Edward Vermilye Huntington (April 26, 1874November 25, 1952) was an American

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, mathematical structure, structure, space, Mathematica ...

Biography

Huntington was awarded the B.A. and the M.A. by

Harvard University Harvard University is a Private university, private Ivy League research university in Cambridge, Massachusetts, United States. Founded in 1636 and named for its first benefactor, the History of the Puritans in North America, Puritan clergyma ...

in 1895 and 1897, respectively. After two years' teaching at

Williams College Williams College is a Private college, private liberal arts colleges in the United States, liberal arts college in Williamstown, Massachusetts, United States. It was established as a men's college in 1793 with funds from the estate of Ephraim ...

, he began a doctorate at the

University of Strasbourg The University of Strasbourg (, Unistra) is a public research university located in Strasbourg, France, with over 52,000 students and 3,300 researchers. Founded in the 16th century by Johannes Sturm, it was a center of intellectual life during ...

, 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 (from German language, German: ', "description of a State (polity), state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data. In applying statistics to a s ...

, unusual for the time, and worked on statistical problems for the USA military during

World War I World War I or the First World War (28 July 1914 – 11 November 1918), also known as the Great War, was a World war, global conflict between two coalitions: the Allies of World War I, Allies (or Entente) and the Central Powers. Fighting to ...

. Huntington's primary research interest was the

foundations of mathematics Foundations of mathematics are the mathematical logic, logical and mathematics, mathematical framework that allows the development of mathematics without generating consistency, self-contradictory theories, and to have reliable concepts of theo ...

. He was one of the "American postulate theorists" (according to Michael Scanlan, the expression is due to John Corcoran), American mathematicians active early in the 20th century (including E. H. Moore and

Oswald Veblen Oswald Veblen (June 24, 1880 – August 10, 1960) 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; while this was lo ...

) who proposed axiom sets for a variety of mathematical systems. In so doing, they helped found what is now known as

metamathematics Metamathematics is the study of mathematics itself using mathematical methods. This study produces metatheory, metatheories, which are Mathematical theory, mathematical theories about other mathematical theories. Emphasis on metamathematics (and ...

and

model theory In mathematical logic, model theory is the study of the relationship between theory (mathematical logic), formal theories (a collection of Sentence (mathematical logic), sentences in a formal language expressing statements about a Structure (mat ...

. Huntington was perhaps the most prolific of the American postulate theorists, devising sets of

axiom An axiom, postulate, or assumption is a statement that is taken to be true, to serve as a premise or starting point for further reasoning and arguments. The word comes from the Ancient Greek word (), meaning 'that which is thought worthy or ...

s (which he called "postulates") for groups,

abelian group In mathematics, 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 the order in which they are written. That is, the group operation is commu ...

geometry Geometry (; ) is a branch of mathematics concerned with properties of space such as the distance, shape, size, and relative position of figures. Geometry is, along with arithmetic, one of the oldest branches of mathematics. A mathematician w ...

, the real number field, and

complex number In mathematics, a complex number is an element of a number system that extends the real numbers with a specific element denoted , called the imaginary unit and satisfying the equation i^= -1; every complex number can be expressed in the for ...

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 A model is an informative representation of an object, person, or system. The term originally denoted the plans of a building in late 16th-century English, and derived via French and Italian ultimately from Latin , . Models can be divided int ...

, 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 A cantor or chanter is a person who leads people in singing or sometimes in prayer. Cantor as a profession generally refers to those leading a Jewish congregation, although it also applies to the lead singer or choir director in Christian contexts. ...

ian

set theory Set theory is the branch of mathematical logic that studies Set (mathematics), sets, which can be informally described as collections of objects. Although objects of any kind can be collected into a set, set theory – as a branch of mathema ...

" (Scanlan 1999). Yet Huntington and the other American postulate theorists played no role in the rise of

axiomatic set theory Set theory is the branch of mathematical logic that studies Set (mathematics), sets, which can be informally described as collections of objects. Although objects of any kind can be collected into a set, set theory – as a branch of mathema ...

then taking place in continental Europe. In 1904, Huntington put

Boolean algebra In mathematics and mathematical logic, Boolean algebra is a branch of algebra. It differs from elementary algebra in two ways. First, the values of the variable (mathematics), variables are the truth values ''true'' and ''false'', usually denot ...

on a sound axiomatic foundation. He revisited Boolean axiomatics in 1933, proving that Boolean algebra required but a single

binary operation In mathematics, a binary operation or dyadic operation is a rule for combining two elements (called operands) to produce another element. More formally, a binary operation is an operation of arity two. More specifically, a binary operation ...

