Friedrich Ernst Peter Hirzebruch

ForMemRS Fellowship of the Royal Society (FRS, ForMemRS and HonFRS) is an award granted by the Fellows of the Royal Society of London to individuals who have made a "substantial contribution to the improvement of natural science, natural knowledge, incl ...

(17 October 1927 – 27 May 2012) was a German mathematician, working in the fields of

topology Topology (from the Greek language, Greek words , and ) is the branch of mathematics concerned with the properties of a Mathematical object, geometric object that are preserved under Continuous function, continuous Deformation theory, deformat ...

complex manifold In differential geometry and complex geometry, a complex manifold is a manifold with a ''complex structure'', that is an atlas (topology), atlas of chart (topology), charts to the open unit disc in the complex coordinate space \mathbb^n, such th ...

s and

algebraic geometry Algebraic geometry is a branch of mathematics which uses abstract algebraic techniques, mainly from commutative algebra, to solve geometry, geometrical problems. Classically, it studies zero of a function, zeros of multivariate polynomials; th ...

, and a leading figure in his generation. He has been described as "the most important mathematician in Germany of the postwar period."

Education

Hirzebruch was born in Hamm,

Westphalia Westphalia (; ; ) is a region of northwestern Germany and one of the three historic parts of the state of North Rhine-Westphalia. It has an area of and 7.9 million inhabitants. The territory of the region is almost identical with the h ...

in 1927. His father, of the same name, was a maths teacher. Hirzebruch studied at the

University of Münster The University of Münster (, until 2023 , WWU) is a public research university located in the city of Münster, North Rhine-Westphalia in Germany. With more than 43,000 students and over 120 fields of study in 15 departments, it is Germany's ...

from 1945 to 1950, with one year at

ETH Zürich ETH Zurich (; ) is a public university in Zurich, Switzerland. Founded in 1854 with the stated mission to educate engineers and scientists, the university focuses primarily on science, technology, engineering, and mathematics. ETH Zurich ra ...

Career

Hirzebruch then held a position at

Erlangen Erlangen (; , ) is a Middle Franconian city in Bavaria, Germany. It is the seat of the administrative district Erlangen-Höchstadt (former administrative district Erlangen), and with 119,810 inhabitants (as of 30 September 2024), it is the smalle ...

, followed by the years 1952–54 at the

Institute for Advanced Study The Institute for Advanced Study (IAS) is an independent center for theoretical research and intellectual inquiry located in Princeton, New Jersey. It has served as the academic home of internationally preeminent scholars, including Albert Ein ...

Princeton, New Jersey The Municipality of Princeton is a Borough (New Jersey), borough in Mercer County, New Jersey, United States. It was established on January 1, 2013, through the consolidation of the Borough of Princeton, New Jersey, Borough of Princeton and Pri ...

. After one year at

Princeton University Princeton University is a private university, private Ivy League research university in Princeton, New Jersey, United States. Founded in 1746 in Elizabeth, New Jersey, Elizabeth as the College of New Jersey, Princeton is the List of Colonial ...

1955–56, he was made a professor at the

University of Bonn The University of Bonn, officially the Rhenish Friedrich Wilhelm University of Bonn (), is a public research university in Bonn, North Rhine-Westphalia, Germany. It was founded in its present form as the () on 18 October 1818 by Frederick Willi ...

, where he remained, becoming director of the '' Max-Planck-Institut für Mathematik'' in 1981. More than 300 people gathered in celebration of his 80th birthday in Bonn in 2007. The Hirzebruch–Riemann–Roch theorem (1954) for

complex manifolds In differential geometry and complex geometry, a complex manifold is a manifold with a ''complex structure'', that is an atlas of charts to the open unit disc in the complex coordinate space \mathbb^n, such that the transition maps are holom ...

was a major advance and quickly became part of the mainstream developments around the classical

Riemann–Roch theorem The Riemann–Roch theorem is an important theorem in mathematics, specifically in complex analysis and algebraic geometry, for the computation of the dimension of the space of meromorphic functions with prescribed zeros and allowed poles. It re ...

