Ellis Robert Kolchin (April 18, 1916 – October 30, 1991) was an American mathematician at

Columbia University Columbia University in the City of New York, commonly referred to as Columbia University, is a Private university, private Ivy League research university in New York City. Established in 1754 as King's College on the grounds of Trinity Churc ...

. He earned a doctorate in mathematics from Columbia University in 1941 under supervision of Joseph Ritt. Shortly after he served in the South Pacific in

World War II World War II or the Second World War (1 September 1939 – 2 September 1945) was a World war, global conflict between two coalitions: the Allies of World War II, Allies and the Axis powers. World War II by country, Nearly all of the wo ...

. He was awarded a

Guggenheim Fellowship Guggenheim Fellowships are Grant (money), grants that have been awarded annually since by the John Simon Guggenheim Memorial Foundation, endowed by the late Simon Guggenheim, Simon and Olga Hirsh Guggenheim. These awards are bestowed upon indiv ...

in 1954 and 1961. Kolchin worked on differential algebra and its relation to differential equations, and founded the modern theory of

linear algebraic group In mathematics, a linear algebraic group is a subgroup of the group of invertible n\times n matrices (under matrix multiplication) that is defined by polynomial equations. An example is the orthogonal group, defined by the relation M^TM = I_n ...

s. He developed many of the basic theorems including an analog of the

Hilbert Basis Theorem In mathematics Hilbert's basis theorem asserts that every ideal of a polynomial ring over a field has a finite generating set (a finite ''basis'' in Hilbert's terminology). In modern algebra, rings whose ideals have this property are called No ...

further developing the

Galois theory In mathematics, Galois theory, originally introduced by Évariste Galois, provides a connection between field (mathematics), field theory and group theory. This connection, the fundamental theorem of Galois theory, allows reducing certain problems ...

of differential equations started by

Liouville Joseph Liouville ( ; ; 24 March 1809 – 8 September 1882) was a French mathematician and engineer. Life and work He was born in Saint-Omer in France on 24 March 1809. His parents were Claude-Joseph Liouville (an army officer) and Thérès ...

. He is an celebrated figure in differential algebra and his book Differential Algebra and Algebraic Groups has been extremely influential in differential algebra,

model theory In mathematical logic, model theory is the study of the relationship between theory (mathematical logic), formal theories (a collection of Sentence (mathematical logic), sentences in a formal language expressing statements about a Structure (mat ...

and beyond. In a book review, Blum writes: ''This book, published after years of careful preparation, is a tour de force of the highest proportions. The author, as is well known, is the leading authority in the field of differential algebra. There are few people working in this area who have not benefited enormously through personal contact with him and none who have not been influenced by his publications. His goal here is to present a unified exposition of the subject, in an algebraic setting, presuming no more than a standard first year graduate course in algebra.'' He gave a famous plenary address at the

International Congress of Mathematicians The International Congress of Mathematicians (ICM) is the largest conference for the topic of mathematics. It meets once every four years, hosted by the International Mathematical Union (IMU). The Fields Medals, the IMU Abacus Medal (known before ...

in 1966 (Moscow) where he outlined Kolchin's problems, a famous collection of unsolved problems in differential algebra. His seminar in differential algebra, the Kolchin Seminar, was the longest ongoing mathematics seminar at Columbia University, ran for over 30 years. It is currently run by the

City University of New York The City University of New York (CUNY, pronounced , ) is the Public university, public university system of Education in New York City, New York City. It is the largest urban university system in the United States, comprising 25 campuses: eleven ...

. His doctoral students include

Azriel Rosenfeld Azriel Rosenfeld (February 19, 1931 – February 22, 2004) was an American Research Professor, a Distinguished University Professor, and Director of the Center for Automation Research at the University of Maryland, College Park, Maryland, where ...

, Irving Adler, and (unofficially) Alexandru Buium.

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* 1916 births 1991 deaths 20th-century American mathematicians Columbia University alumni Columbia University faculty Institute for Advanced Study visiting scholars {{US-mathematician-stub

See also

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