Serge Lang: Difference between revisions

Serge Lang
Serge Lang
	Serge Lang (1927–2005)
Born	May 19, 1927; Paris, France
Died	September 12, 2005 (aged 78); Berkeley, California
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

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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]

Biography and mathematical work

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.

Mathematical books

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 expositor

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).

Activism

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]

List of books

Pregraduate-level textbooks

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)^[14]^[15]^[16]
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. MR 0874113.

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. MR 1415837.

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. MR 1476913. 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. MR 1488961.

Lang, Serge (1999). Complex analysis. Graduate Texts in Mathematics. Vol. 103 (Fourth edition of 1977 original ed.). New York: Springer-Verlag. doi:10.1007/978-1-4757-3083-8. ISBN 0-387-98592-1. MR 1659317.

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. MR 1716449.

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)

Graduate-level textbooks

Lang, Serge (1966). Introduction to transcendental numbers. Reading, MA–London–Don Mills, Ontario: Addison-Wesley Publishing Co. MR 0214547.
Lang, Serge (1972). Introduction to algebraic geometry (Third printing, with corrections, of 1959 original ed.). Reading, MA: Addison-Wesley Publishing Co. MR 0344244.^[17]
Lang, Serge (1978). Elliptic curves: Diophantine analysis. Grundlehren der Mathematischen Wissenschaften. Vol. 231. Berlin–New York: Springer-Verlag. doi:10.1007/978-3-662-07010-9. ISBN 3-540-08489-4. MR 0518817.^[18]
Kubert, Daniel S.; Lang, Serge (1981). Modular units. Grundlehren der Mathematischen Wissenschaften. Vol. 244. New York–Berlin: Springer-Verlag. doi:10.1007/978-1-4757-1741-9. ISBN 0-387-90517-0. MR 0648603.
Lang, Serge (1982). Introduction to algebraic and abelian functions. Graduate Texts in Mathematics. Vol. 89 (Second edition of 1972 original ed.). New York–Berlin: Springer-Verlag. doi:10.1007/978-1-4612-5740-0. ISBN 0-387-90710-6. MR 0681120.
Lang, Serge (1983). Abelian varieties (Reprint of 1959 original ed.). New York–Berlin: Springer-Verlag. doi:10.1007/978-1-4419-8534-7. ISBN 0-387-90875-7. MR 0713430.
Lang, Serge (1983). Complex multiplication. Grundlehren der mathematischen Wissenschaften. Vol. 255. New York: Springer-Verlag. doi:10.1007/978-1-4612-5485-0. ISBN 0-387-90786-6. MR 0713612.
Lang, Serge (1983). Fundamentals of Diophantine geometry. New York: Springer-Verlag. doi:10.1007/978-1-4757-1810-2. ISBN 0-387-90837-4. MR 0715605. Second edition of Diophantine Geometry (1962)^[19]^[20]
Fulton, William; Lang, Serge (1985). Riemann–Roch Algebra. Grundlehren der mathematischen Wissenschaften. Vol. 277. New York: Springer-Verlag. doi:10.1007/978-1-4757-1858-4. ISBN 978-1-4419-3073-6. MR 0801033.
Lang, Serge (1985). SL₂(R). Graduate Texts in Mathematics. Vol. 105 (Reprint of the 1975 original ed.). New York: Springer-Verlag. doi:10.1007/978-1-4612-5142-2. ISBN 0-387-96198-4. MR 0803508.^[21]
Lang, Serge (1987). Elliptic functions. Graduate Texts in Mathematics. Vol. 112. With an appendix by J. Tate (Second edition of 1973 original ed.). New York: Springer-Verlag. doi:10.1007/978-1-4612-4752-4. ISBN 0-387-96508-4. MR 0890960.^[22]
Lang, Serge (1987). Introduction to complex hyperbolic spaces. New York: Springer-Verlag. doi:10.1007/978-1-4757-1945-1. ISBN 0-387-96447-9. MR 0886677.^[23]
Lang, Serge (1988). Introduction to Arakelov theory. New York: Springer-Verlag. doi:10.1007/978-1-4612-1031-3. ISBN 0-387-96793-1. MR 0969124.^[24]
Lang, Serge (1990). Cyclotomic fields I and II. Graduate Texts in Mathematics. Vol. 121. With an appendix by Karl Rubin (Combined second edition of 1978/1980 original ed.). New York: Springer-Verlag. doi:10.1007/978-1-4612-0987-4. ISBN 0-387-96671-4. MR 1029028.
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. MR 1216137. This book is the third edition, previously published under the different titles of Analysis II (1968) and Real Analysis (1983)
Jorgenson, Jay; Lang, Serge (1993). Basic analysis of regularized series and products. Lecture Notes in Mathematics. Vol. 1564. Berlin: Springer-Verlag. doi:10.1007/BFb0077194. ISBN 3-540-57488-3. MR 1284924.
Lang, Serge (1994). Algebraic number theory. Graduate Texts in Mathematics. Vol. 110 (Second edition of 1970 original ed.). New York: Springer-Verlag. doi:10.1007/978-1-4612-0853-2. ISBN 0-387-94225-4. MR 1282723.^[25] The first edition was itself the second edition of Algebraic Numbers (1964)
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. MR 1348400.
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. MR 1363488.^[26]
Lang, Serge (1996). Topics in cohomology of groups. Lecture Notes in Mathematics. Vol. 1625. Chapter X based on letters written by John Tate (Translated from the 1967 French original ed.). Berlin: Springer-Verlag. doi:10.1007/BFb0092624. ISBN 3-540-61181-9. MR 1439508.^[27]
Lang, S. (1997), Survey of Diophantine geometry, Berlin: Springer-Verlag, ISBN 3-540-61223-8, Zbl 0869.11051
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. MR 1666820. 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:

Lang, Serge (2002). Introduction to differentiable manifolds. Universitext (Second ed.). New York: Springer-Verlag. doi:10.1007/b97450. ISBN 0-387-95477-5. MR 1931083.^[28]

