenberg | |
---|---|

Hillel Furstenberg in 2020 | |

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 | Abel Prize 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 |

**Hillel (Harry) Furstenberg** (Hebrew: הלל (הארי) פורסטנברג) (born September 29, 1935 in Berlin) is an American-Israeli mathematician and professor emeritus at the Hebrew University of Jerusalem. He is a member of the Israel Academy of Sciences and Humanities and U.S. National Academy of Sciences and a laureate of the Abel Prize and 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.

## Biography[edit]

Furstenberg was born in 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, shortly before the outbreak of the Second World War.^{[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.

## Academic career[edit]

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]}

From 1959–1960, Furstenberg served as the C. L. E. Moore instructor at the Massachusetts Institute of Technology.^{[3]}

Furstenberg got his first job as an assistant professor in 1961 at the University of Minnesota. Furstenberg was promoted to full professor at Minnesota but moved to Israel in 1965 to join at Hebrew University's Einstein Institute of Mathematics. He retired from Hebrew University in 2003.^{[4]} Furstenberg serves as an Advisory Committee member of The Center for Advanced Studies in Mathematics at Ben Gurion University of the Negev.^{[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 1993, Furstenberg won the Israel Prize and in 2007, the Wolf Prize in mathematics. He is a member of the Israel Academy of Sciences and Humanities (elected 1974),^{[6]} the American Academy of Arts and Sciences (international honorary member since 1995),^{[7]} and the U.S. National Academy of Sciences (elected 1989).^{[8]}

Fustenberg has taught generations of students, including Alexander Lubotzky, Yuval Peres, Tamar Ziegler, Shahar Mozes, and Vitaly Bergelson.^{[9]}

## Research accomplishments[edit]

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.^{[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 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[edit]

In 1958, Furstenberg married Rochelle (née) Cohen, a journalist and literary critic. Together they have five children and sixteen grandchildren.^{[4]}

## Awards[edit]

- 1993 – Furstenberg received the Israel Prize, for exact sciences.
^{[10]} - 1993 – Furstenberg received the Harvey Prize from Technion.
^{[11]} - 2006/7 – He received the Wolf Prize in Mathematics.
^{[12]} - 2006 He delivered the Paul Turán Memorial Lectures.
^{[13]} - 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".
^{[14]}

## Selected publications[edit]

- Furstenberg, Harry,
*Stationary processes and prediction theory*, Princeton, N.J., Princeton University Press, 1960.^{[15]}^{[16]} - Furstenberg, Harry,
*Recurrence in ergodic theory and combinatorial number theory*, Princeton, N.J., Princeton Univ. Press, 1981.^{[17]}^{[18]}

## See also[edit]

## References[edit]

**^**Chang, Kenneth. "Abel Prize in Mathematics Shared by 2 Trailblazers of Probability and Dynamics Hillel Furstenberg, 84, and Gregory Margulis, 74, both retired professors, share the mathematics equivalent of a Nobel Prize." Archived 2020-03-18 at the Wayback Machine,*The New York Times*, March 18, 2020. Accessed March 18, 2020. "Dr. Furstenberg was born in Berlin in 1935. His family, which was Jewish, was able to leave Germany just before the start of World War II and made its way to the United States, settling in New York City in the Washington Heights neighborhood in Manhattan."- ^
^{a}^{b}O'Connor, John J. and Robertson, Edmund F. "Hillel Furstenberg".*MacTutor History of Mathematics archive*. Retrieved 2020-03-22.CS1 maint: uses authors parameter (link) **^**Kenneth Chang (2020-03-18). "Abel Prize in Mathematics Shared by 2 Trailblazers of Probability and Dynamics".*New York Times*. Retrieved 2020-03-22.- ^
^{a}^{b}^{c}"A biography of Hillel Furstenberg".*The Abel Prize*. Retrieved 2020-03-22. **^**"Conference on Probability in Mathematics. Furnstenfest 2003".*Ben-Gurion University*. Retrieved 2020-03-22.**^**"Prof. Hillel Furstenberg".*Israel Academy of Sciences and Humanities*. Retrieved 2020-03-22.**^**"Dr Hillel Furstenberg".*American Academy of Arts and Sciences*. Retrieved 2020-03-22.**^**"Member directory:Hillel Furstenberg".*U.S. National Academy of Sciences*. Retrieved 2020-03-22.**^**"Harry Furstenberg - The Mathematics Genealogy Project".*www.genealogy.math.ndsu.nodak.edu*. Retrieved 2020-03-19.**^**"Israel Prize Official Site – Recipients in 1993 (in Hebrew)". Archived from the original on 2014-10-12.**^**"Prize Winners – Harvey Prize".*Technion – Israel Institute of Technology*. Retrieved 2020-03-22.**^**"Furstenberg and Smale Receive 2006–2007 Wolf Prize" (PDF).*Notices of the American Mathematical Society*.**54**(4): 631–632. 2007.**^**"Turán Memorial Lectures". Archived from the original on 2019-09-21. Retrieved 2019-09-14.**^**Chang, Kenneth (2020-03-18). "Abel Prize in Mathematics Shared by 2 Trailblazers of Probability and Dynamics".*The New York Times*. ISSN 0362-4331. Archived from the original on 2020-03-18. Retrieved 2020-03-18.**^**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. Archived from the original on 2014-05-17. Retrieved 2012-09-24.**^**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. Archived from the original on 2014-05-17. Retrieved 2012-09-24.

## External links[edit]

- 1935 births
- 20th-century American mathematicians
- 21st-century American mathematicians
- Members of the United States National Academy of Sciences
- People from Washington Heights, Manhattan
- Living people
- Abel Prize laureates
- Israel Prize in exact science recipients
- Israel Prize in exact science recipients who were mathematicians
- Hebrew University of Jerusalem faculty
- Members of the Israel Academy of Sciences and Humanities
- Israeli mathematicians
- Princeton University alumni
- University of Minnesota faculty
- Wolf Prize in Mathematics laureates
- Yeshiva University alumni
- German Jews
- American people of German-Jewish descent
- Israeli Jews