Serge Lang (May 19, 1927–September 12, 2005) was a French-born American mathematician. He was known for his work in number theory and for his mathematics textbooks, including the influential Algebra. He was a member of the Bourbaki group. Image File history File links Serge_Lang. ... May 19 is the 139th day of the year in the Gregorian Calendar (140th in leap years). ... 1927 (MCMXXVII) was a common year starting on Saturday (link will take you to calendar). ... September 12 is the 255th day of the year (256th in leap years). ... 2005 (MMV) was a common year starting on Saturday of the Gregorian calendar. ... This article is in need of attention from an expert on the subject. ... Number theory is the formal study of numbers. ... Two textbooks. ... Nicolas Bourbaki is the pseudonym under which a group of mainly French 20th-century mathematicians wrote a series of books of exposition of modern advanced mathematics, beginning in 1935. ...

He was born in Paris in 1927, and moved with his family to California as a teenager. He graduated from Caltech in 1946, and received a doctorate from Princeton University in 1951. He had positions at the University of Chicago and Columbia University (from 1955, leaving 1971 in a dispute). At the time of his death he was professor emeritus of mathematics at Yale University. The Eiffel Tower has become a symbol of Paris throughout the world Paris is Frances capital and largest city, straddling the river Seine in the north central part of the country. ... The California Institute of Technology (commonly referred to as Caltech) is a private, coeducational university located in Pasadena, California, in the United States. ... Princeton University, incorporated as The Trustees of Princeton University, located in Princeton, New Jersey, is the fourth-oldest institution to conduct higher education in the United States. ... The University of Chicago is an elite and prestigious private university principally located in the Hyde Park neighborhood of Chicago, Illinois, founded in 1890 and opened in 1892. ... Columbia University is a private university in the Morningside Heights neighborhood of Manhattan, New York City and a member of the Ivy League. ... A professor is a senior teacher and researcher, usually in a college or university. ... Yale University is a private university in New Haven, Connecticut. ...

Mathematical work

He was a student of Emil Artin at Princeton University. His thesis was on quasi-algebraic closure. He then worked on the geometric analogues of class field theory and diophantine geometry. Later he moved into diophantine approximation and transcendence theory. Emil Artin (March 3, 1898-December 20, 1962) was an Austrian mathematician born in Vienna who spent his career in Germany (mainly in Hamburg) until the Nazi threat when he emigrated to the USA in 1937 where he was at Indiana University 1938-1946, and Princeton University 1946-1958. ... In mathematics, quasi-algebraic closure of a field F is the property that for every homogeneous polynomial P over F in indeterminates X1, ..., XN, and of degree d satisfying d < N has a non-trivial zero over F; that is, for some xi in F, not all 0, we have... In mathematics, class field theory is a major branch of algebraic number theory. ... In mathematics, a Diophantine equation is an equation between two polynomials with integer coefficients with any number of unknowns. ... In number theory, the field of Diophantine approximation, named after Diophantus of Alexandria, deals with the approximation of real numbers by rational numbers. ... In mathematics, transcendence theory investigates transcendental numbers, in a qualitative and quantitative way. ...

A break in research while he was involved in trying to meet 1960s student activism half way caused him (on his own description) difficulties in picking up the threads. He wrote on modular forms and modular units, the idea of a 'distribution' on a profinite group, and value distribution theory. Modular form - Wikipedia /**/ @import /skins-1. ... In mathematics, pro-finite groups are groups that are in a certain sense assembled from finite groups; they share many properties with the finite groups. ... In mathematics, the value distribution theory of holomorphic functions is a division of mathematical analysis. ...

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. This is a glossary of arithmetic and Diophantine geometry in mathematics, areas growing out of the traditional study of Diophantine equations to encompass large parts of number theory and algebraic geometry. ... In mathematics, the Sato-Tate conjecture is a statistical statement about the family of elliptic curves Ep over the finite field with p elements, with p a prime number, obtained from an elliptic curve E over the rational number field, by the process of reduction modulo a prime for almost... This is a glossary of arithmetic and Diophantine geometry in mathematics, areas growing out of the traditional study of Diophantine equations to encompass large parts of number theory and algebraic geometry. ...

Books

He was a prolific writer of mathematical texts, often completing one on his summer vacation. Most are at graduate level and aimed at those intending research in number theory. He wrote calculus texts and also prepared a book on group cohomology for Bourbaki. Number theory is the formal study of numbers. ... Integral and differential calculus is a central branch of mathematics, developed from algebra and geometry. ... In abstract algebra, homological algebra, algebraic topology and algebraic number theory, as well as in applications to group theory proper, group cohomology is a way to study groups using a sequence of functors H n. ...

Lang's Algebra, a graduate-level introduction to abstract algebra, was a distinctive text that ran through numerous updated editions. 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. His textbooks were also noted for the originality of their problems, which drew on the Princeton and Bourbaki traditions. They were (in some cases) marred by mistakes. (Algebraic Numbers, the early form of Algebraic Number Theory, was particularly notorious, with one leading figure in the field saying that all copies should be burned.) For other reasons Lang's work was sometimes criticised as 'vulgarisation', playing on the slightly different emphasis of this term in French and English.^{[citation needed]} Abstract algebra is the field of mathematics concerned with the study of algebraic structures such as groups, rings and fields. ...