Jorgenson, Jay; Lang, Serge (2001). Spherical inversion on SL_n(R). Springer Monographs in Mathematics. New York: Springer-Verlag. doi:10.1007/978-1-4684-9302-3. ISBN 0-387-95115-6. MR 1834111.^[29]
Lang, Serge (2002). Algebra. Graduate Texts in Mathematics. Vol. 211 (Revised third edition of 1965 original ed.). New York: Springer-Verlag. doi:10.1007/978-1-4613-0041-0. ISBN 0-387-95385-X. MR 1878556.
Jorgenson, Jay; Lang, Serge (2005). Pos_n(R) and Eisenstein series. Lecture Notes in Mathematics. Vol. 1868. Berlin: Springer-Verlag. doi:10.1007/b136063. ISBN 978-3-540-25787-5. MR 2166237.
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. MR 2449649.
Jorgenson, Jay; Lang, Serge (2009). Heat Eisenstein series on SL_n(C). Memoirs of the American Mathematical Society. Vol. 201. doi:10.1090/memo/0946. ISBN 978-0-8218-4044-3. MR 2548067.

Other

The File: Case Study in Correction 1977–1979 (1981)
The Beauty of Doing Mathematics: Three Public Dialogues (1985)
Math!: Encounters with High School Students (1985)
Challenges (1997)
Math Talks for Undergraduates (1999)
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.

References

^ 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.
^ ^a ^b Jorgenson, Jay; Krantz, Steven G., eds. (May 2006). "Serge Lang, 1927–2005" (PDF). Notices of the American Mathematical Society. 53 (5): 536–553.
^ Lang, Serge (1951). On quasi algebraic closure. Princeton, N.J.: Princeton University.
^ Serge Lang at the Mathematics Genealogy Project
^ Daniel Bump, "The Lang Map"
^ ^a ^b Change, Kenneth; Warren Leary (September 25, 2005). "Serge Lang, 78, a Gadfly and Mathematical Theorist, Dies". New York Times. Retrieved August 13, 2010.
^ Serge Lang (18 May 1978), "The Professors: A Survey of a Survey", The New York Review of Books available online as reprinted in Challenges
^ ^a ^b Lang, Serge (1981). The File : Case Study in Correction (1977-1979). New York, NY: Springer New York. doi:10.1007/978-1-4613-8145-7. ISBN 978-1-4613-8145-7. Retrieved 4 May 2022.
^ Johnson, George; Laura Mansnerus (May 3, 1987). "Science Academy Rejects Harvard Political Scientist". New York Times. Retrieved August 13, 2010.
^ Lang, Serge (1999). Challenges. New York: Springer. ISBN 978-0-387-94861-4.
^ ^a ^b ^c O'Hara, Michael W.; Lang, Serge (1998). Challenges. Springer Science & Business Media. ISBN 978-0-387-94861-4. Retrieved 4 May 2022.
^ Questions of Scientific Responsibility: The Baltimore Case From the journal Ethics and Behavior Vol. 3 No. 1 (1993) pp. 3–72, Serge Lang, Mathematics Department, Yale University
^ Jorgenson, Jay; Krantz, Steven G., eds. (May 2006). "Serge Lang, 1927–2005" (PDF). Notices of the American Mathematical Society. 53 (5): 536–553.
^ Magill, K. D. (1965-01-01). "Review of A Second Course in Calculus". The American Mathematical Monthly. 72 (9): 1048–1049. doi:10.2307/2313382. JSTOR 2313382.
^ Meacham, R. C. (1966-01-01). "Review of A Second Course in Calculus". Mathematics Magazine. 39 (2): 124. doi:10.2307/2688730. JSTOR 2688730.
^ Niven, Ivan (1970-01-01). "Review of A Second Course in Calculus". Mathematics Magazine. 43 (5): 277–278. doi:10.2307/2688750. JSTOR 2688750.
^ Rosenlicht, M. (1959). "Review: Introduction to algebraic geometry. By Serge Lang" (PDF). Bull. Amer. Math. Soc. 65 (6): 341–342. doi:10.1090/s0002-9904-1959-10361-x.
^ 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/s0273-0979-1980-14756-4.
^ Mordell, L. J. (1964). "Review: Diophantine geometry. By Serge Lang" (PDF). Bull. Amer. Math. Soc. 70 (4): 491–498. doi:10.1090/s0002-9904-1964-11164-2.
^ 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.
^ Langlands, R. P. (1976). "SL₂(R), by Serge Lang" (PDF). Bull. Amer. Math. Soc. 82 (5): 688–691. doi:10.1090/s0002-9904-1976-14109-2.
^ Roquette, Peter (1976). "Review: Elliptic functions, by Serge Lang" (PDF). Bull. Amer. Math. Soc. 82 (4): 523–526. doi:10.1090/s0002-9904-1976-14082-7.
^ 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/s0273-0979-1988-15644-3.
^ 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/s0273-0979-1989-15806-0.
^ Corwin, Lawrence (1972). "Review: Algebraic Number Theory by Serge Lang" (PDF). Bull. Amer. Math. Soc. 78 (5): 690–693. doi:10.1090/s0002-9904-1972-12984-7.
^ 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/s0273-0979-1980-14722-9.
^ 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/s0002-9904-1969-12294-9.
^ Abraham, Ralph (1964). "Review: Introduction to differential manifolds. By Serge Lang" (PDF). Bull. Amer. Math. Soc. 70 (2): 225–227. doi:10.1090/s0002-9904-1964-11089-2.
^ Krötz, Bernhard (2002). "Spherical Inversion on SL_n(R), by Jay Jorgenson and Serge Lang" (PDF). Bull. Amer. Math. Soc. (N.S.). 40 (1): 137–142. doi:10.1090/s0273-0979-02-00962-x.

Sources and further reading

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

O'Connor, John J.; Robertson, Edmund F., "Serge Lang", MacTutor History of Mathematics Archive, University of St Andrews
Serge Lang at the Mathematics Genealogy Project
Obituary from the New York Times
Lang's obituary article in the Yale Daily News

[kalichman-1] 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.

