Biography of Joseph Arkin 

An American Ramanujan


Joseph Arkin, Senior Lecturer for the past eight years in the Department of Mathematical Sciences, United States Military Academy, retired on 23 September 1994.  Joseph Arkin was born on 25 May 1923, at Brooklyn, New York.  He served his country in the Army during World War II and was retired as a disabled American Veteran.  Without any formal education beyond his high school training at Boy's High in Brooklyn, he managed to study on his own and learned the concepts and theoretical foundations of number theory.  He helped others learn about the beauty of mathematics by serving as a part-time instructor at Ramapo Public Schools (1962-67) and as a part-time Visiting Lecturer at Orange County Community College (1962-67).  He has been a member of the American Mathematical Society and the Mathematics Association of America since 1967 and became a charter member of the Fibonacci Society in 1965.

Joseph Arkin began working informally with Academy faculty in 1986 and was formally appointed a Lecturer in the Department of Mathematical Sciences in 1988.  This was his first formal appointment.  In 1990 he was promoted to Senior Lecturer.  His vast knowledge, intuitive understanding of the properties and relationships of numbers, and his drive to solve the deepest mysteries of number theory, gave him the skills and motivation to perform state-of-the-art research and solve some of the most challenging problems in this field.

Joseph Arkin's first published work appeared in the American Mathematical Monthly in 1964.  Since then he has written over 50 articles which have appeared in numerous publications such as the Mathematics Magazine, Fibonacci Quarterly, SIAM Review, Duke Mathematical Journal, Journal of Recreational Mathematics, Notices of the American Mathematical Society, Canadian Journal of Mathematics, Pacific Journal of Mathematics, and Mathematics and Computer Education.  Among his co-authors and collaborators are many distinguished mathematicians and scientists including Paul Erdos, Ron Graham, E.G. Straus, Richard Pollack, Vern Hoggatt, Paul Smith, V.E. Smith, Gerald Bergum, and Stephan Burr.  Joseph Arkin has made over 50 presentations at professional meetings since 1972.  He has attended and presented papers at the American Mathematical Society meetings, the meetings of the Metropolitan Section of the Mathematics Association of America, International Conferences on the Fibonacci Numbers, Number Theory Conferences, and Army Conferences on Applied Mathematics and Computing. Joseph Arkin has been a member of the New York Academy of Science, the Canadian Mathematics Society, and The Calcutta Mathematics Society.  He is a founding editor of Mathematica Militaris, the newsletter for the Mathematics Departments of the United States Service Academies.

Some of Joseph Arkin's, significant results are in the form of extensions and generalizations of earlier classical works of great mathematicians.  Some of his papers of this type are: "An Extension of a Theorem of Ramanujan," "A Note on a Theorem of Jacobi," "Researches on Some Classical Problems," Exploded Myths," "New Observations on Fermat's Last Theorem," "On Euler's Solution to a Problem of Diophantus," and "An Extension of E. B. Straus' Perfect Latin 3-Cube of Order 7.11 Most of his work was performed in several related areas of number theory.  In particular, Arkin made tremendous contributions in the following areas: Fibonacci and other recursive sequences, partitions, tilings, magic square and cubes, and Latin squares and cubes.

Joseph Arkin was presented with an honorary Ph.D. from Brantridge School in England in 1967.  His awards include the Certificate of Appreciation for Patriotic Civilian Service and the Commander's Award for Public Service.  To stay active in mathematics, Joseph Arkin is continuing his research work on number theory, although at a slower pace than his first 30 years of productive mathematics research work.

By COL David C. Arney, 1994.