HAROLD HOTELLING: A Historical Profile

– written by Greer Arthur

Harold Hotelling was an American mathematical statistician and economic theorist. Born in Fulda, Minnesota, in 1895, he died on December 26, 1973, aged 78 in Chapel Hill, North Carolina.

IN 1919, the same year that the United States Constitution established the prohibition of liquor, Guantanamo Bay was acquired as a naval station and the first electric pop-up toaster was invented, a young Harold Hotelling graduated from the University of Washington with a bachelor’s degree in journalism.

Less than one year later, having received encouragement from Eric Temple Bell, a Scottish-born mathematician who taught at the same university, Hotelling returned to academia to embark on a master’s degree course in mathematics. By the end of his life, this significant switch in academic fields would eventually mark the beginning of an esteemed and influential career in statistics and economics.

Hotelling was born in Fulda, Minnesota, on September 29, 1895, to Clair Alberta Hotelling and Lucy Amelia Rawson. During his childhood the family relocated to Seattle, Washington, a decision driven by the changing face of American society and business, caused at least in part by the success of the Ford Motor Company and its revolutionary production of the automobile.

In Seattle, Hotelling studied through school and university until he completed his master’s degree in 1921, at which point he delved into the realm of mathematics even further by undertaking a PhD at Princeton University, New Jersey. A principal focus of Hotelling’s PhD thesis, entitled “Three Dimensional Manifolds of States of Motion”, was topology, a complex yet fundamental mathematical topic that studies a flexible form of geometry.1

After graduating from Princeton University in 1924, Hotelling worked as an associate professor at Stanford University, California, but soon broadened his gaze to a new arena known as statistics. Despite often being associated with mathematics, statistics is an altogether distinct discipline with uniquely useful qualities. As described by John Wilder Tukey (1915-2000), an American mathematician well known for his contribution to the field, “statistics is a science, not a branch of mathematics, but uses mathematical models as essential tools”.2

Statistics is by no means a young science. The primitive origins of statistics can be traced back to remarkably antiquated beginnings, as early as around 450 BCE when Hippias of Elis, a teacher of philosophy in Ancient Greece, calculated the date of the first Olympic Games by averaging the length of reigns of previous Grecian kings.3 Since then, across centuries, empires and dynasties,3 including and beyond America in the 1920s when Hotelling too began to add to the craft, statistics was and still continues to be refined as an invaluable analytical tool.

In search of further training to pursue his new interest in statistics, Hotelling left Stanford and travelled to an agricultural research station in Rothamstead, England, in 1929.4 Here, Hotelling studied for six months with Sir Ronald Aylmer Fisher (1890-1962), an English statistician and biologist famous for his work in population genetics. Fisher’s well known work also included the application of mathematics for the integration of genetics with natural selection.

Upon returning to the mathematics department at Stanford, Hotelling began to apply his newfound techniques in various fields including journalism, food supply and political science.5 In addition to his statistical work, during the 1920s and 1930s Hotelling also made a substantial impact on various economics topics, including game-theory and depreciation.5 His work on depreciation became particularly influential; his incorporation of mathematics in economic reasoning surpassed traditional methods and set a new standard for the field.4

In 1931, Hotelling obtained a professorship at Columbia University, New York, in the Department of Economics, a position he retained until 1946. As well as teaching mathematical economics here, Hotelling developed a statistics teaching program and eventually founded a department of statistics.

Together with Burton Camp and Arthur Robert Crathorne, both professors of mathematics, Hotelling also founded the Institute of Mathematical Statistics, and in 1937 Hotelling was elected Fellow of the American Statistical Association, of which he also served as vice president in 1941. During World War II, alongside Wilson Allen Wallis (1912-1998), an American economist and statistician, and Jacob Wolfowitz (1910-1981), a Polish-born American statistician, Hotelling worked as a charter member of the Statistical Research Group and contributed his statistical expertise to the war effort.

After the war ended, Hotelling left Columbia University to begin a new chapter at the University of North Carolina (UNC) at Chapel Hill, North Carolina, in 1946. Here, Hotelling worked with Gertrude Cox (1900-1978), an American statistician and first woman elected into the International Statistics Institute, to found a faculty of statistics.

During his time at UNC-Chapel Hill, Hotelling was a professor and chair of the Department of Mathematical Statistics, a professor of economics and also associate director of the Institute of Statistics. Hotelling received a promotion to Kenan Professor of Statistics in 1961. Five years later in 1966, Hotelling retired and in 1972 received the North Carolina Award for Contributions to Science.6 In 1973, Hotelling died in Chapel Hill. In honor of his revered career and pioneering work, UNC-Chapel Hill created the Harold Hotelling Professorship in Economics in 1989.

The vast quantities of publications Hotelling wrote and contributed to are a mere fraction of his legacy. Often referred to as a pioneer of mathematical statistics and economics, Hotelling and his life’s work not only had a profound effect on these fields, but also on the establishment of statistics as a science. By founding and supporting different organizations, departments and faculties, Hotelling ensured that his work would have a lasting impact, and by building solid foundations, allowed the science of statistics and economics to evolve and flourish.

REFERENCES

  1. Bruner R. What is topology? Accessed from http://www.math.wayne.edu/~rrb/topology.html
  2. American Statistical Association. Accessed from http://www.amstat.org/asa/what-is-statistics.aspx
  3. Royal Statistical Society and American Statistical Association. Accessed from http://www.statslife.org.uk/images/pdf/timeline-of-statistics.pdf
  4. Arrow KJ, Lehman EL. Harold Hotelling 1895-1973. A biographical memoir. National Academy of Sciences, 2005. Accessed from http://www.nasonline.org/publications/biographical-memoirs/memoir-pdfs/hotelling-harold.pdf
  5. Kruse M. Harold Hotelling. American Statistical Association. Accessed from https://ww2.amstat.org/about/statisticiansinhistory/blocks/dsp_biosinfo.cfm?BioID=7&pf
  6. University of North Carolina at Chapel Hill. Department of Statistics and Operations Research. Accessed from http://stat-or.unc.edu/support
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