[amsobit-2] Jorgenson, Jay; Krantz, Steven G., eds. (May 2006). "Serge Lang, 1927–2005" (PDF). Notices of the American Mathematical Society. 53 (5): 536–553.

[3] Lang, Serge (1951). On quasi algebraic closure. Princeton, N.J.: Princeton University.

[4] Serge Lang at the Mathematics Genealogy Project

[5] Daniel Bump, "The Lang Map"

[nyt-obit-6] Change, Kenneth; Warren Leary (September 25, 2005). "Serge Lang, 78, a Gadfly and Mathematical Theorist, Dies". New York Times. Retrieved August 13, 2010.

[7] Serge Lang (18 May 1978), "The Professors: A Survey of a Survey", The New York Review of Books available online as reprinted in Challenges

[thefile-8] Lang, Serge (1981). The File : Case Study in Correction (1977-1979). New York, NY: Springer New York. doi:10.1007/978-1-4613-8145-7. ISBN 978-1-4613-8145-7. Retrieved 4 May 2022.

[nyt-academy-9] Johnson, George; Laura Mansnerus (May 3, 1987). "Science Academy Rejects Harvard Political Scientist". New York Times. Retrieved August 13, 2010.

[10] Lang, Serge (1999). Challenges. New York: Springer. ISBN 978-0-387-94861-4.

[challenges-11] O'Hara, Michael W.; Lang, Serge (1998). Challenges. Springer Science & Business Media. ISBN 978-0-387-94861-4. Retrieved 4 May 2022.

[12] Questions of Scientific Responsibility: The Baltimore Case From the journal Ethics and Behavior Vol. 3 No. 1 (1993) pp. 3–72, Serge Lang, Mathematics Department, Yale University

[13] Jorgenson, Jay; Krantz, Steven G., eds. (May 2006). "Serge Lang, 1927–2005" (PDF). Notices of the American Mathematical Society. 53 (5): 536–553.

[14] Magill, K. D. (1965-01-01). "Review of A Second Course in Calculus". The American Mathematical Monthly. 72 (9): 1048–1049. doi:10.2307/2313382. JSTOR 2313382.

[15] Meacham, R. C. (1966-01-01). "Review of A Second Course in Calculus". Mathematics Magazine. 39 (2): 124. doi:10.2307/2688730. JSTOR 2688730.

[16] Niven, Ivan (1970-01-01). "Review of A Second Course in Calculus". Mathematics Magazine. 43 (5): 277–278. doi:10.2307/2688750. JSTOR 2688750.

[17] Rosenlicht, M. (1959). "Review: Introduction to algebraic geometry. By Serge Lang" (PDF). Bull. Amer. Math. Soc. 65 (6): 341–342. doi:10.1090/s0002-9904-1959-10361-x.

[18] 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/s0273-0979-1980-14756-4.

[19] Mordell, L. J. (1964). "Review: Diophantine geometry. By Serge Lang" (PDF). Bull. Amer. Math. Soc. 70 (4): 491–498. doi:10.1090/s0002-9904-1964-11164-2.

[20] 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.

[21] Langlands, R. P. (1976). "SL₂(R), by Serge Lang" (PDF). Bull. Amer. Math. Soc. 82 (5): 688–691. doi:10.1090/s0002-9904-1976-14109-2.

[22] Roquette, Peter (1976). "Review: Elliptic functions, by Serge Lang" (PDF). Bull. Amer. Math. Soc. 82 (4): 523–526. doi:10.1090/s0002-9904-1976-14082-7.

[23] 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/s0273-0979-1988-15644-3.

[24] 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/s0273-0979-1989-15806-0.

[25] Corwin, Lawrence (1972). "Review: Algebraic Number Theory by Serge Lang" (PDF). Bull. Amer. Math. Soc. 78 (5): 690–693. doi:10.1090/s0002-9904-1972-12984-7.

[26] 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/s0273-0979-1980-14722-9.

[27] 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/s0002-9904-1969-12294-9.

[28] Abraham, Ralph (1964). "Review: Introduction to differential manifolds. By Serge Lang" (PDF). Bull. Amer. Math. Soc. 70 (2): 225–227. doi:10.1090/s0002-9904-1964-11089-2.

[29] Krötz, Bernhard (2002). "Spherical Inversion on SL_n(R), by Jay Jorgenson and Serge Lang" (PDF). Bull. Amer. Math. Soc. (N.S.). 40 (1): 137–142. doi:10.1090/s0273-0979-02-00962-x.

