Arthur Byron Coble
Encyclopedia
Arthur Byron Coble was an American
mathematician. He did research on finite geometries
and the group theory
related to them, Cremona transformations associated with the Galois theory
of equations, and the relations between hyperelliptic theta functions, irrational binary invariants, the Weddle surface and the Kummer surface. He was President of the American Mathematical Society
from 1933 to 1934.
. His mother Emma was a schoolteacher. When Coble was born, his father Ruben was the manager of a store. Later, he became president of a bank. Coble's parents belonged to Evangelical Lutheran Church. Coble was brought up strictly as an Evangelical Lutheran; however, he rejected this Church when he reached adulthood.
Coble entered Gettysburg College
in 1893, and completed his A.B.
in 1897. He spent a year as a public school teacher. He entered Johns Hopkins University
in 1898 to pursue his graduate studies. He completed his Ph.D. from the university in 1902. His Ph.D.
thesis was The Relation of the Quartic Curve to Conics. His thesis supervisor was English-born mathematician Frank Morley
. Later, Coble recalled how Morley made it "a cardinal point to have on hand a sufficient variety of thesis problems to accommodate particular tastes and capacities."
. One year later, in 1903, he was appointed to Johns Hopkins University as Morley's research assistant. In 1903, he published his doctoral dissertation as The quartic curve as related to conics in the Transactions of the American Mathematical Society and took up the research assistant position in Baltimore, Maryland. In 1902, American businessman Andrew Carnegie
founded the Carnegie Institution of Washington. The research of Coble and Morley were one of the first pieces of research the Institution supported. The funding of the Institute was generous enough to allow Coble to use the grant to travel abroad. He traveled to Germany
where he studied at Greifswald University and the University of Bonn
. He wanted to work with Eduard Study
, who was well known to mathematicians at Johns Hopkins University because he had taught there in 1893.
Coble returned to the United States for the start of the 1904-05 session. He was appointed an instructor in mathematics at Johns Hopkins University.
Coble married Abby Walker Adams Whitney in 1905. They had four children.
Coble was promoted to associate professor at Johns Hopkins University in 1909. He left Johns Hopkins after he was offered a full professorship at the University of Illinois at Urbana-Champaign
(UIUC) in 1918. He remained at Illinois for the rest of his career. He was a visiting professor at the University of Chicago
in 1919 and was at Johns Hopkins University in 1927-28. He became head of the Department of Mathematics at the UIUC in 1934 and he held that position until his retirement in 1947. During these years, Coble served on many University and College Committees, including eleven years on the University Council and eight years on the Executive Committee of the UIUC College of Liberal Arts and Sciences
.
(AMS) from 1912 to 1940. He was vice-president of the AMS in 1917. From 1920 to 1925, he edited the Transactions of the American Mathematical Society. He also was involved with editing the American Journal of Mathematics over many years between 1918 and 1933. From 1933 to 1934, he was President of the AMS. At that time, the AMS was in some financial difficulties. Coble dealt with the problem effectively.
but after teaching for one semester he resigned due to poor health. In 1956, he was involved in a car crash. Because of that crash, he was unable to walk without assistance. He then moved to Lykens, Pennsylvania
and spent his final ten years of his life there. He died on December 8, 1966 in a hospital in Harrisburg, Pennsylvania
.
Coble was interested in finite geometries and the related group theory
, and in the Cremona transformations related to the Galois theory
of equations. Later in his career, Coble also studied the relations between hyperelliptic theta functions, irrational binary invariants, the Weddle surface
and the Kummer surface.
Coble published the monograph Algebraic geometry and theta functions in the tenth volume of American Mathematical Society Colloquium Publications in 1929, and it was republished by the American Mathematical Society in 1961 and 1982.
Coble published Configurations defined by theta functions, which reviewed the invariant theory of Cremona transformations as developed by Coble in his earlier papers, in the Duke Mathematical Journal
in 1939. A linear homogeneous transformation with integral coefficients is associated with a Cremona transformation. These transformations form a group, which Coble studied.
In 1940, Coble published Trilinear forms in the Duke Mathematical Journal. In 1946, he published Ternary and quaternary elimination, which extends work by mathematicians Francis Sowerby Macaulay
and Bartel Leendert van der Waerden
, and also extends work done by Frank Morley and Coble some 20 years earlier.
United States
The United States of America is a federal constitutional republic comprising fifty states and a federal district...
mathematician. He did research on finite geometries
Finite geometry
A finite geometry is any geometric system that has only a finite number of points.Euclidean geometry, for example, is not finite, because a Euclidean line contains infinitely many points, in fact as many points as there are real numbers...
and the 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...
related to them, Cremona transformations associated with the Galois theory
Galois theory
In mathematics, more specifically in abstract algebra, Galois theory, named after Évariste Galois, provides a connection between field theory and group theory...
of equations, and the relations between hyperelliptic theta functions, irrational binary invariants, the Weddle surface and the Kummer surface. He was President of the American Mathematical Society
American Mathematical Society
The American Mathematical Society is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, which it does with various publications and conferences as well as annual monetary awards and prizes to mathematicians.The society is one of the...
from 1933 to 1934.
