Serge Lang

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 best known for his important work in number theory and for writing widely used mathematics textbooks, including the famous book Algebra. For his contributions to mathematics, Lang received the Frank Nelson Cole Prize in 1960 and was part of the influential Bourbaki group of mathematicians.

Beyond mathematics, Lang was also active in social causes. He spoke out strongly against the Vietnam War and worked to stop the National Academies of Science from choosing a new member, Samuel P. Huntington, for their group. Later in his life, Lang became known for his strong views on health issues, where he disagreed with many scientists about the causes of a serious illness called AIDS.

Early life

Serge 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. As a teenager, Lang moved with his family to California, where he graduated from Beverly Hills High School in 1943. He completed his undergraduate education at the California Institute of Technology in 1946 and later earned a PhD in mathematics from Princeton University in 1951.

Lang began his teaching career at the University of Chicago and later worked at Columbia University and Yale University. His academic work focused on many areas of mathematics, including number theory and geometry.

Mathematical books

Serge Lang wrote many books about mathematics, often finishing one each summer. Most of his books were for students learning advanced math. One of his most famous books is Algebra, which helped change how algebra is taught to students. This book went through many updates and influenced many other math books. He also wrote about calculus and group cohomology, sharing ideas from his teacher, Artin.

Awards as expositor

Serge Lang was a dedicated teacher who loved interacting with his students. He was known for his energetic and passionate teaching style, often expressing his enthusiasm loudly in class. Lang received several important awards for his work, including the Leroy P. Steele Prize for Mathematical Exposition in 1999 from the American Mathematical Society and the Frank Nelson Cole Prize in Algebra in 1960 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

Serge Lang was deeply involved in political activism throughout his life. He was a strong supporter of socialist ideas and actively worked against the Vietnam War, even volunteering for a campaign led by Robert Scheer in 1966.

Lang also challenged people he believed were using misleading information or faulty science. He opposed a survey sent to professors in the United States, claiming it had biased questions. He also publicly opposed the nomination of a political scientist to a prestigious science academy, arguing that the research was not truly scientific. Lang kept detailed records of his debates and shared them with others around the world.

List of books

Serge Lang wrote many books about mathematics for students at different levels.

Pregraduate-level textbooks

• A first course in calculus
• Introduction to linear algebra
• Calculus of several variables
• Linear algebra
• Basic mathematics
• Geometry: a high school course
• Undergraduate analysis
• Complex analysis
• Undergraduate algebra

Graduate-level textbooks

• Introduction to transcendental numbers
• Introduction to algebraic geometry
• Frobenius Distributions in GL2-Extensions
• Elliptic curves: Diophantine analysis
• Modular units
• Introduction to algebraic and abelian functions
• Abelian varieties
• Complex multiplication
• Fundamentals of Diophantine geometry
• Riemann–Roch algebra
• SL₂(R)
• Elliptic functions
• Introduction to complex hyperbolic spaces
• Introduction to Arakelov theory
• Cyclotomic fields I and II
• Topics in Nevanlinna Theory
• Real and functional analysis
• Basic Analysis of Regularized Series and Products
• Algebraic number theory
• Introduction to Diophantine approximations
• Introduction to modular forms
• Topics in Cohomology of Groups
• Survey of Diophantine geometry
• Fundamentals of differential geometry
• Introduction to differentiable manifolds
• Algebra
• The heat kernel and theta inversion on SL₂(C)
• Heat Eisenstein series on SL_n(C)

Other

• The file. Case study in correction (1977–1979)
• The beauty of doing mathematics. Three public dialogues
• Math!: Encounters with high school students
• Challenges
• Math talks for undergraduates
• Collected papers. I. 1952–1970
• Collected papers. II. 1971–1977
• Collected papers. III. 1978–1990
• Collected papers. IV. 1990–1996
• Collected papers. V. 1993–1999