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@@ Line 54: / Line 54: @@
 ==List of books==
 {{refbegin}}
+'''Pregraduate-level textbooks'''
-'''Textbooks'''
 {{Columns-list|colwidth=30em|
+* {{cite book|last1=Lang|first1=Serge|title=A first course in calculus|edition=Fifth edition of 1964 original|series=Undergraduate Texts in Mathematics|location=New York|publisher=[[Springer-Verlag]]|year=1986|isbn=978-1-4612-6428-6|doi=10.1007/978-1-4419-8532-3}} The 1964 first edition was reprinted as:
-* {{cite book |isbn=978-0486839806|title=Introduction to Algebraic Geometry|last1=Lang|first1=Serge|date=20 March 2019|url={{Google books|title=Introduction to Algebraic Geometry|8YeRDwAAQBAJ|plainurl=yes}}}}<ref>{{cite journal|author=Rosenlicht, M.|author-link=Maxwell Rosenlicht|title=Review: ''Introduction to algebraic geometry''. By Serge Lang|journal=Bull. Amer. Math. Soc.|year=1959|volume=65|issue=6|pages=341–342|url=http://www.ams.org/journals/bull/1959-65-06/S0002-9904-1959-10361-X/S0002-9904-1959-10361-X.pdf|doi=10.1090/s0002-9904-1959-10361-x|doi-access=free}}</ref>
+**{{cite book |doi=10.1007/978-1-4613-0077-9| title=Short calculus: the original edition of "A First Course in Calculus" | series=Undergraduate Texts in Mathematics | year=2002 | isbn=978-0-387-95327-4|publisher=[[Springer-Verlag]]|location=New York }}
-* {{cite book |isbn=9780486839769|title=Abelian Varieties|last1=Lang|first1=Serge|date=13 February 2019|url={{Google books|title=Abelian Varieties|7YeRDwAAQBAJ|plainurl=yes}}}}
+* {{cite book|last1=Lang|first1=Serge|title=Introduction to linear algebra|edition=Second edition of 1970 original|year=1986|doi=10.1007/978-1-4612-1070-2|publisher=[[Springer-Verlag]]|location=New York|series=Undergraduate Texts in Mathematics|isbn=978-0-387-96205-4}}
-* ''Diophantine Geometry'' (1962)<ref>{{cite journal|author=Mordell, L. J.|author-link=Louis J. Mordell|title=Review: ''Diophantine geometry''. By Serge Lang|journal=Bull. Amer. Math. Soc.|year=1964|volume=70|issue=4|pages=491–498|url=http://www.ams.org/journals/bull/1964-70-04/S0002-9904-1964-11164-2/S0002-9904-1964-11164-2.pdf|doi=10.1090/s0002-9904-1964-11164-2|doi-access=free}}</ref><ref>{{cite journal|author=Lang, Serge|title=Mordell's review, Siegel's letter to Mordell, Diophantine Geomertry, and 20th century mathematics|journal=Gazette des mathématiciens|date=January 1995|issue=63|pages=17–36|url=http://smf4.emath.fr/Publications/Gazette/1995/63/smf_gazette_63_17-36.pdf}}</ref>
+* {{cite book|last1=Lang|first1=Serge|title=Calculus of several variables|edition=Third edition of 1973 original|series=Undergraduate Texts in Mathematics|location=New York|publisher=[[Springer-Verlag]]|year=1987|isbn=978-0-387-96405-8|doi=10.1007/978-1-4612-1068-9}} Originally published as ''A Second Course in Calculus'' (1965)<ref>{{Cite journal|last=Magill|first=K. D.|date=1965-01-01|title=Review of A Second Course in Calculus|jstor=2313382|journal=The American Mathematical Monthly|volume=72|issue=9|pages=1048–1049|doi=10.2307/2313382}}</ref><ref>{{Cite journal|last=Meacham|first=R. C.|date=1966-01-01|title=Review of A Second Course in Calculus|jstor=2688730|journal=Mathematics Magazine|volume=39|issue=2|pages=124|doi=10.2307/2688730}}</ref><ref>{{Cite journal|last=Niven|first=Ivan|author-link=Ivan Niven|date=1970-01-01|title=Review of A Second Course in Calculus|jstor=2688750|journal=Mathematics Magazine|volume=43|issue=5|pages=277–278|doi=10.2307/2688750}}</ref>
-* {{cite book |doi=10.1007/978-1-4419-8532-3| title=A First Course in Calculus | series=Undergraduate Texts in Mathematics | year=1986 | isbn=978-1-4612-6428-6 }}
-**{{cite book |doi=10.1007/978-1-4613-0077-9| title=Short Calculus | series=Undergraduate Texts in Mathematics | year=2002 | isbn=978-0-387-95327-4 }}
+* {{cite book|mr=0874113|last1=Lang|first1=Serge|title=Linear algebra|edition=Third edition of 1966 original|series=Undergraduate Texts in Mathematics|publisher=[[Springer-Verlag]]|location=New York|year=1987|isbn=0-387-96412-6|doi=10.1007/978-1-4757-1949-9}}
+:* {{cite book |title=Solutions manual for Lang's "Linear Algebra"|year=1996|last1=Shakarchi|first1=Rami|publisher=[[Springer-Verlag]]|location=New York|mr=1415837|doi=10.1007/978-1-4612-0755-9|isbn=0-387-94760-4}}
-* ''Algebraic Numbers'' (1964)
+* {{cite book|last1=Lang|first1=Serge|title=Basic mathematics|publisher=[[Springer-Verlag]]|location=New York|year=1988|edition=Reprint of 1971 original}}
-* ''A Second Course in Calculus'' ([[Addison-Wesley]], 1965)<ref>{{Cite journal|last=Magill|first=K. D.|date=1965-01-01|title=Review of A Second Course in Calculus|jstor=2313382|journal=The American Mathematical Monthly|volume=72|issue=9|pages=1048–1049|doi=10.2307/2313382}}</ref><ref>{{Cite journal|last=Meacham|first=R. C.|date=1966-01-01|title=Review of A Second Course in Calculus|jstor=2688730|journal=Mathematics Magazine|volume=39|issue=2|pages=124|doi=10.2307/2688730}}</ref><ref>{{Cite journal|last=Niven|first=Ivan|author-link=Ivan Niven|date=1970-01-01|title=Review of A Second Course in Calculus|jstor=2688750|journal=Mathematics Magazine|volume=43|issue=5|pages=277–278|doi=10.2307/2688750}}</ref> ASIN B0007DW0KS