Early life
Arthur Coble was born on November 3, 1878 in Williamstown, PennsylvaniaWilliamstown, Pennsylvania
Williamstown is a borough in Dauphin County, Pennsylvania, northeast of Harrisburg. Formerly, Anthracite coal mines were here, as well as hosiery mills. In 1900, 2,904 people lived here, and 2,934 lived here in 1910...
. His mother Emma was a schoolteacher. When Coble was born, his father Ruben was the manager of a store. Later, he became president of a bank. Coble's parents belonged to Evangelical Lutheran Church. Coble was brought up strictly as an Evangelical Lutheran; however, he rejected this Church when he reached adulthood.
Coble entered Gettysburg College
Gettysburg College
Gettysburg College is a private four-year liberal arts college founded in 1832, in Gettysburg, Pennsylvania, United States, adjacent to the famous battlefield. Its athletic teams are nicknamed the Bullets. Gettysburg College has about 2,700 students, with roughly equal numbers of men and women...
in 1893, and completed his A.B.
Bachelor of Arts
A Bachelor of Arts , from the Latin artium baccalaureus, is a bachelor's degree awarded for an undergraduate course or program in either the liberal arts, the sciences, or both...
in 1897. He spent a year as a public school teacher. He entered Johns Hopkins University
Johns Hopkins University
The Johns Hopkins University, commonly referred to as Johns Hopkins, JHU, or simply Hopkins, is a private research university based in Baltimore, Maryland, United States...
in 1898 to pursue his graduate studies. He completed his Ph.D. from the university in 1902. His Ph.D.
Doctor of Philosophy
Doctor of Philosophy, abbreviated as Ph.D., PhD, D.Phil., or DPhil , in English-speaking countries, is a postgraduate academic degree awarded by universities...
thesis was The Relation of the Quartic Curve to Conics. His thesis supervisor was English-born mathematician Frank Morley
Frank Morley
Frank Morley was a leading mathematician, known mostly for his teaching and research in the fields of algebra and geometry...
. Later, Coble recalled how Morley made it "a cardinal point to have on hand a sufficient variety of thesis problems to accommodate particular tastes and capacities."
Academic career
In 1902, Coble became an instructor in mathematics at the University of MissouriUniversity of Missouri
The University of Missouri System is a state university system providing centralized administration for four universities, a health care system, an extension program, five research and technology parks, and a publishing press. More than 64,000 students are currently enrolled at its four campuses...
. One year later, in 1903, he was appointed to Johns Hopkins University as Morley's research assistant. In 1903, he published his doctoral dissertation as The quartic curve as related to conics in the Transactions of the American Mathematical Society and took up the research assistant position in Baltimore, Maryland. In 1902, American businessman Andrew Carnegie
Andrew Carnegie
Andrew Carnegie was a Scottish-American industrialist, businessman, and entrepreneur who led the enormous expansion of the American steel industry in the late 19th century...
founded the Carnegie Institution of Washington. The research of Coble and Morley were one of the first pieces of research the Institution supported. The funding of the Institute was generous enough to allow Coble to use the grant to travel abroad. He traveled to Germany
Germany
Germany , officially the Federal Republic of Germany , is a federal parliamentary republic in Europe. The country consists of 16 states while the capital and largest city is Berlin. Germany covers an area of 357,021 km2 and has a largely temperate seasonal climate...
where he studied at Greifswald University and the University of Bonn
University of Bonn
The University of Bonn is a public research university located in Bonn, Germany. Founded in its present form in 1818, as the linear successor of earlier academic institutions, the University of Bonn is today one of the leading universities in Germany. The University of Bonn offers a large number...
. He wanted to work with Eduard Study
Eduard Study
Eduard Study was a German mathematician known for work on invariant theory of ternary forms and for the study of spherical trigonometry. He is also known for contributions to space geometry, hypercomplex numbers, and criticism of early physical chemistry.Study was born in Coburg in the Duchy of...
, who was well known to mathematicians at Johns Hopkins University because he had taught there in 1893.
Coble returned to the United States for the start of the 1904-05 session. He was appointed an instructor in mathematics at Johns Hopkins University.
Coble married Abby Walker Adams Whitney in 1905. They had four children.
Coble was promoted to associate professor at Johns Hopkins University in 1909. He left Johns Hopkins after he was offered a full professorship at the University of Illinois at Urbana-Champaign
University of Illinois at Urbana-Champaign
The University of Illinois at Urbana–Champaign is a large public research-intensive university in the state of Illinois, United States. It is the flagship campus of the University of Illinois system...
