Serge Lang
This article includes a list of references, but its sources remain unclear because it has insufficient inline citations. (May 2016) (Learn how and when to remove this template message) 
Serge Lang  

Serge Lang (1927–2005)


Born 
Paris, France 
May 19, 1927
Died  September 12, 2005 Berkeley, California 
(aged 78)
Residence  United States 
Citizenship  French American 
Alma mater 
California Institute of Technology (B.A.) Princeton University (PhD) 
Known for  Work in number theory 
Awards 
Leroy P. Steele Prize (1999) Cole Prize (1960) 
Scientific career  
Fields  Mathematics 
Institutions 
University of Chicago Columbia University Yale University 
Thesis  On Quasi Algebraic Closure (1951) 
Doctoral advisor  Emil Artin 
Doctoral students 
Newcomb Greenleaf Minhyong Kim Joseph Repka David Rohrlich Stephen Schanuel 
Serge Lang (French: [lɑ̃ɡ]; May 19, 1927 – September 12, 2005) was a Frenchborn American mathematician and activist. He is known for his work in number theory and for his mathematics textbooks, including the influential Algebra. He was a member of the Bourbaki group. At the time of his death he was professor emeritus of mathematics at Yale University.
Contents
Biography
Serge Lang was born in SaintGermainenLaye close to Paris in 1927. Serge had a twin brother who became a basketball coach and a sister who became an actress.^{[1]}
Lang moved with his family to California as a teenager, where he graduated in 1943 from Beverly Hills High School. He subsequently graduated from the California Institute of Technology in 1946, and received a doctorate from Princeton University in 1951. He held faculty positions at the University of Chicago, Columbia University (from 1955, leaving in 1971 in a dispute), and Yale University.
Mathematical work
Lang studied under Emil Artin at Princeton University, writing his thesis on quasialgebraic closure.^{[2]} Lang then worked on the geometric analogues of class field theory and diophantine geometry. Later he moved into diophantine approximation and transcendental number theory, proving the Schneider–Lang theorem.
A break in research while he was involved in trying to meet 1960s student activism halfway caused him (by his own description) difficulties in picking up the threads afterwards. He wrote on modular forms and modular units, the idea of a 'distribution' on a profinite group, and value distribution theory.
He made a number of conjectures in diophantine geometry: Mordell–Lang conjecture, Bombieri–Lang conjecture, Lang's integral point conjecture, Lang–Trotter conjecture, Lang conjecture on Gamma values, Lang conjecture on analytically hyperbolic varieties, Lang's height conjecture...
He introduced the Lang map^{[3]} and the Lang–Steinberg theorem (cf. Lang's theorem) in algebraic groups.
He introduced the Katz–Lang finiteness theorem.
Mathematical books
He was a prolific writer of mathematical texts, often completing one on his summer vacation. Most are at the graduate level. He wrote calculus texts and also prepared a book on group cohomology for Bourbaki.
Lang's Algebra, a graduatelevel introduction to abstract algebra, was a highly influential text that ran through numerous updated editions. His Steele prize citation stated, "Lang's Algebra changed the way graduate algebra is taught...It has affected all subsequent graduatelevel algebra books." It contained ideas of his teacher, Artin; some of the most interesting passages in Algebraic Number Theory also reflect Artin's influence and ideas that might otherwise not have been published in that or any form.
Awards as expositor
Lang was noted for his eagerness for contact with students. Many of his students at Yale considered him to be one of the greatest teachers of mathematics in the world. He won a Leroy P. Steele Prize for Mathematical Exposition (1999) from the American Mathematical Society. In 1960, he won the sixth Frank Nelson Cole Prize in Algebra for his paper Unramified class field theory over function fields in several variables (Annals of Mathematics, Series 2, volume 64 (1956), pp. 285–325).
Activism
This section needs additional citations for verification. (May 2016) (Learn how and when to remove this template message) 
Lang spent much of his professional time engaged in political activism. He was a staunch socialist and active in opposition to the Vietnam War, volunteering for the 1966 antiwar campaign of Robert Scheer (the subject of his book The Scheer Campaign).^{[citation needed]} Lang later quit his position at Columbia in 1971 in protest over the university's treatment of antiwar protesters.
Lang engaged in several efforts to challenge anyone he believed was spreading misinformation or misusing science or mathematics to further their own goals. He attacked the 1977 Survey of the American Professoriate, an opinion questionnaire that Seymour Martin Lipset and E. C. Ladd had sent to thousands of college professors in the United States, accusing it of containing numerous biased and loaded questions.^{[4]} This led to a public and highly acrimonious conflict.