+* {{cite book|last1=Lang|first1=Serge|last2=Murrow|first2=Gene|title=Geometry: a high school course|location=New York|publisher=[[Springer-Verlag]]|year=1988|doi=10.1007/978-1-4757-2022-8|isbn=978-0-387-96654-0}}
-* ''Algebra'' (1965) and many later editions
+* {{cite book|mr=1476913|last1=Lang|first1=Serge|title=Undergraduate analysis|edition=Second|series=Undergraduate Texts in Mathematics|publisher=[[Springer-Verlag]]|location=New York|year=1997|isbn=0-387-94841-4|doi=10.1007/978-1-4757-2698-5}} The first edition (1983) of this title was itself the second edition of ''Analysis I'' (1968)
-* ''Algebraic Structures'' (1966)
+:* {{cite book |doi=10.1007/978-1-4612-1738-1|title=Problems and solutions for "Undergraduate Analysis"|year=1998|last1=Shakarchi|first1=Rami|publisher=[[Springer-Verlag]]|location=New York|mr=1488961|isbn=0-387-98235-3}}
-* ''Introduction to Diophantine Approximations'' (1966)
+* {{cite book|mr=1659317|last1=Lang|first1=Serge|title=Complex analysis|edition=Fourth edition of 1977 original|series=[[Graduate Texts in Mathematics]]|volume=103|publisher=[[Springer-Verlag]]|location=New York|year=1999|isbn=0-387-98592-1|doi=10.1007/978-1-4757-3083-8}}
-* ''Introduction to Transcendental Numbers'' (1966)
+:* {{cite book |doi=10.1007/978-1-4612-1534-9|title=Problems and solutions for "Complex Analysis"|year=1999|last1=Shakarchi|first1=Rami|publisher=[[Springer-Verlag]]|location=New York|mr=1716449|isbn=978-0-387-98831-3}}
-* ''Linear Algebra'' (1966)
+* {{cite book|last1=Lang|first1=Serge|title=Undergraduate algebra|edition=Third edition of 1990 original|series=Undergraduate Texts in Mathematics|publisher=[[Springer-Verlag]]|location=New York|year=2005|isbn=0-387-22025-9|doi=10.1007/0-387-27475-8}} The 1990 first edition was itself a second edition of ''Algebraic Structures'' (1967)
-* ''Rapport sur la Cohomologie des Groupes'' (1966)<ref>{{cite journal|author=Hochschild, G.|author-link=Gerhard Hochschild|title=Review: ''Rapport sur la cohomologie des groupes'' by Serge Lang|journal=Bull. Amer. Math. Soc.|year=1969|volume=75|issue=5|pages=927–929|url=http://www.ams.org/journals/bull/1969-75-05/S0002-9904-1969-12294-9/S0002-9904-1969-12294-9.pdf|doi=10.1090/s0002-9904-1969-12294-9|doi-access=free}}</ref> as ''Topics in Cohomology of Groups'' (1986)
+}}
-* ''A Complete Course in Calculus'' (1968)
+'''Graduate-level textbooks'''
-* ''Analysis I'' (1968)
+{{Columns-list|colwidth=30em|
-* ''Analysis II'' (1969)
+* {{cite book|mr=0214547|last1=Lang|first1=Serge|title=Introduction to transcendental numbers|publisher=[[Addison-Wesley Publishing Co.]]|location=Reading, MA–London–Don Mills, Ontario|year=1966}}
-* ''Real Analysis'' (1969)
-* ''Algebraic Number Theory'' (1970)<ref>{{cite journal|author=Corwin, Lawrence|title=Review: ''Algebraic Number Theory'' by Serge Lang|journal=Bull. Amer. Math. Soc.|year=1972|volume=78|issue=5|pages=690–693|url=http://www.ams.org/journals/bull/1972-78-05/S0002-9904-1972-12984-7/S0002-9904-1972-12984-7.pdf|doi=10.1090/s0002-9904-1972-12984-7|doi-access=free}}</ref>
+* {{cite book|mr=0344244|last1=Lang|first1=Serge|title=Introduction to algebraic geometry|edition=Third printing, with corrections, of 1959 original|publisher=[[Addison-Wesley Publishing Co.]]|location=Reading, MA|year=1972}}<ref>{{cite journal|author=Rosenlicht, M.|author-link=Maxwell Rosenlicht|title=Review: ''Introduction to algebraic geometry''. By Serge Lang|journal=Bull. Amer. Math. Soc.|year=1959|volume=65|issue=6|pages=341–342|url=http://www.ams.org/journals/bull/1959-65-06/S0002-9904-1959-10361-X/S0002-9904-1959-10361-X.pdf|doi=10.1090/s0002-9904-1959-10361-x|doi-access=free}}</ref>
+* {{cite book|mr=0518817|last1=Lang|first1=Serge|title=Elliptic curves: Diophantine analysis|series=Grundlehren der Mathematischen Wissenschaften|volume=231|publisher=[[Springer-Verlag]]|location=Berlin–New York|year=1978|isbn=3-540-08489-4|doi=10.1007/978-3-662-07010-9}}<ref>{{cite journal|author=Baker, Alan|author-link=Alan Baker (mathematician)|title=Review: ''Elliptic curves: Diophantine analysis'', by Serge Lang|journal=Bull. Amer. Math. Soc. (N.S.)|year=1980|volume=2|issue=2|pages=352–354|url=http://www.ams.org/journals/bull/1980-02-02/S0273-0979-1980-14756-4/S0273-0979-1980-14756-4.pdf|doi=10.1090/s0273-0979-1980-14756-4|doi-access=free}}</ref>
-* ''Introduction To Linear Algebra'' (1970)
+* {{cite book|mr=0648603|last1=Kubert|first1=Daniel S.|last2=Lang|first2=Serge|title=Modular units|series=Grundlehren der Mathematischen Wissenschaften|volume=244|publisher=[[Springer-Verlag]]|location=New York–Berlin|year=1981|isbn=0-387-90517-0|doi=10.1007/978-1-4757-1741-9|author-link1=Daniel Kubert}}
-* ''Basic Mathematics'' (1971)
