Early life and education

Kostant grew up in New York City

New York City

New York is the most populous city in the United States and the center of the New York Metropolitan Area, one of the most populous metropolitan areas in the world. New York exerts a significant impact upon global commerce, finance, media, art, fashion, research, technology, education, and...

, where he graduated from the celebrated Stuyvesant High School

Stuyvesant High School

Stuyvesant High School , commonly referred to as Stuy , is a New York City public high school that specializes in mathematics and science. The school opened in 1904 on Manhattan's East Side and moved to a new building in Battery Park City in 1992. Stuyvesant is noted for its strong academic...

 in 1945. He went on to obtain an undergraduate degree in mathematics from Purdue University

Purdue University

Purdue University, located in West Lafayette, Indiana, U.S., is the flagship university of the six-campus Purdue University system. Purdue was founded on May 6, 1869, as a land-grant university when the Indiana General Assembly, taking advantage of the Morrill Act, accepted a donation of land and...

 in 1950. He earned his Ph.D. from the University of Chicago

University of Chicago

The University of Chicago is a private research university in Chicago, Illinois, USA. It was founded by the American Baptist Education Society with a donation from oil magnate and philanthropist John D. Rockefeller and incorporated in 1890...

 in 1954, under the direction of Irving Segal

Irving Segal

Irving Ezra Segal was a mathematician known for work on theoretical quantum mechanics.He was at the Massachusetts Institute of Technology...

, where he wrote a dissertation on representations of Lie groups.

Career in mathematics

After stints at the Institute for Advanced Study

Institute for Advanced Study

The Institute for Advanced Study, located in Princeton, New Jersey, United States, is an independent postgraduate center for theoretical research and intellectual inquiry. It was founded in 1930 by Abraham Flexner...

, Princeton University

Princeton University

Princeton University is a private research university located in Princeton, New Jersey, United States. The school is one of the eight universities of the Ivy League, and is one of the nine Colonial Colleges founded before the American Revolution....

, and UC Berkeley, he joined the faculty at MIT, where he remained until his retirement in 1993. Kostant's work has involved many of the most beautiful ideas in modern mathematics, such as representation theory

Representation theory

Representation theory is a branch of mathematics that studies abstract algebraic structures by representing their elements as linear transformations of vector spaces, and studiesmodules over these abstract algebraic structures...

, Lie group

Lie group

In mathematics, a Lie group is a group which is also a differentiable manifold, with the property that the group operations are compatible with the smooth structure...

s, Lie algebra

Lie algebra

In mathematics, a Lie algebra is an algebraic structure whose main use is in studying geometric objects such as Lie groups and differentiable manifolds. Lie algebras were introduced to study the concept of infinitesimal transformations. The term "Lie algebra" was introduced by Hermann Weyl in the...

s, homogeneous space

Homogeneous space

In mathematics, particularly in the theories of Lie groups, algebraic groups and topological groups, a homogeneous space for a group G is a non-empty manifold or topological space X on which G acts continuously by symmetry in a transitive way. A special case of this is when the topological group,...

s, differential geometry and mathematical physics

Mathematical physics

Mathematical physics refers to development of mathematical methods for application to problems in physics. The Journal of Mathematical Physics defines this area as: "the application of mathematics to problems in physics and the development of mathematical methods suitable for such applications and...

, particularly symplectic geometry. He has given several lectures on the Lie group E8

E8 (mathematics)

In mathematics, E8 is any of several closely related exceptional simple Lie groups, linear algebraic groups or Lie algebras of dimension 248; the same notation is used for the corresponding root lattice, which has rank 8...

. He has been one of the principal developers of the theory of geometric quantization

Geometric quantization

In mathematical physics, geometric quantization is a mathematical approach to defining a quantum theory corresponding to a given classical theory. It attempts to carry out quantization, for which there is in general no exact recipe, in such a way that certain analogies between the classical theory...

. His introduction of the theory of prequantization has led to a remarkable theory of quantum Toda lattices. The Kostant partition function

Kostant partition function

In representation theory, the Kostant partition function, introduced by , of a root system \Delta is the number of ways one can represent a vector as an integral non-negative sum of the positive roots \Delta^+\subset\Delta...

 is named after him.

Kostant's many honors include election to the National Academy of Sciences

United States National Academy of Sciences

The National Academy of Sciences is a corporation in the United States whose members serve pro bono as "advisers to the nation on science, engineering, and medicine." As a national academy, new members of the organization are elected annually by current members, based on their distinguished and...

 in 1978. His students include James Lepowsky

James Lepowsky

James Lepowsky is a professor of mathematics at Rutgers University, New Jersey. Previously he taught at Yale University. He received his Ph.D from M.I.T. in 1970 where his advisor was Bertram Kostant. Lepowsky graduated from Stuyvesant High School in 1961, 16 years after Kostant...

, Moss Sweedler, David Vogan

David Vogan

David Alexander Vogan is a mathematician at M.I.T. who works on unitary representations of simple Lie groups. He is one of the participants in the Atlas of Lie Groups and Representations.-Publications:*Some online by Vogan...

, and Birgit Speh. At present he has almost 90 mathematical descendants.