; it was also a precursor of the

Atiyah–Singer index theorem In differential geometry, the Atiyah–Singer index theorem, proved by Michael Atiyah and Isadore Singer (1963), states that for an elliptic differential operator on a compact manifold, the analytical index (related to the dimension of the space ...

and Grothendieck's powerful generalisation. Hirzebruch's book ''Neue topologische Methoden in der algebraischen Geometrie'' (1956) was a basic text for the 'new methods' of

sheaf theory In mathematics, a sheaf (: sheaves) is a tool for systematically tracking data (such as sets, abelian groups, rings) attached to the open sets of a topological space and defined locally with regard to them. For example, for each open set, the d ...

, in complex algebraic geometry. He went on to write the foundational papers on

topological K-theory In mathematics, topological -theory is a branch of algebraic topology. It was founded to study vector bundles on topological spaces, by means of ideas now recognised as (general) K-theory that were introduced by Alexander Grothendieck. The early ...

with

Michael Atiyah Sir Michael Francis Atiyah (; 22 April 1929 – 11 January 2019) was a British-Lebanese mathematician specialising in geometry. His contributions include the Atiyah–Singer index theorem and co-founding topological K-theory. He was awarded the ...

, and collaborated with

Armand Borel Armand Borel (21 May 1923 – 11 August 2003) was a Swiss mathematician, born in La Chaux-de-Fonds, and was a permanent professor at the Institute for Advanced Study in Princeton, New Jersey, United States from 1957 to 1993. He worked in alg ...

on the theory of

characteristic class In mathematics, a characteristic class is a way of associating to each principal bundle of ''X'' a cohomology class of ''X''. The cohomology class measures the extent to which the bundle is "twisted" and whether it possesses sections. Characterist ...

es. In his later work, he provided a detailed theory of

Hilbert modular surface In mathematics, a Hilbert modular surface or Hilbert–Blumenthal surface is an algebraic surface obtained by taking a quotient of a product of two copies of the upper half-plane by a Hilbert modular group. More generally, a Hilbert modular vari ...

s, with

Don Zagier Don Bernard Zagier (born 29 June 1951) is an American-German mathematician whose main area of work is number theory. He is currently one of the directors of the Max Planck Institute for Mathematics in Bonn, Germany. He was a professor at the ''Co ...

. He even found connections between the Dedekind sum in

number theory Number theory is a branch of pure mathematics devoted primarily to the study of the integers and arithmetic functions. Number theorists study prime numbers as well as the properties of mathematical objects constructed from integers (for example ...

and

differential topology In mathematics, differential topology is the field dealing with the topological properties and smooth properties of smooth manifolds. In this sense differential topology is distinct from the closely related field of differential geometry, which ...

, one of the many discoveries found between these different fields. His work influenced a generation of prominent mathematicians like Kunihiko Kodaira,

John Milnor John Willard Milnor (born February 20, 1931) is an American mathematician known for his work in differential topology, algebraic K-theory and low-dimensional holomorphic dynamical systems. Milnor is a distinguished professor at Stony Brook Uni ...

, Borel, Atiyah,

Raoul Bott Raoul Bott (September 24, 1923 – December 20, 2005) was a Hungarian-American mathematician known for numerous foundational contributions to geometry in its broad sense. He is best known for his Bott periodicity theorem, the Morse–Bott function ...

and

Jean-Pierre Serre Jean-Pierre Serre (; born 15 September 1926) is a French mathematician who has made contributions to algebraic topology, algebraic geometry and algebraic number theory. He was awarded the Fields Medal in 1954, the Wolf Prize in 2000 and the inau ...

. In March 1945, Hirzebruch became a soldier, and in April, in the last weeks of Hitler's rule, he was taken prisoner by the British forces then invading Germany from the west. When a British soldier found that he was studying mathematics, he drove him home, released him, and told him to continue studying. Hirzebruch is famous for organizing the Mathematische Arbeitstagung ("working meetings" in German) in

Bonn University The University of Bonn, officially the Rhenish Friedrich Wilhelm University of Bonn (), is a public research university in Bonn, North Rhine-Westphalia, Germany. It was founded in its present form as the () on 18 October 1818 by Frederick Will ...

