Serge Lang

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Serge Lang (2004)

Serge Lang (born May 19, 1927 in Saint-Germain-en-Laye near Paris , † September 12, 2005 in Berkeley , USA) was a French-American mathematician . He lived in the United States for most of his life. He was best known for his work on algebraic geometry and number theory and as the author of many textbooks. He was a member of the Nicolas Bourbaki writers' collective .

life and work

Lang grew up in Saint-Germain-en-Laye near Paris. His father was a businessman and his mother the concert pianist Helene Schlepianoff. He had a twin brother who became a basketball coach and a sister who became an actress. After the partial occupation of France by German troops, his family emigrated with him to the USA. In 1946, Lang earned a bachelor's degree in physics from the California Institute of Technology . After completing an 18-month military service in the US Army from 1946 to 1947 (during which he was partly stationed in Italy and Germany), he studied at Princeton University , where he worked under Emil Artin in 1951 , whose collected works he later co-edited , with a thesis on the topic of On Quasi Algebraic Closures . In the same year he received his first teaching position there.

From 1952 to 1953 he worked at the Institute for Advanced Study at Princeton; it followed until 1955 a lectureship at the University of Chicago . From 1955 he had a long-term professorship at Columbia University with visiting professorships at Harvard and Princeton Universities . After resigning due to a protest at Columbia University, he taught at Yale from 1972 before retiring in 2005.

His main field of work was Diophantine geometry (a word that he coined himself), i.e. the connection between number theory and algebraic geometry. Here he is also known for his talent for asking the right questions, his numerous guesses. In the 1950s he worked a. a. with the geometric analogues of the class field theory (that is, he studied them using function fields instead of number fields as in the classic case), in the 1960s and the like. a. with the theory of Diophantine approximations and the theory of transcendent numbers. Later he worked a. a. on the construction of number fields with module functions (modular units) and Rolf Nevanlinna's value distribution theory .

Lang had a very lively and very communicative nature, sometimes he could "get into the air" B. with chalk after students who made mistakes on the blackboard - a habit that he obviously took over from his teacher Emil Artin. Although his main interest was in mathematics, he also participated in non-mathematical controversies, e.g. B .:

  • Samuel P. Huntington's assertion that South Africa would be a “contented society” ( Political order in changing societies. 1968), whereby Lang especially disturbed what he saw as pseudo-mathematical arguments of Huntington. In 1986 he organized a (successful) campaign to prevent his admission to the National Academy of Sciences , to which he had just been elected the year before.
  • He also commented on (alleged) falsifications in science, e.g. B. the "Baltimore case". Nobel laureate biochemist David Baltimore stood behind an associate and co-author suspected of falsifying data and was forced to resign as President of Rockefeller University .
  • On the question of the cause of AIDS . In his AIDS debate, he was less concerned with doubts about the cause of the disease than with suspicion that the US health authorities were influencing research for political reasons and suppressing certain alternative research approaches.
  • A questionnaire that the social scientists Ladd and Lipset used to interview American professors in 1979 annoyed him so much that he wrote an entire book ( The File 1981) about it.

He put on long dossiers (his "files"), some of which he also published (his book Challenges ) , on the controversial topics of interest to him during the often years-long (by letter and telephone) discussion processes . In 1971 he resigned from his professorship at Columbia University in New York to protest against the university's actions against opponents of the Vietnam War . At the end of 1966 he also supported the candidacy of the left-wing journalist Robert Scheer for the House of Representatives pre-election for the Democrats in California, who lost just a little, but z. B. got the majority in Berkeley (Lang also wrote a book about this). He was well known among the editors of mathematical journals, because he never ignored criticism or even rejection of articles without comment.

In 1996, after a controversy surrounding his views on AIDS and HIV, Lang resigned from the American Mathematical Society (AMS) on the occasion of an article in the Notices of the AMS on the mathematical treatment of the AIDS epidemic listened for almost 50 years. In the dispute, he prematurely separated from the Bourbaki group, to which he also belonged for a long time. Also in order to take part (well prepared) in discussions in various faculties, he regularly visited Berkeley University for several decades in the summer , where he also had a permanent apartment. He often phoned his co-authors and colleagues for hours every day, often greeting them with just a short "It's me". Almost every year from 1956 to 2003 he took part in the “work conferences” organized by Friedrich Hirzebruch in Bonn.

In Mordell's review, Siegel's letter to Mordell, diophantine geometry and 20th century mathematics , Mitteilungen der DMV ( Deutsche Mathematiker-Vereinigung ) 1994, he comments on Carl's rejection of the abstract direction of mathematics in France and the USA, which was new in the 1960s Ludwig Siegel in a letter to Louis Mordell, who sympathized with him . Mordell had panned Serge Lang's Diophantine Geometry and Siegel expressed his approval, comparing this direction with the “poaching of pigs” in a beautiful garden or the deployment of the SA storm troops.

His numerous textbooks are partly standard works and sometimes even the (almost) only textbooks on a certain area (e.g. his books on Diophantine geometry and Arakelov geometry). For example, his very influential book Algebra (first in 1965) became the model for all later textbooks in the field. Perhaps his most widely used textbook is his undergraduate calculus . There was a joke rumor that "Bourbaki" had given up writing books because Lang had done it (one review even called him a "one-man Bourbaki"). His book on group cohomology emerged from a related Bourbaki project.