+* {{cite book|mr=0681120|last1=Lang|first1=Serge|title=Introduction to algebraic and abelian functions|edition=Second edition of 1972 original|series=[[Graduate Texts in Mathematics]]|volume=89|publisher=[[Springer-Verlag]]|location=New York–Berlin|year=1982|isbn=0-387-90710-6|doi=10.1007/978-1-4612-5740-0}}
-* ''Introduction to Algebraic and Abelian Functions'' (1972)
+* {{cite book|mr=0713430|last1=Lang|first1=Serge|title=Abelian varieties|edition=Reprint of 1959 original|publisher=[[Springer-Verlag]]|location=New York–Berlin|year=1983|isbn=0-387-90875-7|doi=10.1007/978-1-4419-8534-7}}
-* ''Calculus of Several Variables'' (1973)
+* {{cite book|mr=0713612|last1=Lang|first1=Serge|title=Complex multiplication|series=Grundlehren der mathematischen Wissenschaften|volume=255|publisher=[[Springer-Verlag]]|location=New York|year=1983|isbn=0-387-90786-6|doi=10.1007/978-1-4612-5485-0}}
-* ''Elliptic Functions'' (1973)<ref>{{cite journal|author=Roquette, Peter|author-link= Peter Roquette|title=Review: ''Elliptic functions'', by Serge Lang|journal=Bull. Amer. Math. Soc.|year=1976|volume=82|issue=4|pages=523–526|url=http://www.ams.org/journals/bull/1976-82-04/S0002-9904-1976-14082-7/S0002-9904-1976-14082-7.pdf|doi=10.1090/s0002-9904-1976-14082-7}}</ref>
-* ''SL<sub>2</sub>(R)'' (1975)<ref>{{cite journal|author=Langlands, R. P.|author-link=Robert Langlands|title= ''SL<sub>2</sub>(R)'', by Serge Lang|journal=Bull. Amer. Math. Soc.|year=1976|volume=82|issue=5|pages=688–691|url=http://www.ams.org/journals/bull/1976-82-05/S0002-9904-1976-14109-2/S0002-9904-1976-14109-2.pdf|doi=10.1090/s0002-9904-1976-14109-2 |doi-access=free}}</ref>
+* {{cite book|mr=0715605|last1=Lang|first1=Serge|title=Fundamentals of Diophantine geometry|publisher=[[Springer-Verlag]]|location=New York|year=1983|isbn=0-387-90837-4|doi=10.1007/978-1-4757-1810-2}} Second edition of ''Diophantine Geometry'' (1962)<ref>{{cite journal|author=Mordell, L. J.|author-link=Louis J. Mordell|title=Review: ''Diophantine geometry''. By Serge Lang|journal=Bull. Amer. Math. Soc.|year=1964|volume=70|issue=4|pages=491–498|url=http://www.ams.org/journals/bull/1964-70-04/S0002-9904-1964-11164-2/S0002-9904-1964-11164-2.pdf|doi=10.1090/s0002-9904-1964-11164-2|doi-access=free}}</ref><ref>{{cite journal|author=Lang, Serge|title=Mordell's review, Siegel's letter to Mordell, Diophantine Geomertry, and 20th century mathematics|journal=Gazette des mathématiciens|date=January 1995|issue=63|pages=17–36|url=http://smf4.emath.fr/Publications/Gazette/1995/63/smf_gazette_63_17-36.pdf}}</ref>
+* {{cite book |last1=Fulton|first1=William|last2=Lang|first2=Serge|author-link1=William Fulton (mathematician)|doi=10.1007/978-1-4757-1858-4|title=Riemann–Roch Algebra|series=Grundlehren der mathematischen Wissenschaften|year=1985|volume=277|publisher=[[Springer-Verlag]]|location=New York|isbn=978-1-4419-3073-6|mr=0801033}}
-* ''Introduction to Modular Forms'' (1976)<ref>{{cite journal|author=Terras, Audrey|author-link=Audrey Terras|title=Review: ''Introduction to modular forms'', by Serge Lang|journal=Bull. Amer. Math. Soc. (N.S.)|year=1980|volume=2|issue=1|pages=206–214|url=http://www.ams.org/journals/bull/1980-02-01/S0273-0979-1980-14722-9/S0273-0979-1980-14722-9.pdf|doi=10.1090/s0273-0979-1980-14722-9|doi-access=free}}</ref>
+* {{cite book|mr=0803508|last1=Lang|first1=Serge|title=SL<sub>2</sub>(R)|edition=Reprint of the 1975 original|series=[[Graduate Texts in Mathematics]]|volume=105|publisher=[[Springer-Verlag]]|location=New York|year=1985|isbn=0-387-96198-4|doi=10.1007/978-1-4612-5142-2}}<ref>{{cite journal|author=Langlands, R. P.|author-link=Robert Langlands|title= ''SL<sub>2</sub>(R)'', by Serge Lang|journal=Bull. Amer. Math. Soc.|year=1976|volume=82|issue=5|pages=688–691|url=http://www.ams.org/journals/bull/1976-82-05/S0002-9904-1976-14109-2/S0002-9904-1976-14109-2.pdf|doi=10.1090/s0002-9904-1976-14109-2 |doi-access=free}}</ref>
-* ''Complex Analysis'' (1977)
+* {{cite book|mr=0890960|last1=Lang|first1=Serge|title=Elliptic functions|others=With an appendix by [[John Tate (mathematician)|J. Tate]]|edition=Second edition of 1973 original|series=[[Graduate Texts in Mathematics]]|volume=112|publisher=[[Springer-Verlag]]|location=New York|year=1987|isbn=0-387-96508-4|doi=10.1007/978-1-4612-4752-4}}<ref>{{cite journal|author=Roquette, Peter|author-link= Peter Roquette|title=Review: ''Elliptic functions'', by Serge Lang|journal=Bull. Amer. Math. Soc.|year=1976|volume=82|issue=4|pages=523–526|url=http://www.ams.org/journals/bull/1976-82-04/S0002-9904-1976-14082-7/S0002-9904-1976-14082-7.pdf|doi=10.1090/s0002-9904-1976-14082-7}}</ref>
-:* {{cite book |doi=10.1007/978-1-4612-1534-9|title=Problems and Solutions for Complex Analysis|year=1999|last1=Shakarchi|first1=Rami|isbn=978-0-387-98831-3}}