According to one legend in circulation within the Princeton University math community during the 1970s, Lang typed one of his textbooks over a single weekend on a bet; he had military typing experience which contributed to his speed.^{[citation needed]}

Awards as expositor

Lang was noted for his eagerness for contact with students. 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). The Leroy P. Steele Prizes are awarded every year by the American Mathematical Society, for distinguished research work and writing in the field of mathematics. ... The American Mathematical Society (AMS) is dedicated to the interests of mathematical research and education, which it does with various publications and conferences as well as annual monetary awards to mathematicians. ... The Cole Prize is one of two prizes awarded to mathematicians by the American Mathematical Society, one for an outstanding contribution to algebra, and the other for an outstanding contribution to number theory. ...

Character

Lang was volatile and insistent. This laid him open to professional teasing (the comments in the book section have to be seen in this light), and personal ribbing. Lang: "My series of papers on modular units has one idea per paper." Serre: "At most". André Weil (once and only once a collaborator on a paper with Lang): "What Lang needs is a Japanese wife". There were even Lang jokes. Lang, who was a lutenist, walks into a lute shop and says that these are pretty good lutes. Shopkeeper: "Yes, I'm the fifth-best lute maker in the world". Lang: "That's really a coincidence: I'm the fifth-best mathematician in the world".^{[citation needed]} Jean-Pierre Serre (born September 15, 1926) is one of the leading mathematicians of the twentieth century, active in algebraic geometry, number theory and topology. ... André Weil (May 6, 1906 - August 6, 1998) was one of the great mathematicians of the 20th century. ... The lute is a plucked string instrument with a fretted neck and a deep round back. ...

Activism

In addition to being a mathematician, Lang spent much of his time engaged in politics. He was active in opposition to the Vietnam War. He volunteered in the 1966 anti-war campaign of Robert Scheer, (and later wrote a book about it entitled The Scheer Campaign). He later quit his position at Columbia in 1971 over the university's treatment of anti-war protesters. Children run down a road near Trang Bang after an ARVN napalm attack on villages suspected of harboring National Liberation Front fighters in this June, 1972 photo by Huynh Cong Ut, which became a symbol of the international movement against U.S. involvement in Vietnam. ... Robert Scheer, (b. ... 1971 (MCMLXXI) was a common year starting on Friday (the link is to a full 1971 calendar). ...

He was also engaged in several "whistle blowing" crusades 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. This led to a public and highly acrimonious conflict. Seymour Martin Lipset is a political sociologist and a senior fellow at the conservative Hoover Institution. ...

In 1986, he challenged the nomination of political scientist Samuel P. Huntington to the National Academy of Sciences, claiming that his research consisted of "political opinions masquerading as science". The challenge was successful. 1986 (MCMLXXXVI) was a common year starting on Wednesday of the Gregorian calendar. ... Samuel Phillips Huntington (born April 18, 1927) is a political scientist known for his analysis of the relationship between the military and the civil government, his investigation of coup detats, and his thesis that the central political actors of the 21st century will be civilizations rather than nation-states. ... President Harding and the National Academy of Sciences at the White House, Washington, DC, April 1921 The National Academy of Sciences (NAS) is a corporation in the United States whose members serve pro bono as advisers to the nation on science, engineering, and medicine. ...

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 correspondences, collect all these writings together and pointed 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 on the Baltimore affair of alleged scientific misconduct was published in the journal Ethics and Behaviour in January 1993. David Baltimore (born March 7, 1938) is an American biologist and a winner of the 1975 Nobel Prize for Physiology or Medicine. ...

His most controversial political stance was as an AIDS dissident; he maintained that the prevailing scientific consensus that HIV causes AIDS has not been backed up by reliable scientific research, yet for political/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. The AIDS reappraisal movement (or AIDS dissident movement) is a loosely-connected group of activists, journalists, citizens, scientists, researchers, and doctors who deny, challenge, or question, in various ways, the mainstream scientific consensus that the Human Immunodeficiency Virus (HIV) is the cause of Acquired Immune Deficiency Syndrome (AIDS). ... Human immunodeficiency virus, commonly known by the initialism HIV, formerly known as HTLV-III and lymphadenopathy-associated virus, is a retrovirus that primarily infects vital components of the human immune system such as CD4+ T cells, macrophages and dendritic cells. ... Acquired immunodeficiency syndrome, or Acquired Immune Deficiency Syndrome (or acronym AIDS or Aids), is a collection of symptoms and infections resulting from the specific damage to the immune system caused by infection with the human immunodeficiency virus (HIV). ... Scientific method as envisaged by one of its early exponents, Sir Isaac Newton, is fundamental to the investigation and acquisition of new knowledge based upon physical evidence. ...

Later in his life, Lang expanded his "challenges" to include the humanities. For example, he fought the decision by Yale University to hire Daniel Kevles, a historian of science, because he disagreed with Kevles' book The Baltimore Case. Daniel J. Kevles is Stanley Woodward Professor of History at Yale University, a position he assumed in 2001. ...

External links

• Serge Lang at the Mathematics Genealogy Project
• Serge Lang on HIV/AIDS
• Interview with Serge Lang by Anthony Liversidge (1993). Lang describes at length his method of File making.
• Obituary in Yale Daily News
• AIDS Wiki article