Branko Grünbaum

Short description: Yugoslav American mathematician

Branko Grünbaum

Branko Grünbaum in 1975

Born| 2 October 1929

Osijek, Kingdom of Yugoslavia

Died| 14 September 2018(2018-09-14) (aged 88)

Seattle, Washington, U.S.

Nationality| Croatian American
Alma mater| Hebrew University of Jerusalem
Awards| Lester R. Ford Award (1976)
Carl B. Allendoerfer Award (1978)
Leroy P. Steele Prize (2005)
Scientific career
Fields| Mathematics
Institutions| University of Washington
Thesis| On Some Properties of Minkowski Spaces (1957)
Doctoral advisor| Aryeh Dvoretzky
Doctoral students|

* Leah Berman
* Joram Lindenstrauss
* Micha Perles

Branko Grünbaum (Hebrew: ברנקו גרונבאום; 2 October 1929 – 14 September 2018)[1] was a Croatian-born mathematician of Jewish descent[2] and a professor emeritus at the University of Washington in Seattle. He received his Ph.D. in 1957 from Hebrew University of Jerusalem in Israel.[3]

## Contents

* 1 Life
* 2 Works
* 3 Books
* 3.1 as editor
* 4 See also
* 5 References
* 6 Further reading
* 7 External links

## Life

Grünbaum was born in Osijek, then part of the Kingdom of Yugoslavia, on 2 October 1929. His father was Jewish and his mother was Catholic, so during World War II the family survived the Holocaust by living at his Catholic grandmother's home. After the war, as a high school student, he met Zdenka Bienenstock, a Jew who had lived through the war hidden in a convent while the rest of her family were killed. Grünbaum became a student at the University of Zagreb, but grew disenchanted with the communist ideology of the Socialist Federal Republic of Yugoslavia, applied for emigration to Israel, and traveled with his family and Zdenka to Haifa in 1949.[4]

In Israel, Grünbaum found a job in Tel Aviv, but in 1950 returned to the study of mathematics,[4] at the Hebrew University of Jerusalem.[1] He earned a master's degree in 1954 and in the same year married Zdenka, who continued as a master's student in chemistry. He served a tour of duty as an operations researcher in the Israeli Air Force beginning in 1955, and he and Zdenka had the first of their two sons in 1956.[4] He completed his Ph.D. in 1957;[4][3] his dissertation concerned convex geometry and was supervised by Aryeh Dvoretzky.[3]

After finishing his military service in 1958, Grünbaum and his family came to the US so that Grünbaum could become a postdoctoral researcher at the Institute for Advanced Study. He then became a visiting researcher at the University of Washington in 1960. He agreed to return to Israel as a lecturer at the Hebrew University, but his plans were disrupted by the Israeli authorities determining that he was not a Jew (because his mother was not Jewish) and annulling his marriage; he and Zdenka remarried in Seattle before their return.[4]

Grünbaum remained affiliated with the Hebrew University until 1966, taking long research visits to the University of Washington and in 1965–1966 to Michigan State University. However, during the Michigan visit, learning of another case similar to their marriage annulment, he and Zdenka decided to stay in the US instead of returning to Israel, where Zdenka was still a doctoral student in chemistry. Grünbaum was given a full professorship at the University of Washington in 1966, and he remained there until retiring in 2001.[4]

## Works

Grünbaum authored over 200 papers, mostly in discrete geometry, an area in which he is known for various classification theorems. He wrote on the theory of abstract polyhedra.

His paper on line arrangements may have inspired a paper by N. G. de Bruijn on quasiperiodic tilings (the most famous example of which is the Penrose tiling of the plane). This paper is also cited by the authors of a monograph on hyperplane arrangements as having inspired their research.

Grünbaum's rotationally symmetrical 5-set Venn diagram, 1975

Grünbaum also devised a multi-set generalisation of Venn diagrams. He was an editor and a frequent contributor to Geombinatorics.

Grünbaum's classic monograph Convex Polytopes, first published in 1967, became the main textbook on the subject. His monograph Tilings and Patterns, coauthored with G. C. Shephard, helped to rejuvenate interest in this classic field, and has proved popular with nonmathematical audiences, as well as with mathematicians.

In 1976 Grünbaum won a Lester R. Ford Award for his expository article Venn diagrams and independent families of sets.[5] In 2004, Gil Kalai and Victor Klee edited a special issue of Discrete and Computational Geometry in his honor, the "Grünbaum Festschrift". In 2005, Grünbaum was awarded the Leroy P. Steele Prize for Mathematical Exposition from the American Mathematical Society. He was a Guggenheim Fellow, a Fellow of the AAAS and in 2012 he became a fellow of the American Mathematical Society.[6][7] Grünbaum supervised 19 Ph.D.s and currently has at least 200 mathematical descendants.[3]

## Books

* Grünbaum, Branko (2003), Kaibel, Volker, ed., Convex Polytopes, Graduate Texts in Mathematics, 221 (2nd ed.), Springer-Verlag, ISBN 0-387-00424-6 .[8]
* Arrangements and Spreads, Regional Conference Series in Mathematics, 10, Providence, R.I.: American Mathematical Society, 1972, ISBN 0-8218-1659-4 .[9]
* Grünbaum, Branko; Shephard, G. C. (1987), Tilings and Patterns, New York: W. H. Freeman, ISBN 0-7167-1193-1 .[10]
* Configurations of Points and Lines, Graduate Studies in Mathematics, 103, American Mathematical Society, 2009, ISBN 978-0-8218-4308-6 .[11]

