James J. Andrews (mathematician)
Encyclopedia
James J. Andrews was an American mathematician, a professor of mathematics at Florida State University
who specialized in knot theory
, topology
, and group theory
.
Andrews was born March 18, 1930, in Seneca Falls, New York. He did his undergraduate studies at Hofstra College, and earned his doctorate in 1957 from the University of Georgia
under the supervision of M. K. Fort, Jr.
He worked at Oak Ridge National Laboratory
, the University of Georgia, and the University of Washington before joining the FSU faculty in 1961. He retired in 1994, and died July 28, 1998 in Tallahassee, Florida
.
Andrews is known with Morton L. Curtis
for the Andrews–Curtis conjecture
concerning Nielsen transformation
s of balanced group presentations
. Andrews and Curtis formulated the conjecture in a 1965 paper; it remains open.
Florida State University
The Florida State University is a space-grant and sea-grant public university located in Tallahassee, Florida, United States. It is a comprehensive doctoral research university with medical programs and significant research activity as determined by the Carnegie Foundation...
who specialized in knot theory
Knot theory
In topology, knot theory is the study of mathematical knots. While inspired by knots which appear in daily life in shoelaces and rope, a mathematician's knot differs in that the ends are joined together so that it cannot be undone. In precise mathematical language, a knot is an embedding of a...
, topology
Topology
Topology is a major area of mathematics concerned with properties that are preserved under continuous deformations of objects, such as deformations that involve stretching, but no tearing or gluing...
, and group theory
Group theory
In mathematics and abstract algebra, group theory studies the algebraic structures known as groups.The concept of a group is central to abstract algebra: other well-known algebraic structures, such as rings, fields, and vector spaces can all be seen as groups endowed with additional operations and...
.
Andrews was born March 18, 1930, in Seneca Falls, New York. He did his undergraduate studies at Hofstra College, and earned his doctorate in 1957 from the University of Georgia
University of Georgia
The University of Georgia is a public research university located in Athens, Georgia, United States. Founded in 1785, it is the oldest and largest of the state's institutions of higher learning and is one of multiple schools to claim the title of the oldest public university in the United States...
under the supervision of M. K. Fort, Jr.
M. K. Fort, Jr.
Marion Kirkland ‘Kirk’ Fort, Jr. was an American mathematician, specializing in general topology. The topological spaces called Fort space and Arens–Fort space are named after him....
He worked at Oak Ridge National Laboratory
Oak Ridge National Laboratory
Oak Ridge National Laboratory is a multiprogram science and technology national laboratory managed for the United States Department of Energy by UT-Battelle. ORNL is the DOE's largest science and energy laboratory. ORNL is located in Oak Ridge, Tennessee, near Knoxville...
, the University of Georgia, and the University of Washington before joining the FSU faculty in 1961. He retired in 1994, and died July 28, 1998 in Tallahassee, Florida
Tallahassee, Florida
Tallahassee is the capital of the U.S. state of Florida. It is the county seat and only incorporated municipality in Leon County, and is the 128th largest city in the United States. Tallahassee became the capital of Florida, then the Florida Territory, in 1824. In 2010, the population recorded by...
.
Andrews is known with Morton L. Curtis
Morton L. Curtis
Morton Landers Curtis was an American mathematician, an expert on group theory and the W. L. Moody, Jr. Professor of Mathematics at Rice University....
for the Andrews–Curtis conjecture
Andrews–Curtis conjecture
In mathematics, the Andrews–Curtis conjecture states that every balanced presentation of the trivial group can be transformed into a trivial presentation by a sequence of Nielsen transformations on the relators together with conjugations of relators, named after James J. Andrews and Morton L....
concerning Nielsen transformation
Nielsen transformation
In mathematics, especially in the area of abstract algebra known as combinatorial group theory, Nielsen transformations, named after Jakob Nielsen, are certain automorphisms of a free group which are a non-commutative analogue of row reduction and one of the main tools used in studying free groups,...
s of balanced group presentations
Presentation of a group
In mathematics, one method of defining a group is by a presentation. One specifies a set S of generators so that every element of the group can be written as a product of powers of some of these generators, and a set R of relations among those generators...
. Andrews and Curtis formulated the conjecture in a 1965 paper; it remains open.