Friedrich Hirzebruch

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Friedrich Hirzebruch at the DMV annual conference 1980 in Dortmund

Friedrich Ernst Peter Hirzebruch , also Friedrich EP Hirzebruch or Fritz Hirzebruch , (born October 17, 1927 in Hamm ; † May 27, 2012 in Bonn ) was a German mathematician .

He is known both for his pioneering work in modern algebraic geometry using topological methods and as a science organizer who made a prominent contribution to the international integration of German mathematicians after the Second World War.


Hirzebruch was the oldest of four children of the math teacher Dr. Fritz Hirzebruch and Martha Holtschmidt. In the Second World War he was an anti-aircraft helper and he was drafted as a soldier in March 1945, after which he was briefly a prisoner of war on the Rhine meadows near Remagen. From 1945 to 1950 he studied mathematics , physics and mathematical logic at the Westphalian Wilhelms University in Münster (with Heinrich Behnke and Karl Stein ) and at the Eidgenössische Technische Hochschule Zürich (1949/50) (with Heinz Hopf ). It was 1950 when Heinrich Behnke and Heinz Hopf (stimulator of the thesis) with the work "About four-dimensional Riemann surfaces ambiguous analytic functions of two complex variables" (published in the Annals of Mathematics in 1951, 1953) to Dr. rer. nat. PhD . He was initially a research assistant at the Mathematical Institute of the University of Erlangen with Otto Haupt and Georg Nöbeling . From 1952 to 1954 he worked at the Institute for Advanced Study in Princeton , where he worked particularly with Kunihiko Kodaira , as well as with Donald Spencer , Raoul Bott and Armand Borel . There he drew international attention to himself with the sentence by Hirzebruch-Riemann-Roch (and in preparation for it his signature sentence ) ( Jean-Pierre Serre lectured on this in the Séminaire Nicolas Bourbaki and Hirzebruch himself at the International Congress of Mathematicians in Amsterdam in 1954). In 1955 he completed his habilitation for mathematics in Münster with the book New Topological Methods in Algebraic Geometry, which was later published as a book .

Following an assistant professorship at Princeton University , USA, in the years 1955/1956 he received a call to a professorship at the Rheinische Friedrich-Wilhelms University in Bonn (a specially newly created chair of mathematics in addition to that of Ernst Peschl and Wolfgang Krull ) where he taught until his retirement in 1993. He declined calls to Göttingen, Chicago, MIT, Munich, Berlin, Zurich, Princeton, Berkeley and Heidelberg, among others. He developed Bonn into a leading mathematical center in Germany and began in 1957 with the internationally renowned annual Bonn “work conferences”. He was visiting professor at the University of California, Berkeley , Harvard University , University of Pennsylvania , Mathematical Sciences Research Institute (Berkeley), Collège de France (Paris), Institut des Hautes Etudes Scientifiques (Bures-sur-Yvette), University of Oxford , University from Amsterdam , Kabul University, Beijing Chinese Academy of Sciences , Kyōto University , Instituto de Matematica Pura e Aplicada Rio de Janeiro.

Gravestone in the Poppelsdorf cemetery

He is the founding director of the Max Planck Institute for Mathematics in Bonn, which emerged in 1980 from the Collaborative Research Center for Theoretical Mathematics at the University of Bonn , which he founded in 1969 . He headed the institute from 1981 to 1995 and was the only director at the institute until 1995. He was also President of the German Mathematicians Association 1961/1962 and 1990, President of the European Mathematical Society (EMS) from 1990 to 1994, and Chairman of the Scientific Council of the International Banach Center for Mathematics from 1993 to 2002. He had over 50 doctoral students.

Friedrich Hirzebruch had been married to Ingeborg Spitzley since 1952 and had three children.

Hirzebruch was buried in the Poppelsdorf cemetery . On his tombstone there are images of the five Platonic solids , with the icosahedron , which also serves as the symbol of the Max Planck Institute for Mathematics, in the center. Due to their diverse cross-connections, the five bodies were among Hirzebruch's favorite objects in mathematics.


Friedrich Hirzebruch (right) together with Michael Atiyah , with whom he worked several times. (1977)

Hirzebruch researched in particular in the areas of algebraic geometry , topology , number theory and singularity theory . His work New Topological Methods in Algebraic Geometry , published in several editions between 1956 and 1995 and translated into English, Japanese and Russian, is a standard work. With the theorem by Hirzebruch-Riemann-Roch , named after him , which introduced one of the most important developments in modern mathematics, he laid the basis for his international reputation in 1954. The theorem equates the arithmetic gender (defined as the alternating sum of the dimensions of the cohomology groups of the sheaf of the intersections of a unitary vector bundle) with the Todd class . It was proven by Hirzebruch in the 1950s with cobordism theory (about which he exchanged ideas with René Thom ). He first proved his signature sentence (Princeton, 1953) as a preparation. Today the Atiyah-Singer index set is used , which unified this whole area. With Armand Borel , he gave a new interpretation of Weyl's character formulas for Lie groups with his generalization of the Riemann-Roch theorem. In the 1960s he founded the topological K-theory with Michael Atiyah , a cohomology theory with vector bundles (in the book Ebbinghaus et al. "Numbers" he gives an example of their application to the classification of division algebras). In the 1970s he examined a. a. algebraic surfaces such as Hilbert's module surfaces . Another area of ​​work, especially in the 1960s, was the topology of singularities (exotic spheres, etc.), an area in which his student Egbert Brieskorn also achieved significant results in the 1960s.

A problem on the topology of algebraic varieties posed by Hirzebruch in 1954 was solved by Dieter Kotschick in 2009 .

