Thomas Storer (American mathematician)

Thomas Frederick Storer (1938 – November 9, 2006) was a Navajo American mathematician who studied combinatorics and cyclotomy. He was a professor at the University of Michigan, and was one of the first Native Americans to become a PhD mathematician. In addition to his mathematical research, teaching, and mentoring, Storer also did notable work on string figures.

Storer, a citizen of the Navajo Nation, was born in 1938.^[1] He attended the University of California, Los Angeles for his bachelors degree, with the help of a football scholarship.^[2][3] He went on to the University of Southern California for his graduate work, receiving an MA in 1962, and a PhD in 1964.^[2][4] His thesis was titled A Family of Generalized Difference Sets, and was advised by Albert Whiteman.^[4] Storer was one of the first Native Americans to complete a PhD in mathematics; Native Hawaiian Edwin Mookini completed his PhD in the same year, at the same institution.^[1][5][6]

In 1965, after a short period in residence in Princeton, New Jersey at the Institute for Advanced Study,^[7] Storer went to the University of Michigan, where he remained for the rest of his career.^[8] He was promoted to full professor in 1979, and retired to emeritus status in 2001.^[3][9]

At the University of Michigan, Storer was known as a teacher and mentor. In 1985, he received the Amoco Foundation Good Teaching Award.^[9] Storer was an advocate for Native American causes on the University of Michigan campus, and learned the language spoken by the Ojibwe people in Michigan.^[3][9] Ten doctoral students completed their PhDs with Storer as their thesis advisor, including Peyton Young (co-advised with Jack Edmonds).^[4]

Storer also wrote several works on string figures, the designs formed by manipulating string around one's fingers. His bibliography on the topic went through three editions.^[3] He also wrote a monograph on string figures, which appeared as a two-volume special issue of the Bulletin of String Figures Association.^[1]

In his monograph, he devised a notation system for compactly and precisely describing string figures.^[1] The International String Figure Association began recommending that contributors use either the older notation of Haddon and Rivers, or else a modified, more verbose version of Storer's notation.^[10]

For example, Storer's monograph encodes the sequence of steps for making the Osage 2-Diamonds string figure (pictured) as follows:^[11]: 84

${\displaystyle {\underline {O}}.A:\square 1\vert }$ ${\displaystyle \star {\overrightarrow {1}}({\underline {5f}})\#\vert }$ ${\displaystyle {\overrightarrow {1}}(2n)\#N1\vert }$ ${\displaystyle {\overleftarrow {2}}\downarrow (1-{\text{⧌}}):<2(\#):\square 5\vert }$ ${\displaystyle ({\text{palms away)}}.}$

Here, the fingers are encoded with the numerals 1 through 5, with 1 representing the thumb and 5 representing the little finger. The notation describes a sequence of movements of a loop held by one finger (a "functor", written before a set of parentheses), relative to a loop held by another finger (an "object", written inside parentheses). The symbol ${\displaystyle \square }$ denotes releasing a loop of string, while the vertical line ${\displaystyle \vert }$ denotes moving hands apart so that the string is not slack.^{[1][11]: 1–28}

Storer was married to Karen Storer for a period of over 30 years. He had two daughters.^[3][9] Storer died on November 9, 2006.^[2][9]

• Storer, Thomas (1967). Cyclotomy and difference sets. Lectures in Advanced Mathematics. Vol. 2. Markham Publishing Co. MR 0217033. Zbl 0157.03301.
• Storer, Thomas (2000). String Figure Bibliography (PDF) (3rd ed.). ISFA Press. ISBN 0-9651467-5-8. Earlier editions: 1st ed. (1985), Bulletin of SFA, vol. 12; 2nd ed. (1996), ISFA Press, ISBN 0965146715.
• Storer, T. (1988). "String Figures". Bulletin of String Figures Association. 16 (Supplemental Issue in Two Parts). Nippon Ayatori Kyokai: 410 pages.

• Difference sets