(UIUC) in 1918. He remained at Illinois for the rest of his career. He was a visiting professor at 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 1919 and was at Johns Hopkins University in 1927-28. He became head of the Department of Mathematics at the UIUC in 1934 and he held that position until his retirement in 1947. During these years, Coble served on many University and College Committees, including eleven years on the University Council and eight years on the Executive Committee of the UIUC College of Liberal Arts and Sciences
UIUC College of Liberal Arts and Sciences
The College of Liberal Arts and Sciences is the largest college in the University of Illinois at Urbana-Champaign, created in 1913 through the merger of the College of Literature and Arts and the College of Science. It has nationally ranked programs in chemistry, psychology and speech communications...
.
American Mathematical Society
Coble was active with the American Mathematical SocietyAmerican Mathematical Society
The American Mathematical Society is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, which it does with various publications and conferences as well as annual monetary awards and prizes to mathematicians.The society is one of the...
(AMS) from 1912 to 1940. He was vice-president of the AMS in 1917. From 1920 to 1925, he edited the Transactions of the American Mathematical Society. He also was involved with editing the American Journal of Mathematics over many years between 1918 and 1933. From 1933 to 1934, he was President of the AMS. At that time, the AMS was in some financial difficulties. Coble dealt with the problem effectively.
Later life
After his retirement, he accepted a one-year post at Haverford CollegeHaverford College
Haverford College is a private, coeducational liberal arts college located in Haverford, Pennsylvania, United States, a suburb of Philadelphia...
but after teaching for one semester he resigned due to poor health. In 1956, he was involved in a car crash. Because of that crash, he was unable to walk without assistance. He then moved to Lykens, Pennsylvania
Lykens, Pennsylvania
Lykens is a borough in Dauphin County, Pennsylvania, southwest of Pottsville. Anthracite coal mining sustained the people who numbered 2,762 in 1900 and 2,943 in 1910...
and spent his final ten years of his life there. He died on December 8, 1966 in a hospital in Harrisburg, Pennsylvania
Harrisburg, Pennsylvania
Harrisburg is the capital of Pennsylvania. As of the 2010 census, the city had a population of 49,528, making it the ninth largest city in Pennsylvania...
.
Research
Early mathematicial research papers written by Coble when he was teaching at Johns Hopkins University, include: On the relation between the three-parameter groups of a cubic space curve and a quadric surface (1906); An application of the form-problems associated with certain Cremona groups to the solution of equations of higher degree (1908); An application of Moore's cross-ratio group to the solution of the sextic equation (1911); An application of finite geometry to the characteristic theory of the odd and even theta functions (1913); and Point sets and allied Cremona groups (1915).Coble was interested in finite geometries and the related 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...
, and in the Cremona transformations related to the Galois theory
Galois theory
In mathematics, more specifically in abstract algebra, Galois theory, named after Évariste Galois, provides a connection between field theory and group theory...
of equations. Later in his career, Coble also studied the relations between hyperelliptic theta functions, irrational binary invariants, the Weddle surface
Weddle surface
In algebraic geometry, a Weddle surface is a quartic surface in 3-dimensional projective space, given by the locus of vertices of the 3-dimensional family of cones passing through 6 points in general position, and studied by ....
and the Kummer surface.
Coble published the monograph Algebraic geometry and theta functions in the tenth volume of American Mathematical Society Colloquium Publications in 1929, and it was republished by the American Mathematical Society in 1961 and 1982.
Coble published Configurations defined by theta functions, which reviewed the invariant theory of Cremona transformations as developed by Coble in his earlier papers, in the Duke Mathematical Journal
Duke Mathematical Journal
Duke Mathematical Journal is a peer-reviewed mathematics journal published by Duke University Press. It was established in 1935. The founding editors-in-chief were David Widder, Arthur Coble, and Joseph Miller Thomas. The first issue included a paper by Solomon Lefschetz...
in 1939. A linear homogeneous transformation with integral coefficients is associated with a Cremona transformation. These transformations form a group, which Coble studied.
In 1940, Coble published Trilinear forms in the Duke Mathematical Journal. In 1946, he published Ternary and quaternary elimination, which extends work by mathematicians Francis Sowerby Macaulay
Francis Sowerby Macaulay
Francis Sowerby Macaulay FRS was an English mathematician who made significant contributions to algebraic geometry. He is most famous for his 1916 book, The Algebraic Theory of Modular Systems, which greatly influenced the later course of algebraic geometry...
and Bartel Leendert van der Waerden
Bartel Leendert van der Waerden
Bartel Leendert van der Waerden was a Dutch mathematician and historian of mathematics....
, and also extends work done by Frank Morley and Coble some 20 years earlier.