Serge Lang | |
---|---|

Born | Paris, France | May 19, 1927

Died | September 12, 2005 | (aged 78)

Citizenship | French American |

Education | California Institute of Technology (B.A.) Princeton University (Ph.D.) |

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 | Minhyong Kim Stephen Schanuel |

**Serge Lang** (French: [lɑ̃ɡ]; May 19, 1927 – September 12, 2005) was a French-American mathematician and activist who taught at Yale University for most of his career. He is known for his work in number theory and for his mathematics textbooks, including the influential *Algebra*. He received the Frank Nelson Cole Prize in 1960 and was a member of the Bourbaki group.

As an activist, Lang campaigned against the Vietnam War, and also successfully fought against the nomination of the political scientist Samuel P. Huntington to the National Academies of Science. Later in his life, Lang was an HIV/AIDS denialist. He claimed that HIV had not been proven to cause AIDS and protested Yale's research into HIV/AIDS.^{[1]}

Lang was born in Saint-Germain-en-Laye, close to Paris, in 1927. He had a twin brother who became a basketball coach and a sister who became an actress.^{[2]} Lang moved with his family to California as a teenager, where he graduated in 1943 from Beverly Hills High School. He subsequently graduated with an A.B. from the California Institute of Technology in 1946. He then received a Ph.D. in mathematics 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.

Lang studied at Princeton University, writing his thesis titled "On quasi algebraic closure" under the supervision of Emil Artin,^{[3]}^{[4]} and 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–Trotter conjecture, and the Lang conjecture on analytically hyperbolic varieties. He introduced the Lang map,^{[5]} the Katz–Lang finiteness theorem, and the Lang–Steinberg theorem (cf. Lang's theorem) in algebraic groups.

Lang 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 graduate-level 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 graduate-level 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.

Lang was noted for his eagerness for contact with students. He was described as a passionate teacher who would throw chalk at students who he believed were not paying attention. One of his colleagues recalled: "He would rant and rave in front of his students. He would say, 'Our two aims are truth and clarity, and to achieve these I will shout in class.'"^{[6]} 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).

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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 anti-war 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 anti-war 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. Lang said it contained numerous biased and loaded questions.^{[7]} This led to a public and highly acrimonious conflict as detailed in his book *The File : Case Study in Correction (1977-1979)*.^{[8]}

In 1986, Lang mounted what the *New York Times* described as a "one-man challenge" against the nomination of political scientist Samuel P. Huntington to the National Academy of Sciences.^{[6]} 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.^{[9]} Lang's detailed description of these events, "Academia, Journalism, and Politics: A Case Study: The Huntington Case", occupies the first 222 pages of his 1998 book *Challenges*.^{[10]}

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 mathematicians and other interested parties throughout the world.^{[2]} Some of the files were published in his books *Challenges*^{[11]} and *The File : Case Study in Correction (1977-1979)*.^{[8]} His extensive file criticizing Nobel laureate David Baltimore was published in the journal *Ethics and Behaviour* in January 1993^{[12]} and in his book *Challenges*.^{[11]} 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 HIV/AIDS denialist.^{[13]} He maintained that the prevailing scientific consensus that HIV causes AIDS had not been backed up by reliable scientific research, yet for political and commercial reasons further research questioning the current point of view was suppressed. In public he was very outspoken about this point and a portion of *Challenges* is devoted to this issue.^{[11]}

- Lang, Serge (20 March 2019).
*Introduction to Algebraic Geometry*. ISBN 978-0486839806.^{[14]} - Lang, Serge (13 February 2019).
*Abelian Varieties*. ISBN 9780486839769. *Diophantine Geometry*(1962)^{[15]}^{[16]}*Introduction to Differentiable Manifolds*. Universitext. 2002. doi:10.1007/b97450. ISBN 978-0-387-95477-6.^{[17]}*A First Course in Calculus*. Undergraduate Texts in Mathematics. 1986. doi:10.1007/978-1-4419-8532-3. ISBN 978-1-4612-6428-6.*Short Calculus*. Undergraduate Texts in Mathematics. 2002. doi:10.1007/978-1-4613-0077-9. ISBN 978-0-387-95327-4.

*Algebraic Numbers*(1964)*A Second Course in Calculus*(Addison-Wesley, 1965)^{[18]}^{[19]}^{[20]}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)^{[21]}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)^{[22]}*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)^{[23]}*SL*(1975)_{2}(R)^{[24]}*Introduction to Modular Forms*(1976)^{[25]}*Complex Analysis*(1977)*Cyclotomic Fields*(1978)*Elliptic Curves: Diophantine Analysis*(1978)^{[26]}*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)*Riemann-Roch Algebra*. Grundlehren der mathematischen Wissenschaften. Vol. 277. 1985. doi:10.1007/978-1-4757-1858-4. ISBN 978-1-4419-3073-6.*Introduction To Complex Hyperbolic Spaces*(1987)^{[27]}*Geometry*(1988)*Introduction to Arakelov Theory*(1988)^{[28]}*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)- Lang, S. (1997),
*Survey of Diophantine geometry*, Berlin: Springer-Verlag, ISBN 3-540-61223-8, Zbl 0869.11051 *Fundamentals of Differential Geometry*(1999)*Math Talks for Undergraduates*(1999)- Shakarchi, Rami (1999).
*Problems and Solutions for Complex Analysis*. doi:10.1007/978-1-4612-1534-9. ISBN 978-0-387-98831-3. - Lang, Serge (29 May 2013).
*Collected Papers I: 1952-1970*. ISBN 978-1-4614-6136-4. - Lang, Serge (29 August 2013).
*Collected Papers II: 1971–1977*. ISBN 978-1461461371. - Lang, Serge (2 March 2013).
*Collected Papers III: 1978–1990*. ISBN 9781461461395. - Lang, Serge (29 May 2013).
*Collected Papers IV: 1990-1996*. ISBN 978-1461461388. - Lang, Serge (2 March 2013).
*Collected Papers V: 1993-1999*. ISBN 9780387950303. *Spherical Inversion on SL*(2001) with Jay Jorgenson_{n}(R)^{[29]}*Pos*(2005) with Jay Jorgenson_{n}(R) and Eisenstein Series*The Heat Kernel and Theta Inversion on SL*(2008) with Jay Jorgenson_{2}(C)*Heat Eisenstein series on SL*(2009) with Jay Jorgenson_{n}(C)