Arthur Byron Coble (November 3, 1878 – December 8, 1966) was an American mathematician. He did research on
finite geometries and the
group theory
In abstract algebra, group theory studies the algebraic structures known as group (mathematics), groups.
The concept of a group is central to abstract algebra: other well-known algebraic structures, such as ring (mathematics), rings, field ...
related to them,
Cremona transformations associated with the
Galois theory
In mathematics, Galois theory, originally introduced by Évariste Galois, provides a connection between field theory and group theory. This connection, the fundamental theorem of Galois theory, allows reducing certain problems in field theory to ...
of equations, and the relations between
hyperelliptic theta function
In mathematics, theta functions are special functions of several complex variables. They show up in many topics, including Abelian varieties, moduli spaces, quadratic forms, and solitons. As Grassmann algebras, they appear in quantum field ...
s, irrational binary invariants, the Weddle surface and the
Kummer surface
In algebraic geometry, a Kummer quartic surface, first studied by , is an irreducible nodal surface of degree 4 in \mathbb^3 with the maximal possible number of 16 double points. Any such surface is the Kummer variety of the Jacobian varie ...
. He was President of the
American Mathematical Society
The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, ...
from 1933 to 1934.
Biography
Early life
Arthur Coble was born on November 3, 1878, in
Williamstown, Pennsylvania
Williamstown is a borough in Dauphin County, Pennsylvania, United States. The borough is northeast of Harrisburg. Formerly, anthracite coal mines and hosiery mills were located in the borough. The population was 1,303 at the 2020 census.
William ...
. 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 is a private liberal arts college in Gettysburg, Pennsylvania. Founded in 1832, the campus is adjacent to the Gettysburg Battlefield. Gettysburg College has about 2,600 students, with roughly equal numbers of men and women. ...
in 1893, and completed his
A.B.
Bachelor of arts (BA or AB; from the Latin ', ', or ') is a bachelor's degree awarded for an undergraduate program in the arts, or, in some cases, other disciplines. A Bachelor of Arts degree course is generally completed in three or four yea ...
in 1897. He spent a year as a public school teacher. He entered
Johns Hopkins University
Johns Hopkins University (Johns Hopkins, Hopkins, or JHU) is a private research university in Baltimore, Maryland. Founded in 1876, Johns Hopkins is the oldest research university in the United States and in the western hemisphere. It consi ...
in 1898 to pursue his graduate studies. He completed his Ph.D. from the university in 1902. His
Ph.D.
A Doctor of Philosophy (PhD, Ph.D., or DPhil; Latin: or ') is the most common degree at the highest academic level awarded following a course of study. PhDs are awarded for programs across the whole breadth of academic fields. Because it is ...
thesis was ''The Relation of the Quartic Curve to Conics''. His thesis supervisor was English-born mathematician
Frank Morley
Frank Morley (September 9, 1860 – October 17, 1937) was a leading mathematician, known mostly for his teaching and research in the fields of algebra and geometry. Among his mathematical accomplishments was the discovery and proof of the celebr ...
.
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 Missouri
The University of Missouri (Mizzou, MU, or Missouri) is a public land-grant research university in Columbia, Missouri. It is Missouri's largest university and the flagship of the four-campus University of Missouri System. MU was founded in ...
. 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
Baltimore ( , locally: or ) is the List of municipalities in Maryland, most populous city in the U.S. state of Maryland, fourth most populous city in the Mid-Atlantic (United States), Mid-Atlantic, and List of United States cities by popula ...
. In 1902, American businessman
Andrew Carnegie
Andrew Carnegie (, ; November 25, 1835August 11, 1919) was a Scottish-American industrialist and philanthropist. Carnegie led the expansion of the American steel industry in the late 19th century and became one of the richest Americans i ...
founded the
Carnegie Institution of Washington
The Carnegie Institution of Washington (the organization's legal name), known also for public purposes as the Carnegie Institution for Science (CIS), is an organization in the United States established to fund and perform scientific research. Th ...
