Robert McDowell Thrall (1914–2006) was an American mathematician and a pioneer of

operations research Operations research ( en-GB, operational research) (U.S. Air Force Specialty Code: Operations Analysis), often shortened to the initialism OR, is a discipline that deals with the development and application of analytical methods to improve decis ...

Biography

Thrall graduated in 1935 with BA from

Illinois College Illinois College is a private liberal arts college in Jacksonville, Illinois. It is affiliated with the United Church of Christ and the Presbyterian Church (USA). It was the second college founded in Illinois, but the first to grant a degree ( ...

and in 1937 with MA and PhD in mathematics from the

University of Illinois 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 Univer ...

. From 1937 to 1969 he was a professor of mathematics at the

University of Michigan , mottoeng = "Arts, Knowledge, Truth" , former_names = Catholepistemiad, or University of Michigania (1817–1821) , budget = $10.3 billion (2021) , endowment = $17 billion (2021)As o ...

in Ann Arbor. In 1969 he became a professor in the newly founded department of Mathematical Sciences (''i.e.'' applied mathematics) at Rice University. He chaired the department from 1969 to 1974. In 1977 he received a joint appointment in Rice's newly established Graduate School of Business, where he taught

decision analysis Decision analysis (DA) is the discipline comprising the philosophy, methodology, and professional practice necessary to address important decisions in a formal manner. Decision analysis includes many procedures, methods, and tools for identifyi ...

to MBA Students. He retired from Rice University as professor emeritus in 1984. At the beginning of his career, Thrall's research was in

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 ...

ring theory In algebra, ring theory is the study of rings—algebraic structures in which addition and multiplication are defined and have similar properties to those operations defined for the integers. Ring theory studies the structure of rings, their r ...

, and

representation theory Representation theory is a branch of mathematics that studies abstract algebraic structures by ''representing'' their elements as linear transformations of vector spaces, and studies modules over these abstract algebraic structures. In essen ...

. His research accomplishments during that period include the celebrated hooklength formula for the dimension of an irreducible representation of a

symmetric group In abstract algebra, the symmetric group defined over any set is the group whose elements are all the bijections from the set to itself, and whose group operation is the composition of functions. In particular, the finite symmetric group ...

, or equivalently the number of

standard Young tableaux In mathematics, a Young tableau (; plural: tableaux) is a combinatorial object useful in representation theory and Schubert calculus. It provides a convenient way to describe the group representations of the symmetric and general linear groups and ...

of a given shape (with J. Sutherland Frame and G. de B. Robinson) and the influential Brauer-Thrall conjectures (with

Richard Brauer Richard Dagobert Brauer (February 10, 1901 – April 17, 1977) was a leading German and American mathematician. He worked mainly in abstract algebra, but made important contributions to number theory. He was the founder of modular represent ...

). For two years, from 1940 to 1942, he was a visiting scholar at the

Institute for Advanced Study The Institute for Advanced Study (IAS), located in Princeton, New Jersey, in the United States, is an independent center for theoretical research and intellectual inquiry. It has served as the academic home of internationally preeminent schola ...

. During WW II he began to study operations research and development of mathematical models for military applications. From 1957 to 1961 he was the editor-in-chief of ''Management Science'', as successor to C. West Churchman. From 1961 to 1965 Thrall was an associate editor for the journal. He was the 16th president of

The Institute of Management Sciences The Institute for Operations Research and the Management Sciences (INFORMS) is an international society for practitioners in the fields of operations research (O.R.), management science, and analytics. It was established in 1995 with the merger of ...

(TIMS) (now

INFORMS The Institute for Operations Research and the Management Sciences (INFORMS) is an international society for practitioners in the fields of operations research (O.R.), management science, and analytics. It was established in 1995 with the merger o ...

) for a one-year term in 1969–1970. He was elected to the 2002 class of

Fellow A fellow is a concept whose exact meaning depends on context. In learned or professional societies, it refers to a privileged member who is specially elected in recognition of their work and achievements. Within the context of higher education ...

s of the

Institute for Operations Research and the Management Sciences The Institute for Operations Research and the Management Sciences (INFORMS) is an international society for practitioners in the fields of operations research (O.R.), management science, and analytics. It was established in 1995 with the merger of ...

. With

William W. Cooper William Wager Cooper (July 23, 1914 – June 20, 2012) was an American operations researcher, known as a father of management science and as "Mr. Linear Programming".. He was the founding president of The Institute of Management Sciences, founding ...

Rajiv Banker Rajiv D. Banker''(born 1953, deceased March 1, 2023)was an accounting researcher and educator, recognized by the Institute for Scientific Information ( Web of Science) as one of the 150 most influential researchers in economics and business. He i ...

, and other collaborators, he wrote a number of important papers on

data envelopment analysis Data envelopment analysis (DEA) is a nonparametric method in operations research and economics for the estimation of production frontiers.Charnes et al (1978) DEA has been applied in a large range of fields including international banking, econom ...

(DEA). Thrall was the author or co-author of over 100 articles in scholarly journals, as well as several books. He married Natalie Hunter in 1936. His wife died in 2004. Upon his death he was survived by a daughter, two sons, three grandchildren, and three great-grandchildren.

Selected publications

Articles

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Books

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References

{{DEFAULTSORT:Thrall, Robert M. 1914 births 2006 deaths 20th-century American mathematicians 21st-century American mathematicians Algebraists Operations researchers Illinois College alumni University of Illinois Urbana-Champaign alumni Rice University faculty University of Michigan faculty Fellows of the Institute for Operations Research and the Management Sciences