Edward Vermilye Huntington
Encyclopedia
Edward Vermilye Huntington (April 26 1874, Clinton, New York
, USA -- November 25, 1952, Cambridge, Massachusetts
, USA) was an American
mathematician
.
Edward Vermilye Huntington was awarded the B.A. and the M.A. by Harvard University
in 1895 and 1897, respectively. After two years' teaching at Williams College
, he began a doctorate at the University of Strasbourg
, which was awarded in 1901. He then spent his entire career at Harvard, retiring in 1941. He taught in the engineering school, becoming Professor of Mechanics in 1919. Although Huntington's research was mainly in pure mathematics, he valued teaching mathematics to engineering students. He advocated mechanical calculators and had one in his office. He had an interest in statistics
, unusual for the time, and worked on statistical problems for the USA military during World War I
.
Huntington's primary research interest was the foundations of mathematics
. He was one of the "American postulate theorists" (the term is Scanlan's), American mathematicians active early in the 20th century (including E. H. Moore
and Oswald Veblen
) who proposed axiom sets for a variety of mathematical systems. In so doing, they helped found what are now known as metamathematics
and model theory
.
Huntington was perhaps the most prolific of the American postulate theorists, devising sets of axiom
s (which he called "postulates") for groups
, abelian group
s, geometry
, the real number field, and complex number
s. His 1902 axiomatization of the real numbers has been characterized as "one of the first successes of abstract mathematics" and as having "filled the last gap in the foundations of Euclidean geometry". Huntington excelled at proving axioms independent of each other by finding a sequence of models
, each one satisfying all but one of the axioms in a given set. His 1917 book The Continuum and Other Types of Serial Order was in its day "...a widely read introduction to Cantor
ian set theory
." (Scanlan 1999) Yet Huntington and the other American postulate theorists played no role in the rise of axiomatic set theory then taking place in continental Europe.
In 1904, Huntington put Boolean algebra on a sound axiomatic foundation. He revisited Boolean axiomatics in 1933, proving that Boolean algebra required but a single binary operation
(denoted below by infix
'+') that commutes and associates, and a single unary operation
, complementation, denoted by a postfix prime. The only further axiom Boolean algebra requires is:
'+(a '+b)' = a,
now known as Huntington's axiom.
Revising a method from Joseph Adna Hill
, Huntington is credited with the Method of Equal Proportions or Huntington-Hill method
of apportionment of seats in the U.S. House of Representatives to the states, as a function of their populations determined in the U.S. censushttp://www.ams.org/featurecolumn/archive/apportion2.html. This mathematical algorithm has been used in the U.S. since 1941 and is currently the method used.
In 1919, Huntington was the first President of the Mathematical Association of America
, which he helped found. He was elected to the American Academy of Arts and Sciences
in 1913, and to the American Philosophical Society
in 1933.
Clinton, Oneida County, New York
Clinton is a village in Oneida County, New York, United States. The population was 1,952 at the 2000 census. It was named for George Clinton, a royal governor of the colony of New York....
, USA -- November 25, 1952, Cambridge, Massachusetts
Cambridge, Massachusetts
Cambridge is a city in Middlesex County, Massachusetts, United States, in the Greater Boston area. It was named in honor of the University of Cambridge in England, an important center of the Puritan theology embraced by the town's founders. Cambridge is home to two of the world's most prominent...
, USA) was an American
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....
.
Edward Vermilye Huntington was awarded the B.A. and the M.A. by Harvard University
Harvard University
Harvard University is a private Ivy League university located in Cambridge, Massachusetts, United States, established in 1636 by the Massachusetts legislature. Harvard is the oldest institution of higher learning in the United States and the first corporation chartered in the country...
in 1895 and 1897, respectively. After two years' teaching at Williams College
Williams College
Williams College is a private liberal arts college located in Williamstown, Massachusetts, United States. It was established in 1793 with funds from the estate of Ephraim Williams. Originally a men's college, Williams became co-educational in 1970. Fraternities were also phased out during this...
, he began a doctorate at the University of Strasbourg
University of Strasbourg
The University of Strasbourg in Strasbourg, Alsace, France, is the largest university in France, with about 43,000 students and over 4,000 researchers....
, which was awarded in 1901. He then spent his entire career at Harvard, retiring in 1941. He taught in the engineering school, becoming Professor of Mechanics in 1919. Although Huntington's research was mainly in pure mathematics, he valued teaching mathematics to engineering students. He advocated mechanical calculators and had one in his office. He had an interest in statistics
Statistics
Statistics is the study of the collection, organization, analysis, and interpretation of data. It deals with all aspects of this, including the planning of data collection in terms of the design of surveys and experiments....
, unusual for the time, and worked on statistical problems for the USA military during World War I
World War I
World War I , which was predominantly called the World War or the Great War from its occurrence until 1939, and the First World War or World War I thereafter, was a major war centred in Europe that began on 28 July 1914 and lasted until 11 November 1918...
.
Huntington's primary research interest was the foundations of mathematics
Foundations of mathematics
Foundations of mathematics is a term sometimes used for certain fields of mathematics, such as mathematical logic, axiomatic set theory, proof theory, model theory, type theory and recursion theory...
. He was one of the "American postulate theorists" (the term is Scanlan's), American mathematicians active early in the 20th century (including E. H. Moore
E. H. Moore
Eliakim Hastings Moore was an American mathematician.-Life:Moore, the son of a Methodist minister and grandson of US Congressman Eliakim H. Moore, discovered mathematics through a summer job at the Cincinnati Observatory while in high school. He learned mathematics at Yale University, where he was...
and Oswald Veblen
Oswald Veblen
Oswald Veblen was an American mathematician, geometer and topologist, whose work found application in atomic physics and the theory of relativity. He proved the Jordan curve theorem in 1905.-Life:...