. 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,, officially the Federal Republic of Germany, is a country in Central Europe. It is the second most populous country in Europe after Russia, and the most populous member state of the European Union. Germany is situated betwe ...
where he studied at Greifswald University and the
University of Bonn
The Rhenish Friedrich Wilhelm University of Bonn (german: Rheinische Friedrich-Wilhelms-Universität Bonn) is a public research university located in Bonn, North Rhine-Westphalia, Germany. It was founded in its present form as the ( en, Rhine ...
. He wanted to work with
Eduard Study
Eduard Study ( ), more properly Christian Hugo Eduard Study (March 23, 1862 – January 6, 1930), was a German mathematician known for work on invariant theory of ternary forms (1889) and for the study of spherical trigonometry. He is also known f ...
, 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
The University of Illinois Urbana-Champaign (U of I, Illinois, University of Illinois, or UIUC) is a public land-grant research university in Illinois in the twin cities of Champaign and Urbana. It is the flagship institution of the Univ ...
(UIUC) in 1918. He remained at Illinois for the rest of his career. He was a visiting professor at the
University of Chicago
The University of Chicago (UChicago, Chicago, U of C, or UChi) is a private university, private research university in Chicago, Illinois. Its main campus is located in Chicago's Hyde Park, Chicago, Hyde Park neighborhood. The University of Chic ...
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
The College of Liberal Arts and Sciences (LAS) is the largest college of the University of Illinois Urbana-Champaign. The college was established in 1913 through the merger of the College of Literature and Arts and the College of Science. The c ...
.
American Mathematical Society
Coble was active with the
American Mathematical Society
The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, ...
(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
By the time he retired in 1947 his health was already deteriorating due to Parkinson's disease. After his retirement, he accepted a one-year post at
Haverford College 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.
Research
Early mathematical 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
In abstract algebra, group theory studies the algebraic structures known as group (mathematics), groups.
The concept of a group is central to abstract algebra: other well-known algebraic structures, such as ring (mathematics), rings, field ...
, and in the Cremona transformations related to the
Galois theory
In mathematics, Galois theory, originally introduced by Évariste Galois, provides a connection between field theory and group theory. This connection, the fundamental theorem of Galois theory, allows reducing certain problems in field theory to ...
of equations. Later in his career, Coble also studied the relations between
hyperelliptic theta function
In mathematics, theta functions are special functions of several complex variables. They show up in many topics, including Abelian varieties, moduli spaces, quadratic forms, and solitons. As Grassmann algebras, they appear in quantum field ...
s,
irrational binary invariants, the
Weddle surface and the
Kummer surface
In algebraic geometry, a Kummer quartic surface, first studied by , is an irreducible nodal surface of degree 4 in \mathbb^3 with the maximal possible number of 16 double points. Any such surface is the Kummer variety of the Jacobian varie ...
.
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
Francis Sowerby Macaulay FRS (11 February 1862, Witney – 9 February 1937, Cambridge) was an English mathematician who made significant contributions to algebraic geometry. He is known for his 1916 book ''The Algebraic Theory of Modular Systems ...
and
Bartel Leendert van der Waerden
Bartel Leendert van der Waerden (; 2 February 1903 – 12 January 1996) was a Dutch mathematician and historian of mathematics.
Biography
Education and early career
Van der Waerden learned advanced mathematics at the University of Amster ...
, and also extends work done by Frank Morley and Coble some 20 years earlier.
See also
*
Coble curve
*
Coble surface
*
Coble variety
*
Coble hypersurface
Notes
External links
*
Arthur B. Coble Papers, 1903-53
{{DEFAULTSORT:Coble, Arthur Byron
1878 births
1966 deaths
20th-century American mathematicians
Group theorists
Johns Hopkins University alumni
Johns Hopkins University faculty
University of Illinois Urbana-Champaign faculty
University of Chicago faculty
Presidents of the American Mathematical Society
Mathematicians from Pennsylvania
University of Missouri mathematicians
University of Missouri faculty