In 1986, Lang mounted what the New York Times described as a "oneman challenge" against the nomination of political scientist Samuel P. Huntington to the National Academy of Sciences.^{[5]} Lang described Huntington's research, in particular his use of mathematical equations to demonstrate that South Africa was a “satisfied society”, as "pseudoscience", arguing that it gave "the illusion of science without any of its substance." Despite support for Huntington from the Academy's social and behavioral scientists, Lang's challenge was successful, and Huntington was twice rejected for Academy membership. Huntington's supporters argued that Lang's opposition was political rather than scientific in nature.^{[6]}
Lang kept his political correspondence and related documentation in extensive "files". He would send letters or publish articles, wait for responses, engage the writers in further correspondence, collect all these writings together and point out what he considered contradictions. He often mailed these files to people he considered important; some of them were also published in his books Challenges (ISBN 0387948619) and The File (ISBN 038790607X). His extensive file criticizing Nobel laureate David Baltimore was published in the journal Ethics and Behaviour in January 1993.^{[7]} Lang fought the decision by Yale University to hire Daniel Kevles, a historian of science, because Lang disagreed with Kevles' analysis in The Baltimore Case.
Lang's most controversial political stance was as an AIDS denialist; he maintained that the prevailing scientific consensus that HIV causes AIDS has not been backed up by reliable scientific research, yet for political and commercial reasons further research questioning the current point of view is suppressed. In public he was very outspoken about this point and a portion of Challenges is devoted to this issue.
List of books
 Introduction to Algebraic Geometry (1958)^{[8]}
 Abelian Varieties (1959)
 Diophantine Geometry (1962)^{[9]}^{[10]}
 Introduction To Differentiable Manifolds (1962)^{[11]}
 A First Course in Calculus (1964), as Short Calculus (2001)
 Algebraic Numbers (1964)
 A Second Course in Calculus (AddisonWesley, 1965)^{[12]}^{[13]}^{[14]} ASIN B0007DW0KS
 Algebra (1965) and many later editions
 Algebraic Structures (1966)
 Introduction to Diophantine Approximations (1966)
 Introduction to Transcendental Numbers (1966)
 Linear Algebra (1966)
 Rapport sur la Cohomologie des Groupes (1966)^{[15]} as Topics in Cohomology of Groups (1986)
 A Complete Course in Calculus (1968)
 Analysis I (1968)
 Analysis II (1969)
 Real Analysis (1969)
 Algebraic Number Theory (1970)^{[16]}
 Introduction To Linear Algebra (1970)
 Basic Mathematics (1971)
 Differential Manifolds (1972)
 Introduction to Algebraic and Abelian Functions (1972)
 Calculus of Several Variables (1973)
 Elliptic Functions (1973)^{[17]}
 SL_{2}(R) (1975)^{[18]}
 Introduction to Modular Forms (1976)^{[19]}
 Complex Analysis (1977)
 Cyclotomic Fields (1978)
 Elliptic Curves: Diophantine Analysis (1978)^{[20]}
 Modular Units (1981) with Dan Kubert
 The File: Case Study in Correction 1977–1979 (1981)
 Undergraduate Analysis (1983)
 Complex Multiplication (1983)
 Fundamentals Of Diophantine Geometry (1983)
 The Beauty of Doing Mathematics: Three Public Dialogues (1985)
 Math!: Encounters with High School Students (1985)
 RiemannRoch Algebra (1985) with William Fulton
 Introduction To Complex Hyperbolic Spaces (1987)^{[21]}
 Geometry (1988)
 Introduction to Arakelov Theory (1988)^{[22]}
 Cyclotomic Fields II (1989)
 Undergraduate Algebra (1990)
 Real and Functional Analysis (1993)
 Differential and Riemannian Manifolds (1995)
 Basic Analysis of Regularized Series and Products (1993) with Jay Jorgenson
 Challenges (1997)
 Survey On Diophantine Geometry (1997)
 Fundamentals of Differential Geometry (1999)
 Math Talks for Undergraduates (1999)
 Problems and Solutions for Complex Analysis (1999) with Rami Shakarchi
 Collected Papers I: 1952–1970 (2000)
 Collected Papers II: 1971–1977 (2000)
 Collected Papers III: 1978–1990 (2000)
 Collected Papers IV: 1990–1996 (2000)
 Collected Papers V: 1993–1999 (Springer, 2000) ISBN 9780387950303
 Spherical Inversion on SL_{n}(R) (2001) with Jay Jorgenson^{[23]}
 Pos_{n}(R) and Eisenstein Series (2005) with Jay Jorgenson
 The Heat Kernel and Theta Inversion on SL_{2}(C) (2008) with Jay Jorgenson
 Heat Eisenstein series on SL_{n}(C) (2009) with Jay Jorgenson
Notes
 ^ Jorgenson, Jay; Krantz, Steven G., eds. (May 2006). "Serge Lang, 1927–2005" (PDF). Notices of the American Mathematical Society. 53 (5): 536–553.
 ^ Serge Lang at the Mathematics Genealogy Project
 ^ Daniel Bump, "The Lang Map"
 ^ Serge Lang (18 May 1978), "The Professors: A Survey of a Survey", The New York Review of Books available online as reprinted in Challenges
 ^ Change, Kenneth; Warren Leary (September 25, 2005). "Serge Lang, 78, a Gadfly and Mathematical Theorist, Dies". New York Times. Retrieved August 13, 2010.