### as editor

* Davis, Chandler; Grünbaum, B.; Sherk, F. A., eds. (2012), The Geometric Vein: The Coxeter Festschrift, Springer Science & Business Media, ISBN 978-1-4612-5648-9

## See also

* Configuration (geometry)
* Convex uniform honeycomb
* Elongated square gyrobicupola
* Goldner–Harary graph
* Pentagram map
* Simplicial sphere
* Star coloring
* Star polygon
* Grünbaum's theorem
* Grünbaum–Rigby configuration

## References

1. ↑ 1.0 1.1 Choi, Rose (September 18, 2018), Branko Grünbaum (1929—2018), University of Washington Mathematics Department, https://math.washington.edu/news/2018/09/18/branko-grunbaum-1929-2018
2. ↑ Branko Grünbaum, Hrvatska enciklopedija LZMK.
3. ↑ 3.0 3.1 3.2 3.3 Branko Grünbaum at the Mathematics Genealogy Project
4. ↑ 4.0 4.1 4.2 4.3 4.4 4.5 Williams, Gordon (2018), "Branko Grünbaum, Geometer", Ars Mathematica Contemporanea 15 (1), https://amc-journal.eu/index.php/amc/article/view/1848/1274
5. ↑ Grünbaum, Branko (1975), "Venn diagrams and independent families of sets", Mathematics Magazine 48 (1): 12–23, doi:10.2307/2689288, Bibcode: 1975MathM..48...12G, http://www.maa.org/programs/maa-awards/writing-awards/venn-diagrams-and-independent-families-of-sets
6. ↑ List of Fellows of the American Mathematical Society, retrieved 2013-01-19.
7. ↑ Pircea, M., ed. (2011), The Best Writing on Mathematics 2010, Princeton University Press, ISBN 9780691148410
8. ↑ Reviews of Convex Polytopes:
* Sallee, G. T., "Review of 1st ed.", MathSciNet
* Jucovič, E., "Review of 1st ed." (in de), zbMATH
* Fenchel, Werner (Winter 1968), "Review of 1st ed.", American Scientist 56 (4): 476A–477A
* Baxandall, P. R. (October 1969), "Review of 1st ed.", The Mathematical Gazette 53 (385): 342–343, doi:10.2307/3615008
* Ehrig, G., "Review of 2nd ed." (in de), zbMATH
* Zvonkin, Alexander (2004), "Review of 2nd ed.", MathSciNet
* Lord, Nick (March 2005), "Review of 2nd ed.", The Mathematical Gazette 89 (514): 164–166, doi:10.1017/S0025557200177307
* McMullen, Peter (July 2005), "Review of 2nd ed.", Combinatorics, Probability and Computing 14 (4): 623–626, doi:10.1017/s0963548305226998
9. ↑ Reviews of Arrangements and Spreads:
* Jucovič, E., "none", zbMATH
* Coxeter, H. S. M., "none", MathSciNet
10. ↑ Reviews of Tilings and Patterns:
* Schulte, E., "none", zbMATH
* Malkevitch, Joseph (May 22, 1987), "Shapes in the plane", Science, New Series 236 (4804): 996–997, doi:10.1126/science.236.4804.996, PMID 17812775
* Wenzel, John A. (September 1987), "none", The Mathematics Teacher 80 (6): 497–498
* Senechal, Marjorie (September–October 1987), "none", American Scientist 75 (5): 521–522
* Fejes Tóth, L. (October 1987), "none", Bulletin of the American Mathematical Society 17 (2): 369–373, doi:10.1090/s0273-0979-1987-15600-x
* Williams, H. C. (December 1987), "none", The Mathematical Gazette 71 (458): 347–348, doi:10.2307/3617109
* Coxeter, H. S. M. (1988), "none", Mathematical Reviews
* Roman, Tiberiu (1988), "none", Bulletin mathématique de la Société des Sciences Mathématiques de la République Socialiste de Roumanie, Nouvelle Série 32 (4): 379–380
* Golomb, Solomon W. (January 1988), "none", American Mathematical Monthly 95 (1): 63–64, doi:10.2307/2323457
* Donegan, Joe (February 1990), "none", The Mathematics Teacher 83 (2): 167
* Schwarzenberger, R. L. E. (March 1988), "none", Bulletin of the London Mathematical Society 20 (2): 167–170, doi:10.1112/blms/20.2.167
* Garcia, Paul (June 1990), "none", The Mathematical Gazette 74 (468): 207–209, doi:10.2307/3619416
* Paufler, P. (1991), "none", Crystal Research and Technology (Wiley) 26 (8): 1038, doi:10.1002/crat.2170260812
* Satzer, William J. (November 2016), "Review", MAA Reviews (Mathematical Association of America), https://www.maa.org/press/maa-reviews/tilings-and-patterns
11. ↑ Reviews of Configurations of Points and Lines:
* Riesinger, Rolf, "none", zbMATH
* Glass, Darren (November 2009), "Review", MAA Reviews (Mathematical Association of America), https://www.maa.org/press/maa-reviews/configurations-of-points-and-lines

## Further reading

* Kahle, Matthew (2019), "Branko Grünbaum in many dimensions", Geombinatorics 28 (3): 140–146
* "Guest Editors' Foreword", Discrete & Computational Geometry 64 (2): 229–232, June 2020, doi:10.1007/s00454-020-00214-y

## External links

* Personal web page

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