+* {{cite book|mr=0886677|last1=Lang|first1=Serge|title=Introduction to complex hyperbolic spaces|publisher=[[Springer-Verlag]]|location=New York|year=1987|isbn=0-387-96447-9|doi=10.1007/978-1-4757-1945-1}}<ref>{{cite journal|author=Green, Mark|title=Review: ''Introduction to complex hyperbolic spaces'' by Serge Lang|journal=Bull. Amer. Math. Soc. (N.S.)|year=1988|volume=18|issue=2|pages=188–191|url=https://projecteuclid.org/euclid.bams/1183554537|doi=10.1090/s0273-0979-1988-15644-3|doi-access=free}}</ref>
-* ''Cyclotomic Fields'' (1978)
-* ''Elliptic Curves: Diophantine Analysis'' (1978)<ref>{{cite journal|author=Baker, Alan|author-link=Alan Baker (mathematician)|title=Review: ''Elliptic curves: Diophantine analysis'', by Serge Lang|journal=Bull. Amer. Math. Soc. (N.S.)|year=1980|volume=2|issue=2|pages=352–354|url=http://www.ams.org/journals/bull/1980-02-02/S0273-0979-1980-14756-4/S0273-0979-1980-14756-4.pdf|doi=10.1090/s0273-0979-1980-14756-4|doi-access=free}}</ref>
+* {{cite book|mr=0969124|last1=Lang|first1=Serge|title=Introduction to Arakelov theory|publisher=[[Springer-Verlag]]|location=New York|year=1988|isbn=0-387-96793-1|doi=10.1007/978-1-4612-1031-3}}<ref>{{cite journal|author=Silverman, Joseph H.|author-link=Joseph H. Silverman|title=Review: ''Introduction to Arakelov theory'', by Serge Lang|journal=Bull. Amer. Math. Soc. (N.S.)|year=1989|volume=21|issue=1|pages=171–176|url=http://www.ams.org/journals/bull/1989-21-01/S0273-0979-1989-15806-0/S0273-0979-1989-15806-0.pdf|doi=10.1090/s0273-0979-1989-15806-0|doi-access=free}}</ref>
+* {{cite book|mr=1029028|last1=Lang|first1=Serge|title=Cyclotomic fields I and II|edition=Combined second edition of 1978/1980 original|others=With an appendix by [[Karl Rubin]]|series=[[Graduate Texts in Mathematics]]|volume=121|publisher=[[Springer-Verlag]]|location=New York|year=1990|isbn=0-387-96671-4|doi=10.1007/978-1-4612-0987-4}}
-* ''Modular Units'' (1981) with Dan Kubert
+* {{cite book|mr=1216137|last1=Lang|first1=Serge|title=Real and functional analysis|edition=Third|series=[[Graduate Texts in Mathematics]]|volume=142|publisher=[[Springer-Verlag]]|location=New York|year=1993|isbn=0-387-94001-4|doi=10.1007/978-1-4612-0897-6}} This book is the third edition, previously published under the different titles of ''Analysis II'' (1968) and ''Real Analysis'' (1983)
-* ''Undergraduate Analysis'' (1983)
+* {{cite book|mr=1284924|last1=Jorgenson|first1=Jay|last2=Lang|first2=Serge|title=Basic analysis of regularized series and products|series=[[Lecture Notes in Mathematics]]|volume=1564|publisher=[[Springer-Verlag]]|location=Berlin|year=1993|isbn=3-540-57488-3|doi=10.1007/BFb0077194}}
-* ''Complex Multiplication'' (1983)
+* {{cite book|mr=1282723|last1=Lang|first1=Serge|title=Algebraic number theory|edition=Second edition of 1970 original|series=[[Graduate Texts in Mathematics]]|volume=110|publisher=[[Springer-Verlag]]|location=New York|year=1994|isbn=0-387-94225-4|doi=10.1007/978-1-4612-0853-2}}<ref>{{cite journal|author=Corwin, Lawrence|title=Review: ''Algebraic Number Theory'' by Serge Lang|journal=Bull. Amer. Math. Soc.|year=1972|volume=78|issue=5|pages=690–693|url=http://www.ams.org/journals/bull/1972-78-05/S0002-9904-1972-12984-7/S0002-9904-1972-12984-7.pdf|doi=10.1090/s0002-9904-1972-12984-7|doi-access=free}}</ref> The first edition was itself the second edition of ''Algebraic Numbers'' (1964)
-* ''Fundamentals Of Diophantine Geometry'' (1983)
+* {{cite book|mr=1348400|last1=Lang|first1=Serge|title=Introduction to Diophantine approximations|edition=Second edition of 1966 original|publisher=[[Springer-Verlag]]|location=New York|year=1995|isbn=0-387-94456-7|doi=10.1007/978-1-4612-4220-8}}
-* {{cite book |doi=10.1007/978-1-4757-1858-4|title=Riemann-Roch Algebra|series=Grundlehren der mathematischen Wissenschaften|year=1985|volume=277|isbn=978-1-4419-3073-6}}
-* ''Introduction To Complex Hyperbolic Spaces'' (1987)<ref>{{cite journal|author=Green, Mark|title=Review: ''Introduction to complex hyperbolic spaces'' by Serge Lang|journal=Bull. Amer. Math. Soc. (N.S.)|year=1988|volume=18|issue=2|pages=188–191|url=https://projecteuclid.org/euclid.bams/1183554537|doi=10.1090/s0273-0979-1988-15644-3|doi-access=free}}</ref>
+* {{cite book|mr=1363488|last1=Lang|first1=Serge|title=Introduction to modular forms|others=With appendixes by [[Don Zagier|D. Zagier]] and [[Walter Feit]]|edition=Corrected reprint of the 1976 original|series=Grundlehren der mathematischen Wissenschaften|volume=222|publisher=[[Springer-Verlag]]|location=Berlin|year=1995|isbn=3-540-07833-9|doi=10.1007/978-3-642-51447-0}}<ref>{{cite journal|author=Terras, Audrey|author-link=Audrey Terras|title=Review: ''Introduction to modular forms'', by Serge Lang|journal=Bull. Amer. Math. Soc. (N.S.)|year=1980|volume=2|issue=1|pages=206–214|url=http://www.ams.org/journals/bull/1980-02-01/S0273-0979-1980-14722-9/S0273-0979-1980-14722-9.pdf|doi=10.1090/s0273-0979-1980-14722-9|doi-access=free}}</ref>
