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.
Awards as expositorEdit
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.'" 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).
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). 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. This led to a public and highly acrimonious conflict as detailed in his book The File : Case Study in Correction (1977-1979).
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. 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. 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.
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. Some of the files were published in his books Challenges and The File : Case Study in Correction (1977-1979). His extensive file criticizing Nobel laureate David Baltimore was published in the journal Ethics and Behaviour in January 1993 and in his book Challenges. 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. 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.
List of booksEdit
Lang, Serge (1986). A first course in calculus. Undergraduate Texts in Mathematics (Fifth edition of 1964 original ed.). New York: Springer-Verlag. doi:10.1007/978-1-4419-8532-3. ISBN 978-1-4612-6428-6. The 1964 first edition was reprinted as:
Short calculus: the original edition of "A First Course in Calculus". Undergraduate Texts in Mathematics. New York: Springer-Verlag. 2002. doi:10.1007/978-1-4613-0077-9. ISBN 978-0-387-95327-4.
Lang, Serge (1986). Introduction to linear algebra. Undergraduate Texts in Mathematics (Second edition of 1970 original ed.). New York: Springer-Verlag. doi:10.1007/978-1-4612-1070-2. ISBN 978-0-387-96205-4.
Lang, Serge (1987). Calculus of several variables. Undergraduate Texts in Mathematics (Third edition of 1973 original ed.). New York: Springer-Verlag. doi:10.1007/978-1-4612-1068-9. ISBN 978-0-387-96405-8. Originally published as A Second Course in Calculus (1965)
Lang, Serge (1987). Linear algebra. Undergraduate Texts in Mathematics (Third edition of 1966 original ed.). New York: Springer-Verlag. doi:10.1007/978-1-4757-1949-9. ISBN 0-387-96412-6. MR0874113.
Shakarchi, Rami (1996). Solutions manual for Lang's "Linear Algebra". New York: Springer-Verlag. doi:10.1007/978-1-4612-0755-9. ISBN 0-387-94760-4. MR1415837.
Lang, Serge (1988). Basic mathematics (Reprint of 1971 original ed.). New York: Springer-Verlag.
Lang, Serge; Murrow, Gene (1988). Geometry: a high school course. New York: Springer-Verlag. doi:10.1007/978-1-4757-2022-8. ISBN 978-0-387-96654-0.
Lang, Serge (1997). Undergraduate analysis. Undergraduate Texts in Mathematics (Second ed.). New York: Springer-Verlag. doi:10.1007/978-1-4757-2698-5. ISBN 0-387-94841-4. MR1476913. The first edition (1983) of this title was itself the second edition of Analysis I (1968)
Shakarchi, Rami (1998). Problems and solutions for "Undergraduate Analysis". New York: Springer-Verlag. doi:10.1007/978-1-4612-1738-1. ISBN 0-387-98235-3. MR1488961.
Shakarchi, Rami (1999). Problems and solutions for "Complex Analysis". New York: Springer-Verlag. doi:10.1007/978-1-4612-1534-9. ISBN 978-0-387-98831-3. MR1716449.
Lang, Serge (2005). Undergraduate algebra. Undergraduate Texts in Mathematics (Third edition of 1990 original ed.). New York: Springer-Verlag. doi:10.1007/0-387-27475-8. ISBN 0-387-22025-9. The 1990 first edition was itself a second edition of Algebraic Structures (1967)
Lang, Serge (1993). Real and functional analysis. Graduate Texts in Mathematics. Vol. 142 (Third ed.). New York: Springer-Verlag. doi:10.1007/978-1-4612-0897-6. ISBN 0-387-94001-4. MR1216137. This book is the third edition, previously published under the different titles of Analysis II (1968) and Real Analysis (1983)
Lang, Serge (1995). Introduction to Diophantine approximations (Second edition of 1966 original ed.). New York: Springer-Verlag. doi:10.1007/978-1-4612-4220-8. ISBN 0-387-94456-7. MR1348400.
Lang, Serge (1995). Introduction to modular forms. Grundlehren der mathematischen Wissenschaften. Vol. 222. With appendixes by D. Zagier and Walter Feit (Corrected reprint of the 1976 original ed.). Berlin: Springer-Verlag. doi:10.1007/978-3-642-51447-0. ISBN 3-540-07833-9. MR1363488.
Lang, Serge (1999). Fundamentals of differential geometry. Graduate Texts in Mathematics. Vol. 191. New York: Springer-Verlag. doi:10.1007/978-1-4612-0541-8. ISBN 0-387-98593-X. MR1666820. This book is the fourth edition, previously published under the different titles of Introduction to Differentiable Manifolds (1962), Differential Manifolds (1972), and Differential and Riemannian Manifolds (1995). Lang also published a distinct second edition (preserving the title of the 1962 original) so as to provide a companion volume to Fundamentals of Differential Geometry which covers a portion of the same material, but with the more elementary exposition confined to finite-dimensional manifolds:
Jorgenson, Jay; Lang, Serge (2008). The heat kernel and theta inversion on SL2(C). Springer Monographs in Mathematics. New York: Springer. doi:10.1007/978-0-387-38032-2. ISBN 978-0-387-38031-5. MR2449649.
Lang, Serge (2000). Collected papers. I. 1952–1970. Springer Collected Works in Mathematics. New York: Springer. ISBN 0-387-98802-5. MR1772967.
Lang, Serge (2000). Collected papers. II. 1971–1977. Springer Collected Works in Mathematics. New York: Springer. ISBN 0-387-98803-3. MR1770235.
Lang, Serge (2000). Collected papers. III. 1978–1990. Springer Collected Works in Mathematics. New York: Springer. ISBN 0-387-98800-9. MR1781669.
Lang, Serge (2000). Collected papers. IV. 1990–1996. Springer Collected Works in Mathematics. New York: Springer. ISBN 0-387-98804-1. MR1781668.
Lang, Serge (2001). Collected papers. V. 1993–1999. Springer Collected Works in Mathematics. New York: Springer. ISBN 0-387-95030-3. MR1781684.
^Kalichman, Seth (2009). Denying AIDS: Conspiracy Theories, Pseudoscience, and Human Tragedy. Springer. p. 182. ISBN 9780387794761. Lang descended into HIV/AIDS denialism and protested what he saw as the unjust treatment of Duesberg. He conducted a flawed analysis of Duesberg's grant failings and called into question the entire NIH review process. He also caused a bit of commotion on the Yale campus when AIDS speakers visited. He protested the appointment of former Global AIDS Program Director at the World Health Organization Michael Merson as Yale's Dean of Public Health and launched a series of letter writing campaigns to Yale administrators about the role the university was playing in the global AIDS conspiracy.