 ^ Johnson, George; Laura Mansnerus (May 3, 1987). "Science Academy Rejects Harvard Political Scientist". New York Times. Retrieved August 13, 2010.
 ^ Questions of Scientific Responsibility: The Baltimore Case Reprinted from the journal Ethics and Behavior Vol. 3 No. 1 (1993) pp. 3–72, Serge Lang, Mathematics Department, Yale University
 ^ Rosenlicht, M. (1959). "Review: Introduction to algebraic geometry. By Serge Lang" (PDF). Bull. Amer. Math. Soc. 65 (6): 341–342. doi:10.1090/s00029904195910361x.
 ^ Mordell, L. J. (1964). "Review: Diophantine geometry. By Serge Lang" (PDF). Bull. Amer. Math. Soc. 70 (4): 491–498. doi:10.1090/s000299041964111642.
 ^ Lang, Serge (January 1995). "Mordell's review, Siegel's letter to Mordell, Diophantine Geomertry, and 20th century mathematics" (PDF). Gazette des mathématiciens (63): 17–36.
 ^ Abraham, Ralph (1964). "Review: Introduction to differential manifolds. By Serge Lang" (PDF). Bull. Amer. Math. Soc. 70 (2): 225–227. doi:10.1090/s000299041964110892.
 ^ Magill, K. D. (19650101). "Review of A Second Course in Calculus". The American Mathematical Monthly. 72 (9): 1048–1049. JSTOR 2313382. doi:10.2307/2313382.
 ^ Meacham, R. C. (19660101). "Review of A Second Course in Calculus". Mathematics Magazine. 39 (2): 124–124. JSTOR 2688730. doi:10.2307/2688730.
 ^ Niven, Ivan (19700101). "Review of A Second Course in Calculus". Mathematics Magazine. 43 (5): 277–278. JSTOR 2688750. doi:10.2307/2688750.
 ^ Hochschild, G. (1969). "Review: Rapport sur la cohomologie des groupes by Serge Lang" (PDF). Bull. Amer. Math. Soc. 75 (5): 927–929. doi:10.1090/s000299041969122949.
 ^ Corwin, Lawrence (1972). "Review: Algebraic Number Theory by Serge Lang" (PDF). Bull. Amer. Math. Soc. 78 (5): 690–693. doi:10.1090/s000299041972129847.
 ^ Roquette, Peter (1976). "Review: Elliptic functions, by Serge Lang" (PDF). Bull. Amer. Math. Soc. 82 (4): 523–526. doi:10.1090/s000299041976140827.
 ^ Langlands, R. P. (1976). "SL2(R), by Serge Lang" (PDF). Bull. Amer. Math. Soc. 82 (5): 688–691. doi:10.1090/s000299041976141092.
 ^ Terras, Audrey (1980). "Review: Introduction to modular forms, by Serge Lang" (PDF). Bull. Amer. Math. Soc. (N.S.). 2 (1): 206–214. doi:10.1090/s027309791980147229.
 ^ Baker, Alan (1980). "Review: Elliptic curves: Diophantine analysis, by Serge Lang" (PDF). Bull. Amer. Math. Soc. (N.S.). 2 (2): 352–354. doi:10.1090/s027309791980147564.
 ^ Green, Mark (1988). "Review: Introduction to complex hyperbolic spaces by Serge Lang". Bull. Amer. Math. Soc. (N.S.). 18 (2): 188–191. doi:10.1090/s027309791988156443.
 ^ Silverman, Joseph H. (1989). "Review: Introduction to Arakelov theory, by Serge Lang" (PDF). Bull. Amer. Math. Soc. (N.S.). 21 (1): 171–176. doi:10.1090/s027309791989158060.
 ^ Krötz, Bernhard (2002). "Spherical Inversion on SLn(R), by Jay Jorgenson and Serge Lang" (PDF). Bull. Amer. Math. Soc. (N.S.). 40 (1): 137–142. doi:10.1090/s027309790200962x.
References
 Steele Prize citation and Lang's acceptance (AMS Notices, April 1999)
 Jorgenson, Jay; Krantz, Steven G., eds. (May 2006). "Serge Lang, 1927–2005" (PDF). Notices of the American Mathematical Society. 53 (5): 536–553.
 Jorgenson, Jay; Krantz, Steven G., eds. (April 2007). "The Mathematical Contributions of Serge Lang" (PDF). Notices of the AMS. 54 (4): 476–497.
External links
Wikiquote has quotations related to: Serge Lang 
 Serge Lang at the Mathematics Genealogy Project
 Obituary from the New York Times
 Lang's obituary article in the Yale Daily News
 People from SaintGermainenLaye
 1927 births
 2005 deaths
 20thcentury American mathematicians
 21stcentury American mathematicians
 American nonfiction writers
 Nicolas Bourbaki
 Number theorists
 Princeton University alumni
 University of Chicago faculty
 Columbia University faculty
 Yale University faculty
 California Institute of Technology alumni
 HIV/AIDS denialists
 American anti–Vietnam War activists
 French emigrants to the United States
 Institute for Advanced Study visiting scholars
 Guggenheim Fellows
 Textbook writers