Serge Lang

Serge Lang (French: lɑ̃ɡ; May 19, 1927 – September 12, 2005) was a French-American mathematician who taught at Yale University for most of his career. He is best known for his work in number theory and for writing many popular math textbooks, including the famous book Algebra. For his work, Lang won the Frank Nelson Cole Prize in 1960 and was part of the Bourbaki group of mathematicians.

Lang was also active in social causes. He spoke out 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 life, Lang shared strong opinions on health issues, where he disagreed with many scientists about the causes of a serious illness.

Early life

Serge Lang was born in Saint-Germain-en-Laye, near Paris, in 1927. He had a twin brother who became a basketball coach and a sister who became an actress. When he was a teenager, Lang’s family moved to California. He finished high school at Beverly Hills High School in 1943. He studied at the California Institute of Technology and graduated in 1946. He then earned a PhD in mathematics from Princeton University in 1951.

Lang started teaching at the University of Chicago. He also worked at Columbia University and Yale University. He studied many parts of mathematics, such as number theory and geometry.

Mathematical books

Serge Lang wrote many books about mathematics. He often finished one book each summer. Most of his books were for students learning advanced math. One of his most famous books is Algebra. This book helped change how algebra is taught to students. The book was updated many times and influenced many other math books. He also wrote about calculus and group cohomology. He shared ideas from his teacher, Artin, in these books.

Awards as expositor

Serge Lang was a dedicated teacher who loved working with his students. He taught with energy and passion, often showing his excitement in class. Lang received several important awards for his teaching, including the Leroy P. Steele Prize for Mathematical Exposition in 1999 from the American Mathematical Society. He also won the Frank Nelson Cole Prize in Algebra in 1960 for his paper "Unramified class field theory over function fields in several variables" in the Annals of Mathematics.

Activism

Serge Lang was very active in politics all his life. He believed in socialist ideas and worked hard to stop the Vietnam War. In 1966, he volunteered for a campaign led by Robert Scheer.

Lang also spoke out when he thought people were using wrong or misleading information. He argued against a survey sent to professors in the United States, saying the questions were unfair. He also opposed a political scientist being named to a top science group, saying the research was not good science. Lang kept notes about his debates and shared them with people worldwide.

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