Perfect Numbers

Summary

Editor's Note: This short pedagogical note appears very early in the history of the Magazine. Written by a student, Zena Garrett, at Mississippi Delta State Teachers College, it describes how she worked, under the direction of her teacher, identified only as “Miss Dale,” to find the next perfect number after 6 and 28. (Perfect numbers are positive integers that equal the sum of their proper divisors.) The directions she was given–“we were instructed to work alone and forbidden to use the library”–sound strikingly like the Moore Method, pioneered only somewhat earlier by R. L. Moore at the University of Pennsylvania and the University of Texas. Miss Garrett succeeded in finding 496 and 8128 and then went on to find the formula 2^n-1(2ⁿ - 1), with 2ⁿ - 1 a prime, for even perfect numbers. (No odd perfect numbers are known.) This piece appeared at a time when most of the articles in the Magazine were concerned with commercial arithmetic, high school algebra and articles on how to teach, so this was one of the early articles to explore a more advanced mathematical question, albeit as an early example of undergraduate research.

Ms. Garrett was 18 when she wrote this article and is still alive and living in Massachusetts. She did not go on in mathematics but instead earned a master's in English at UCLA, became a sculptor, wrote short stories and a book, The House in the Mulberry Tree, and eventually moved on to architecture (without degrees in the field), mainly involved in restoration and preservation of old houses in New York and the Hamptons.