(denoted below by

infix An infix is an affix inserted inside a word stem (an existing word or the core of a family of words). It contrasts with '' adfix,'' a rare term for an affix attached to the outside of a stem, such as a prefix or suffix. When marking text for ...

'+') that commutes and associates, and a single

unary operation In mathematics, a unary operation is an operation with only one operand, i.e. a single input. This is in contrast to ''binary operations'', which use two operands. An example is any function , where is a set; the function is a unary operation ...

, complementation, denoted by a postfix prime. The only further axiom Boolean algebra requires is: :(''a'' '+''b'' ')'+(''a'' '+''b'')' = ''a'', now known as Huntington's axiom. Revising a method from

Joseph Adna Hill Joseph Adna Hill (1860–1938) was an American statistician. Biography Joseph Adna Hill was born at Stewartstown, New Hampshire on May 5, 1860. He was descended from "an elite, old-line New England family," and attended many well-regarded educ ...

, Huntington is credited with the method of equal proportions or

Huntington–Hill method The Huntington–Hill method, sometimes called method of equal proportions, is a highest averages method for assigning seats in a legislature to political parties or states. Since 1941, this method has been used to apportion the 435 seats in the U ...

apportionment The legal term apportionment (; Mediaeval Latin: , derived from , share), also called delimitation, is in general the distribution or allotment of proper shares, though may have different meanings in different contexts. Apportionment can refer ...

of seats in the

U.S. House of Representatives The United States House of Representatives is a chamber of the bicameral United States Congress; it is the lower house, with the U.S. Senate being the upper house. Together, the House and Senate have the authority under Article One of th ...

to the states, as a function of their populations determined in the U.S. Census

This mathematical algorithm has been used in the U.S. since 1941 and is currently the method used. In 1919, Huntington was the third President of the

Mathematical Association of America The Mathematical Association of America (MAA) is a professional society that focuses on mathematics accessible at the undergraduate level. Members include university A university () is an educational institution, institution of tertiary edu ...

, which he helped found as a charter member and its first vice-president. He was elected to the

American Academy of Arts and Sciences The American Academy of Arts and Sciences (The Academy) is one of the oldest learned societies in the United States. It was founded in 1780 during the American Revolution by John Adams, John Hancock, James Bowdoin, Andrew Oliver, and other ...

in 1913 and the

American Philosophical Society The American Philosophical Society (APS) is an American scholarly organization and learned society founded in 1743 in Philadelphia that promotes knowledge in the humanities and natural sciences through research, professional meetings, publicat ...

in 1933. In 1942 he was elected as a Fellow of the American Statistical Association.View/Search Fellows of the ASA
, accessed 2016-07-23.

Notes

References

* Scanlan, M. (1999) "Edward Vermilye Huntington,"

American National Biography The ''American National Biography'' (ANB) is a 24-volume biographical encyclopedia set that contains about 17,400 entries and 20 million words, first published in 1999 by Oxford University Press under the auspices of the American Council of Lea ...

11: 534-36,

Oxford University Press Oxford University Press (OUP) is the publishing house of the University of Oxford. It is the largest university press in the world. Its first book was printed in Oxford in 1478, with the Press officially granted the legal right to print books ...

External links

*
Photograph of E. V. Huntington
courtesy of the

.
NEW SETS OF INDEPENDENT POSTULATES FOR THE ALGEBRA OF LOGIC, WITH SPECIAL REFERENCE TO WHITEHEAD AND RUSSELL’S PRINCIPIA MATHEMATICA^*
by EDWARD V. HUNTINGTON from January 1933 {{DEFAULTSORT:Huntington, Edward Vermilye 1874 births 1952 deaths Harvard University alumni Williams College faculty University of Strasbourg alumni Harvard University Department of Mathematics faculty Fellows of the American Statistical Association Presidents of the Mathematical Association of America 20th-century American mathematicians People from Clinton, Oneida County, New York Members of the American Philosophical Society