, beginning in 1957, and the first speakers include Atiyah,

Jacques Tits Jacques Tits () (12 August 1930 – 5 December 2021) was a Belgian-born French mathematician who worked on group theory and incidence geometry. He introduced Tits buildings, the Tits alternative, the Tits group, and the Tits metric. Early life ...

Alexander Grothendieck Alexander Grothendieck, later Alexandre Grothendieck in French (; ; ; 28 March 1928 – 13 November 2014), was a German-born French mathematician who became the leading figure in the creation of modern algebraic geometry. His research ext ...

, Hans Grauert,

Nicolaas Kuiper Nicolaas Hendrik Kuiper (; 28 June 1920 – 12 December 1994) was a Dutch mathematician, known for Kuiper's test and proving Kuiper's theorem. He also contributed to the Nash embedding theorem. Kuiper studied at University of Leiden in 1937- ...

, and Hirzebruch himself. It allowed international cooperation in the mathematical world for the last 60 years and was a major source of developments in

geometry Geometry (; ) is a branch of mathematics concerned with properties of space such as the distance, shape, size, and relative position of figures. Geometry is, along with arithmetic, one of the oldest branches of mathematics. A mathematician w ...

group theory In abstract algebra, group theory studies the algebraic structures known as group (mathematics), groups. The concept of a group is central to abstract algebra: other well-known algebraic structures, such as ring (mathematics), rings, field ( ...

as well as

mathematical physics Mathematical physics is the development of mathematics, mathematical methods for application to problems in physics. The ''Journal of Mathematical Physics'' defines the field as "the application of mathematics to problems in physics and the de ...

in a few decades' time. He also established the

Max Planck Institute for Mathematics The Max Planck Institute for Mathematics (, MPIM) is a research institute located in Bonn, Germany. It is named in honor of the German physicist Max Planck and forms part of the Max Planck Society (''Max-Planck-Gesellschaft''), an association o ...

at Bonn in 1980. The institute became the place for the Arbeitstagung and Hirzebruch was its director until 1995. The second Arbeitstagung began in 1993 and continues to this day. From 1970 to 1971 he was the Donegall Lecturer in Mathematics at

Trinity College Dublin Trinity College Dublin (), officially titled The College of the Holy and Undivided Trinity of Queen Elizabeth near Dublin, and legally incorporated as Trinity College, the University of Dublin (TCD), is the sole constituent college of the Unive ...

. According to the

Mathematics Genealogy Project The Mathematics Genealogy Project (MGP) is a web-based database for the academic genealogy of mathematicians.. it contained information on 300,152 mathematical scientists who contributed to research-level mathematics. For a typical mathematicia ...

, Hirzebruch has supervised the doctoral studies of 52 mathematicians. Some of them include Egbert Brieskorn, Matthias Kreck,

, Detlef Gromoll, Klaus Jänich, Lothar Göttsche, Dietmar Arlt, Winfried Scharlau, Walter Neumann, Wolfgang Meyer, Kang Zuo, Hans Scheerer, Erich Ossa, Klaus Lamotke, Eduardo Mendoza, Dimitrios Dais and Friedhelm Waldhausen. Hirzebruch died at the age of 84 on 27 May 2012.