) who proposed axiom sets for a variety of mathematical systems. In so doing, they helped found what are now known as metamathematics
Metamathematics
Metamathematics is the study of mathematics itself using mathematical methods. This study produces metatheories, which are mathematical theories about other mathematical theories...
and model theory
Model theory
In mathematics, model theory is the study of mathematical structures using tools from mathematical logic....
.
Huntington was perhaps the most prolific of the American postulate theorists, devising sets of axiom
Axiom
In traditional logic, an axiom or postulate is a proposition that is not proven or demonstrated but considered either to be self-evident or to define and delimit the realm of analysis. In other words, an axiom is a logical statement that is assumed to be true...
s (which he called "postulates") for groups
Group (mathematics)
In mathematics, a group is an algebraic structure consisting of a set together with an operation that combines any two of its elements to form a third element. To qualify as a group, the set and the operation must satisfy a few conditions called group axioms, namely closure, associativity, identity...
, abelian group
Abelian group
In abstract algebra, an abelian group, also called a commutative group, is a group in which the result of applying the group operation to two group elements does not depend on their order . Abelian groups generalize the arithmetic of addition of integers...
s, geometry
Geometry
Geometry arose as the field of knowledge dealing with spatial relationships. Geometry was one of the two fields of pre-modern mathematics, the other being the study of numbers ....
, the real number field, and complex number
Complex number
A complex number is a number consisting of a real part and an imaginary part. Complex numbers extend the idea of the one-dimensional number line to the two-dimensional complex plane by using the number line for the real part and adding a vertical axis to plot the imaginary part...
s. His 1902 axiomatization of the real numbers has been characterized as "one of the first successes of abstract mathematics" and as having "filled the last gap in the foundations of Euclidean geometry". Huntington excelled at proving axioms independent of each other by finding a sequence of models
Model theory
In mathematics, model theory is the study of mathematical structures using tools from mathematical logic....
, each one satisfying all but one of the axioms in a given set. His 1917 book The Continuum and Other Types of Serial Order was in its day "...a widely read introduction to Cantor
Georg Cantor
Georg Ferdinand Ludwig Philipp Cantor was a German mathematician, best known as the inventor of set theory, which has become a fundamental theory in mathematics. Cantor established the importance of one-to-one correspondence between the members of two sets, defined infinite and well-ordered sets,...
ian set theory
Set theory
Set theory is the branch of mathematics that studies sets, which are collections of objects. Although any type of object can be collected into a set, set theory is applied most often to objects that are relevant to mathematics...
." (Scanlan 1999) Yet Huntington and the other American postulate theorists played no role in the rise of axiomatic set theory then taking place in continental Europe.
In 1904, Huntington put Boolean algebra on a sound axiomatic foundation. He revisited Boolean axiomatics in 1933, proving that Boolean algebra required but a single binary operation
Binary operation
In mathematics, a binary operation is a calculation involving two operands, in other words, an operation whose arity is two. Examples include the familiar arithmetic operations of addition, subtraction, multiplication and division....
(denoted below by infix
Infix notation
Infix notation is the common arithmetic and logical formula notation, in which operators are written infix-style between the operands they act on . It is not as simple to parse by computers as prefix notation or postfix notation Infix notation is the common arithmetic and logical formula notation,...
'+') that commutes and associates, and a single unary operation
Unary operation
In mathematics, a unary operation is an operation with only one operand, i.e. a single input. Specifically, it is a functionf:\ A\to Awhere A is a set. In this case f is called a unary operation on A....
, complementation, denoted by a postfix prime. The only further axiom Boolean algebra requires is:
'+(a '+b)' = a,
now known as Huntington's axiom.
Revising a method from Joseph Adna Hill
Joseph Adna Hill
Joseph Adna Hill was an American statistician, born at Stewartstown, New Hampshire; he graduated from Harvard University in 1885 and from the University of Halle in 1892...
, Huntington is credited with the Method of Equal Proportions or Huntington-Hill method
Huntington-Hill method
The Huntington–Hill method of apportionment assigns seats by finding a modified divisor D such that each constituency's priority quotient , using the geometric mean of the lower and upper quota for the divisor, yields the correct number of seats that minimizes the percentage differences in the size...
of apportionment of seats in the U.S. House of Representatives to the states, as a function of their populations determined in the U.S. censushttp://www.ams.org/featurecolumn/archive/apportion2.html. This mathematical algorithm has been used in the U.S. since 1941 and is currently the method used.
In 1919, Huntington was the first President of the Mathematical Association of America
Mathematical Association of America
The Mathematical Association of America is a professional society that focuses on mathematics accessible at the undergraduate level. Members include university, college, and high school teachers; graduate and undergraduate students; pure and applied mathematicians; computer scientists;...
, which he helped found. He was elected to the American Academy of Arts and Sciences
American Academy of Arts and Sciences
The American Academy of Arts and Sciences is an independent policy research center that conducts multidisciplinary studies of complex and emerging problems. The Academy’s elected members are leaders in the academic disciplines, the arts, business, and public affairs.James Bowdoin, John Adams, and...
in 1913, and to the American Philosophical Society
American Philosophical Society
The American Philosophical Society, founded in 1743, and located in Philadelphia, Pa., is an eminent scholarly organization of international reputation, that promotes useful knowledge in the sciences and humanities through excellence in scholarly research, professional meetings, publications,...
in 1933.
External links
- MacTutor biography: Edward Vermilye Huntington
- University of York: Portraits of Staticians. Photograph Courtesy of the Mathematical Association of America. All Right Reserved