Henry Morgan Ward"New York, New York City Births, 1846-1909," database, FamilySearch (https://familysearch.org/ark:/61903/1:1:2WWG-V9Y : 11 February 2018), Henry Morgan Ward, 20 Aug 1901; citing Manhattan, New York, New York, United States, reference cn 32514 New York Municipal Archives, New York; FHL microfilm 1,983,307. (August 20, 1901 – June 26, 1963) was an American mathematician, a professor of

mathematics Mathematics is a field of study that discovers and organizes methods, Mathematical theory, theories and theorems that are developed and Mathematical proof, proved for the needs of empirical sciences and mathematics itself. There are many ar ...

at the

California Institute of Technology The California Institute of Technology (branded as Caltech) is a private research university in Pasadena, California, United States. The university is responsible for many modern scientific advancements and is among a small group of institutes ...

Education and career

Ward was born in New York City. He studied at

University of California, Berkeley The University of California, Berkeley (UC Berkeley, Berkeley, Cal, or California), is a Public university, public Land-grant university, land-grant research university in Berkeley, California, United States. Founded in 1868 and named after t ...

, receiving his BA in 1924. He obtained his Ph.D. in mathematics from Caltech in 1928, with a dissertation titled ''The Foundations of General Arithmetic''; his advisor was

Eric Temple Bell Eric Temple Bell (7 February 1883 – 21 December 1960) was a Scottish-born mathematician, educator and science fiction writer who lived in the United States for most of his life. He published non-fiction using his given name and fiction ...

.. He became a research fellow at Caltech, and then in 1929 a member of the faculty; he remained at Caltech until his death in 1963.Collection Profile: Morgan Ward (1901–1963)
, Caltech Library, retrieved 2010-09-12. Among his doctoral students was Robert P. Dilworth, who also became a Caltech professor. Ward is the academic ancestor of over 500 mathematicians and computer scientists through Dilworth and another of his students, Donald A. Darling.

Research

Ward's research interests included the study of

recurrence relation In mathematics, a recurrence relation is an equation according to which the nth term of a sequence of numbers is equal to some combination of the previous terms. Often, only k previous terms of the sequence appear in the equation, for a parameter ...

s and the

divisibility In mathematics, a divisor of an integer n, also called a factor of n, is an integer m that may be multiplied by some integer to produce n. In this case, one also says that n is a ''Multiple (mathematics), multiple'' of m. An integer n is divis ...

properties of their solutions,

diophantine equation ''Diophantine'' means pertaining to the ancient Greek mathematician Diophantus. A number of concepts bear this name: *Diophantine approximation In number theory, the study of Diophantine approximation deals with the approximation of real n ...

s including

Euler's sum of powers conjecture In number theory, Euler's conjecture is a disproved conjecture related to Fermat's Last Theorem. It was proposed by Leonhard Euler in 1769. It states that for all integers and greater than 1, if the sum of many th powers of positive integers ...

and equations between

monomial In mathematics, a monomial is, roughly speaking, a polynomial which has only one term. Two definitions of a monomial may be encountered: # A monomial, also called a power product or primitive monomial, is a product of powers of variables with n ...

abstract algebra In mathematics, more specifically algebra, abstract algebra or modern algebra is the study of algebraic structures, which are set (mathematics), sets with specific operation (mathematics), operations acting on their elements. Algebraic structur ...

lattice theory A lattice is an abstract structure studied in the mathematical subdisciplines of order theory and abstract algebra. It consists of a partially ordered set in which every pair of elements has a unique supremum (also called a least upper bou ...

and

residuated lattice In abstract algebra, a residuated lattice is an algebraic structure that is simultaneously a lattice (order), lattice ''x'' ≤ ''y'' and a monoid ''x''•''y'' which admits operations ''x''\''z'' and ''z''/''y'', loosely analogous to division or i ...

functional equation In mathematics, a functional equation is, in the broadest meaning, an equation in which one or several functions appear as unknowns. So, differential equations and integral equations are functional equations. However, a more restricted meaning ...

s and functional iteration, and

numerical analysis Numerical analysis is the study of algorithms that use numerical approximation (as opposed to symbolic computation, symbolic manipulations) for the problems of mathematical analysis (as distinguished from discrete mathematics). It is the study of ...

.. He also worked with the

National Science Foundation The U.S. National Science Foundation (NSF) is an Independent agencies of the United States government#Examples of independent agencies, independent agency of the Federal government of the United States, United States federal government that su ...

on the reform of the elementary school mathematics curriculum, and with Clarence Ethel Hardgrove he wrote the textbook ''Modern Elementary Mathematics'' (Addison-Wesley, 1962). Ward's works are collected in the Caltech library. A

symposium In Ancient Greece, the symposium (, ''sympósion'', from συμπίνειν, ''sympínein'', 'to drink together') was the part of a banquet that took place after the meal, when drinking for pleasure was accompanied by music, dancing, recitals, o ...

in his memory was held at Caltech on November 21–22, 1963. ''Ward

quasigroups In mathematics, especially in abstract algebra, a quasigroup is an algebraic structure that resembles a group in the sense that " division" is always possible. Quasigroups differ from groups mainly in that the associative and identity element prop ...

'' are named after him, following his paper on alternative set of

group A group is a number of persons or things that are located, gathered, or classed together. Groups of people * Cultural group, a group whose members share the same cultural identity * Ethnic group, a group whose members share the same ethnic iden ...

axioms 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 f ...

Personal life

Ward died of a heart attack in

Duarte, California Duarte () is a city in Los Angeles County, California, United States. As of the 2020 United States census, 2020 census, the city population was 21,727. It is bounded to the north by the San Gabriel Mountains, to the north and west by the cities ...

References

{{DEFAULTSORT:Ward, Morgan 20th-century American mathematicians Lattice theorists California Institute of Technology alumni California Institute of Technology faculty 1901 births 1963 deaths California Institute of Technology fellows