Stephen Schanuel
Encyclopedia
Stephen H. Schanuel is an American
mathematician
working in the fields of abstract algebra
and number theory
, more specifically category theory
and measure theory.
While he was a graduate student at University of Chicago
, he discovered Schanuel's lemma
, an essential lemma in homological algebra
. Schanuel received his Ph.D.
in mathematics
from Columbia University
in 1963, under the supervision of Serge Lang
. Shortly thereafter he stated a conjecture
in the field of transcendence theory
which remains an important open problem to this day. Schanuel is currently a professor of mathematics at University at Buffalo
.
United States
The United States of America is a federal constitutional republic comprising fifty states and a federal district...
mathematician
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
working in the fields of abstract algebra
Abstract algebra
Abstract algebra is the subject area of mathematics that studies algebraic structures, such as groups, rings, fields, modules, vector spaces, and algebras...
and number theory
Number theory
Number theory is a branch of pure mathematics devoted primarily to the study of the integers. Number theorists study prime numbers as well...
, more specifically category theory
Category theory
Category theory is an area of study in mathematics that examines in an abstract way the properties of particular mathematical concepts, by formalising them as collections of objects and arrows , where these collections satisfy certain basic conditions...
and measure theory.
While he was a graduate student at 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...
, he discovered Schanuel's lemma
Schanuel's lemma
In mathematics, especially in the area of algebra known as module theory, Schanuel's lemma, namead after Stephen Schanuel, allows one to compare how far modules depart from being projective...
, an essential lemma in homological algebra
Homological algebra
Homological algebra is the branch of mathematics which studies homology in a general algebraic setting. It is a relatively young discipline, whose origins can be traced to investigations in combinatorial topology and abstract algebra at the end of the 19th century, chiefly by Henri Poincaré and...
. Schanuel received his Ph.D.
Ph.D.
A Ph.D. is a Doctor of Philosophy, an academic degree.Ph.D. may also refer to:* Ph.D. , a 1980s British group*Piled Higher and Deeper, a web comic strip*PhD: Phantasy Degree, a Korean comic series* PhD Docbook renderer, an XML renderer...
in mathematics
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
from Columbia University
Columbia University
Columbia University in the City of New York is a private, Ivy League university in Manhattan, New York City. Columbia is the oldest institution of higher learning in the state of New York, the fifth oldest in the United States, and one of the country's nine Colonial Colleges founded before the...
in 1963, under the supervision of Serge Lang
Serge Lang
Serge Lang was a French-born American mathematician. He was known for his work in number theory and for his mathematics textbooks, including the influential Algebra...
. Shortly thereafter he stated a conjecture
Schanuel's conjecture
In mathematics, specifically transcendence theory, Schanuel's conjecture is a conjecture made by Stephen Schanuel in the 1960s concerning the transcendence degree of certain field extensions of the rational numbers.-Statement:The conjecture is as follows:...
in the field of transcendence theory
Transcendence theory
Transcendence theory is a branch of number theory that investigates transcendental numbers, in both qualitative and quantitative ways.-Transcendence:...
which remains an important open problem to this day. Schanuel is currently a professor of mathematics at University at Buffalo
University at Buffalo, The State University of New York
University at Buffalo, The State University of New York, also commonly known as the University at Buffalo or UB, is a public research university and a "University Center" in the State University of New York system. The university was founded by Millard Fillmore in 1846. UB has multiple campuses...
.