Serge Lang was known for taking care of his students. He invited them to eat and listen to music, and secretly supported some of them (as well as other people in need) financially. His doctoral students include a. Minhyong Kim , Stephen Schanuel , Marvin Greenberg , William Cherry and David Rohrlich . He also gave lectures to a wider audience and to students (he made books out of some). Music was a hobby he pursued intensively at times (he also composed and played the piano and the lute), which he gave up from one day to the next in favor of other activities.



I want to make people think. (quoted from Hirzebruch in his obituary in the Notices of the AMS)

Your notation sucks. (a popular comment by Lang, in case something bothered him)


Serge Lang is the author of more than 50 books and over 120 articles.


  • Collected papers , 5 vols., Springer 2000

Books to introduce mathematics:

  • Maths! - Encounters between a scientist and students , vieweg 1990
  • The fascination of mathematics - a scientist presents himself to the public , vieweg 1989 (Original The Beauty of doing mathematics - 3 public dialogues ), Springer 1985, (including William Thurston's classification of three-dimensional hyperbolic manifolds)
  • Basic mathematics , Springer 1988

Books on algebra:

  • Algebra , 3rd edition, Addison-Wesley 1993 / Springer 2002 (he received the Steele Prize especially for this book)
  • Linear Algebra , Springer 1989
  • Introduction to linear algebra , Springer 1997
  • Undergraduate algebra , Springer 1990, 2nd ed.
  • Algebraic structures , Göttingen 1979 (first Algebraic structures 1967)
  • Topics in the cohomology of groups , Springer 1986 (first French Rapport sur la cohomologie des groupes , New York, Benjamin 1966)
  • SL 2 (R) , Springer 1985 (first 1975) (including representation theory of these groups according to Harish-Chandra )

Books on analysis, differential geometry, complex analysis:

  • A first course in calculus , Springer 1986, 5th edition (first 1964), 2001 as Short calculus
  • Undergraduate Analysis , Springer 2005, 4th ed.
  • Calculus of several variables , Springer 1996
  • Complex analysis , Springer 1993
  • Real and functional analysis , Springer 1993, 3rd ed.
  • Differential manifolds Springer 1985 (first 1972), as well as Differential and Riemannian manifolds , Springer 1996
  • Fundamentals of differential geometry , Springer 1999
  • An introduction to differentible manifolds , Springer 2002
  • with Cherry Topics in Nevanlinna Theory , Springer, Lecture Notes in Mathematics, 1990 (as a basis for understanding Paul Vojta's proof of Mordell's conjecture / Faltings ' theorem)
  • Introduction to complex hyperbolic spaces , Springer 1987
  • with Jay Jorgensen The heat kernel and Theta inversion on SL (2, C) , Springer 2007 (Lang's last research area)
  • this. Explicit formulas for regularized products and series , Springer 1994
  • this. Basic analysis of regularized products and series , Springer 1993

Books on number theory, arithmetic geometry:

  • Introduction to diophantine approximations , Springer 1995, revised new edition (first 1966)
  • Introduction to algebraic number theory , Springer 1994, 2nd edition ( Algebraic Numbers was published by Addison-Wesley in 1964)
  • Complex multiplication , Springer 1983
  • Introduction to transcendental numbers , Addison-Wesley 1966
  • Diophantine geometry , Springer 1990 (in the Encyclopaedia of mathematical sciences series , Volume 3 of the Number theory department )
  • Fundamentals of diophantine geometry , Springer 1983
  • Cyclotomic fields , Vol. 1 and 2, Springer 1978, 1980, 2nd edition in one volume 1990 (with contribution from Karl Rubin )
  • with Daniel Kubert Modular units , Springer 1981
  • Introduction to Arakelov theory , Springer 1988
  • with Hale Trotter Frobenius distributions on GL 2 -extensions , Springer 1976

Books on algebraic geometry, Abelian varieties , algebraic functions, elliptic curves:

  • Introduction to algebraic geometry , New York, Interscience, 1958
  • Abelian varieties , Springer 1983 (first 1959)
  • with William Fulton Riemann-Roch Algebra , Springer 1985
  • Introduction to modular forms , Springer 1996, 2nd ed.
  • Elliptic functions , 2nd ed., Springer 1985 (first 1973)
  • Elliptic curves - diophantine analysis , Springer 1978
  • Introduction to algebraic and abelian functions , 2nd ed., Springer 1982

Other books:

  • with Murrow Geometry - a high school course , 2nd edition, Springer 1988
  • Challenges , Springer 1998 (a book with some of its controversies)
  • The File , Springer 1981

Some essays and reviews:

Some of Lang's works, e.g. B. Report on diophantine approximations Bull. SMF 1965, Integral points on curves , Pub.Math.IHES 1960 are online here: [1]


  • Review of Serge Lang's book Challenges by Steven Krantz, Mathematical Intelligencer 1999, No. 3
  • Biography in the Notices of the AMS 1999, No. 4 on the occasion of the award of the Steele Prize (he also comments there on his dispute with the AMS)

Web links

Individual evidence

  1. Also published in Gazette des Mathematiciens, Notices of the American Mathematical Society 1995. Online as a PDF file  ( page no longer available , search in web archivesInfo: The link was automatically marked as defective. Please check the link according to the instructions and then remove this notice.@1@ 2Template: Toter Link /  
  2. Serge Lang in the Mathematics Genealogy Project (English)Template: MathGenealogyProject / Maintenance / id used