Honours and awards

Amongst many other honours, Hirzebruch was awarded the

Wolf Prize in Mathematics The Wolf Prize in Mathematics is awarded almost annually by the Wolf Foundation in Israel. It is one of the six Wolf Prizes established by the Foundation and awarded since 1978; the others are in Agriculture, Chemistry, Medicine, Physics and Arts. ...

in 1988 and a Lobachevsky Medal in 1989. The government of Japan awarded him the

Order of the Sacred Treasure The is a Japanese Order (distinction), order, established on 4 January 1888 by Emperor Meiji as the Order of Meiji. Originally awarded in eight classes (from 8th to 1st, in ascending order of importance), since 2003 it has been awarded in six c ...

in 1996 and the Seki-Takakazu prize of the Mathematical Society of Japan (MSJ) in 1997.L'Harmattan web site (in French)
Order with gold and silver rays Hirzebruch won an Einstein Medal of the Albert Einstein Society in Bern in 1999, and received the Cantor medal in 2004. Hirzebruch was a foreign member of numerous academies and societies, including the

United States National Academy of Sciences The National Academy of Sciences (NAS) is a United States nonprofit, non-governmental organization. NAS is part of the National Academies of Sciences, Engineering, and Medicine, along with the National Academy of Engineering (NAE) and the Nati ...

, the

Russian Academy of Sciences The Russian Academy of Sciences (RAS; ''Rossíyskaya akadémiya naúk'') consists of the national academy of Russia; a network of scientific research institutes from across the Russian Federation; and additional scientific and social units such ...

, the

Royal Society The Royal Society, formally The Royal Society of London for Improving Natural Knowledge, is a learned society and the United Kingdom's national academy of sciences. The society fulfils a number of roles: promoting science and its benefits, re ...

and the

French Academy of Sciences The French Academy of Sciences (, ) is a learned society, founded in 1666 by Louis XIV at the suggestion of Jean-Baptiste Colbert, to encourage and protect the spirit of French Scientific method, scientific research. It was at the forefron ...

. In 1980–81 he delivered the first Sackler Distinguished Lecture in Israel. He was also a member of academies of Russia, Poland, Ukraine, Israel, Finland, Hungary, Netherlands,

Göttingen Göttingen (, ; ; ) is a college town, university city in Lower Saxony, central Germany, the Capital (political), capital of Göttingen (district), the eponymous district. The River Leine runs through it. According to the 2022 German census, t ...

, Austria, and Ireland as well as the

Academia Europaea The Academia Europaea is a pan-European Academy of humanities, letters, law, and sciences. The Academia was founded in 1988 as a functioning Europe-wide Academy that encompasses all fields of scholarly inquiry. It acts as co-ordinator of Europe ...

and the European Academy of Arts and Sciences. Hirzebruch was the president of the

German Mathematical Society The German Mathematical Society (, DMV) is the main professional society of German mathematicians and represents German mathematics within the European Mathematical Society (EMS) and the International Mathematical Union (IMU). It was founded in ...

in 1962 and 1990, first after the foundation of a separate Eastern German mathematical due to the German division, and then again after the collapse of the wall which led to the unification of the East and West German Mathematical societies. He was also the first President of the

European Mathematical Society The European Mathematical Society (EMS) is a European organization dedicated to the development of mathematics in Europe. Its members are different mathematical societies in Europe, academic institutions and individual mathematicians. The curren ...

from 1990 to 1994. In this way, he rebuilt the mathematical life in both Germany and Europe after the war.

References

External links

{{DEFAULTSORT:Hirzebruch, Friedrich 1927 births 2012 deaths Albert Einstein Medal recipients Algebraic geometers Foreign members of the Royal Society Foreign members of the USSR Academy of Sciences Foreign members of the Russian Academy of Sciences Knights Commander of the Order of Merit of the Federal Republic of Germany Members of the French Academy of Sciences Institute for Advanced Study visiting scholars Donegall Lecturers of Mathematics at Trinity College Dublin Foreign associates of the National Academy of Sciences People from Hamm People from the Province of Westphalia Recipients of the Order of the Sacred Treasure Recipients of the Pour le Mérite (civil class) University of Münster alumni Academic staff of the University of Erlangen-Nuremberg Academic staff of the University of Bonn Wolf Prize in Mathematics laureates German Army personnel of World War II Members of the German Academy of Sciences at Berlin 20th-century German mathematicians 21st-century German mathematicians German prisoners of war in World War II held by the United Kingdom Presidents of the European Mathematical Society Max Planck Institute directors Recipients of the Cothenius Medal Presidents of the German Mathematical Society