+* {{cite book|mr=1439508|last1=Lang|first1=Serge|title=Topics in cohomology of groups|edition=Translated from the 1967 French original|others=Chapter X based on letters written by [[John Tate (mathematician)|John Tate]]|series=[[Lecture Notes in Mathematics]]|volume=1625|publisher=[[Springer-Verlag]]|location=Berlin|year=1996|isbn=3-540-61181-9|doi=10.1007/BFb0092624}}<ref>{{cite journal|author=Hochschild, G.|author-link=Gerhard Hochschild|title=Review: ''Rapport sur la cohomologie des groupes'' by Serge Lang|journal=Bull. Amer. Math. Soc.|year=1969|volume=75|issue=5|pages=927–929|url=http://www.ams.org/journals/bull/1969-75-05/S0002-9904-1969-12294-9/S0002-9904-1969-12294-9.pdf|doi=10.1090/s0002-9904-1969-12294-9|doi-access=free}}</ref>
-* ''Geometry'' (1988)
-* ''Introduction to Arakelov Theory'' (1988)<ref>{{cite journal|author=Silverman, Joseph H.|author-link=Joseph H. Silverman|title=Review: ''Introduction to Arakelov theory'', by Serge Lang|journal=Bull. Amer. Math. Soc. (N.S.)|year=1989|volume=21|issue=1|pages=171–176|url=http://www.ams.org/journals/bull/1989-21-01/S0273-0979-1989-15806-0/S0273-0979-1989-15806-0.pdf|doi=10.1090/s0273-0979-1989-15806-0|doi-access=free}}</ref>
-* ''Cyclotomic Fields II'' (1989)
-* ''Undergraduate Algebra'' (1990)
-* ''Real and Functional Analysis'' (1993)
-* ''Basic Analysis of Regularized Series and Products'' (1993) with Jay Jorgenson
 * {{citation |first=S. |last=Lang |title=Survey of Diophantine geometry |publisher=[[Springer-Verlag]] |location=Berlin |year=1997 |isbn=3-540-61223-8 | zbl=0869.11051| url={{Google books|title=Survey of Diophantine geometry|ZePysv04D6oC|plainurl=yes}}}}
 * {{cite book|mr=1666820|last1=Lang|first1=Serge|title=Fundamentals of differential geometry|series=[[Graduate Texts in Mathematics]]|volume=191|publisher=[[Springer-Verlag]]|location=New York|year=1999|isbn=0-387-98593-X|doi=10.1007/978-1-4612-0541-8}} 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:
 :* {{cite book|mr=1931083|last1=Lang|first1=Serge|title=Introduction to differentiable manifolds|edition=Second|series=Universitext|publisher=[[Springer-Verlag]]|location=New York|year=2002|isbn=0-387-95477-5|doi=10.1007/b97450}}<ref>{{cite journal|author=Abraham, Ralph|author-link=Ralph Abraham (mathematician)|title=Review: ''Introduction to differential manifolds''. By Serge Lang|journal=Bull. Amer. Math. Soc.|year=1964|volume=70|issue=2|pages=225–227|url=http://www.ams.org/journals/bull/1964-70-02/S0002-9904-1964-11089-2/S0002-9904-1964-11089-2.pdf|doi=10.1090/s0002-9904-1964-11089-2|doi-access=free}}</ref>
-* ''Spherical Inversion on SL<sub>n</sub>(R)'' (2001) with Jay Jorgenson<ref>{{cite journal|author=Krötz, Bernhard|title= ''Spherical Inversion on SL<sub>n</sub>(R)'', by Jay Jorgenson and Serge Lang|journal=Bull. Amer. Math. Soc. (N.S.)|year=2002|volume=40|issue=1|pages=137–142|url=http://www.ams.org/journals/bull/2003-40-01/S0273-0979-02-00962-X/S0273-0979-02-00962-X.pdf|doi=10.1090/s0273-0979-02-00962-x|doi-access=free}}</ref>
+* {{cite book|mr=1834111|last1=Jorgenson|first1=Jay|last2=Lang|first2=Serge|title=Spherical inversion on SL<sub>n</sub>(R)|series=Springer Monographs in Mathematics|publisher=[[Springer-Verlag]]|location=New York|year=2001|isbn=0-387-95115-6|doi=10.1007/978-1-4684-9302-3}}<ref>{{cite journal|author=Krötz, Bernhard|title= ''Spherical Inversion on SL<sub>n</sub>(R)'', by Jay Jorgenson and Serge Lang|journal=Bull. Amer. Math. Soc. (N.S.)|year=2002|volume=40|issue=1|pages=137–142|url=http://www.ams.org/journals/bull/2003-40-01/S0273-0979-02-00962-X/S0273-0979-02-00962-X.pdf|doi=10.1090/s0273-0979-02-00962-x|doi-access=free}}</ref>
+* {{cite book|mr=1878556|last1=Lang|first1=Serge|title=Algebra|edition=Revised third edition of 1965 original|doi=10.1007/978-1-4613-0041-0|series=[[Graduate Texts in Mathematics]]|volume=211|publisher=[[Springer-Verlag]]|location=New York|year=2002|isbn=0-387-95385-X}}
-* ''Pos<sub>n</sub>(R) and Eisenstein Series'' (2005) with Jay Jorgenson
+* {{cite book|mr=2166237|last1=Jorgenson|first1=Jay|last2=Lang|first2=Serge|title=Pos<sub>n</sub>(R) and Eisenstein series|series=[[Lecture Notes in Mathematics]]|volume=1868|publisher=[[Springer-Verlag]]|location=Berlin|year=2005|isbn=978-3-540-25787-5|doi=10.1007/b136063}}
-* ''The Heat Kernel and Theta Inversion on SL<sub>2</sub>(C)'' (2008) with Jay Jorgenson
+* {{cite book|mr=2449649|last1=Jorgenson|first1=Jay|last2=Lang|first2=Serge|title=The heat kernel and theta inversion on SL<sub>2</sub>(C)|series=Springer Monographs in Mathematics|publisher=[[Springer Science+Business Media|Springer]]|location=New York|year=2008|isbn=978-0-387-38031-5|doi=10.1007/978-0-387-38032-2}}
-* ''Heat Eisenstein series on SL<sub>n</sub>(C)'' (2009) with Jay Jorgenson
+* {{cite book|mr=2548067|last1=Jorgenson|first1=Jay|last2=Lang|first2=Serge|title=Heat Eisenstein series on SL<sub>n</sub>(C)|series=[[Memoirs of the American Mathematical Society]]|volume=201|year=2009|issue=946|isbn=978-0-8218-4044-3|doi=10.1090/memo/0946}}
 }}
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