Friedrich Hirzebruch created the "Mathematical Working Conference", which has brought together the international elite mathematicians at Bonn University since 1957. At the first workshop in 1957 were Alexander Grothendieck , Michael Atiyah, Hans Grauert , Nicolaas Kuiper and Jacques Tits . The Collaborative Research Center (SFB) "Theoretical Mathematics" he set up achieved international renown and existed from 1969 to 1985. It earned special recognition through the establishment of the Max Planck Institute for Mathematics in Bonn, which emerged from the SFB in the early 1980s.

In 1958 he gave a plenary lecture at the International Congress of Mathematicians in Edinburgh (Complex Manifolds) .

His doctoral students include a. Don Zagier , Friedhelm Waldhausen , Egbert Brieskorn , Klaus Jänich , Detlef Gromoll , Klaus Lamotke , Winfried Scharlau , Matthias Kreck , Lothar Göttsche and Bernhelm Booß-Bavnbek .

Many of his books, essays and lectures are characterized by a special educational skill.

honors and awards

Hirzebruch has received numerous national and international awards and honorary doctorates from the universities of Warwick (1980), Göttingen (1982), Oxford (1984), Wuppertal (1987), Notre Dame (1989), Trinity College, Dublin (1992), Athens (1993) , Potsdam (1995), Konstanz (1999) and Augsburg (2007). He was a member of the German Academy of Sciences Leopoldina zu Halle , the Bavarian Academy of Sciences , the North Rhine-Westphalian Academy of Sciences and Arts in Düsseldorf , the Academy of Sciences and Literature in Mainz , the Heidelberg Academy of Sciences , the Academy of Sciences to Göttingen , the Saxon Academy of Sciences and the Berlin-Brandenburg Academy of Sciences , the science academies in the Netherlands, Ukraine, Russia, France, Great Britain, Poland and Ireland and the Academia Europaea . He was also an honorary member of the Austrian Academy of Sciences , the National Academy of Sciences (1986) and the American Academy of Arts and Sciences (1992).

1962 and 1990 he was President of the German Mathematicians Association .

Hirzebruch was in the selection for the Fields Medal in the first round in 1958, the top candidate of 38 (proposed by five committee members). The chairman of the committee, Heinz Hopf , excluded him, however, because he had recently become a professor at a prestigious university and, in Hopf's opinion, did not need any further funding.

The German National Academic Foundation awards the Hirzebruch doctoral award for mathematics, natural and engineering sciences every year.

In 2019, a street on the new Poppelsdorf campus of the University of Bonn was named after Hirzebruch.

Fonts (selection)

Based on lectures by Hirzebruch:

Some articles available online:


  • Christian Blohmann: Fritz Hirzebruch: October 17, 1927 - May 27, 2012. In: Annual Report 2012 of the Max Planck Society, Beileger , pp. 25–27.
  • Wulf-Dieter Geyer: Friedrich Hirzebruch October 17, 1927– May 27, 2012. In: Bavarian Academy of Sciences, Yearbook 2012 , Munich 2013, pp. 179–182. pdf
  • Willi Jäger: Friedrich Hirzebruch (October 17, 1927– May 27, 2012). In: Yearbook of the Heidelberg Academy of Sciences for 2012 , Heidelberg 2013, pp. 164–166.
  • Don Zagier: Obituary for Friedrich Hirzebruch. In: North Rhine-Westphalian Academy of Sciences and Arts. Yearbook 2014 , pp. 116–121.
  • Don Zagier: The life and work of Friedrich Hirzebruch , Annual Report DMV, Volume 117, 2015, pp. 93–132. pdf
  • S.-T. Yau (Ed.): The founders of index theory: reminiscences of Atiyah, Bott, Hirzebruch and Singer, International Press, Somerville 2003.
  • Winfried Scharlau : The good fortune to be a mathematician. Friedrich Hirzebruch and his time , Springer 2016, ISBN 978-3-658-14756-3 , doi : 10.1007 / 978-3-658-14757-0

Web links

Commons : Friedrich Hirzebruch  - Collection of images, videos and audio files

Individual evidence

  1. Laudation of the German Mathematicians Association for the Cantor Medal .
  2. In the Short Lectures , Volume 2 of the conference reports, p. 232, The Riemann-Roch Theorem and Todd's arithmetic gender for algebraic manifolds
  3. Winfried Scharlau: The luck to be a mathematician. Friedrich Hirzebruch and his time , Springer 2016, p. 371 ff., Doi : 10.1007 / 978-3-658-14757-0_34
  4. ^ Hirzebruch The Signature Theorem. Reminiscences and recreation . Prospects in Mathematics, Annals of Mathematical Studies, Volume 70, 1971, pp. 3-31.
  5. Interview by Hirzebruch, Mitteilungen DMV, Volume 19, 2011, Issue 2, 86–89, there p. 88, doi : 10.1515 / dmvm-2011-0039
  6. ^ Gabriele Dörflinger: Mathematics in the Heidelberg Academy of Sciences . 2014, p. 27.
  7. 90 years, 90 heads. In: A series of portraits for the 90th anniversary of the German National Academic Foundation. December 1, 2018, accessed May 4, 2020 .
  8. ^ Jean-Marie Thiébaud: L'Ordre du Trésor sacré (Japon). In: Editions L'Harmattan. L'Harmattan, December 2007, accessed July 27, 2009 (French).
  9. ^ Abel Committee
  10. Michael Barany, The Fields Medal should return to its roots , Nature, January 12, 2018
  11. Winners of the 2020 doctoral prizes , German National Academic Foundation, May 11, 2020
  12. Street naming in the area of ​​the Poppelsdorf university campus. (PDF; 133 KB) In: Ratsinformationssystem. City of Bonn, July 9, 2019, accessed on April 13, 2020 .