Title: Three Mathematical Vignettes: Millennial, Promiscuous, and
Abstract: In the first century A.D., the Introduction to Arithmetic, by Nicomachus of Gerasa and Mathematics Useful for Understanding Plato by Theon of Smyrna were one the few sources of knowledge of formal Greek arithmetic in the Middle Ages. The books are philosophical in nature, contain few original results, and no formal proofs. They abound, however, in intriguing observations in number theory. We discuss and extend some of the number theoretic results found in these ancient volumes. Secondly, we discuss the promiscuous scheme proposed by John Colson, Lucasian Professor of Mathematics at Cambridge, for avoiding the use of the digits 6,7,8, and 9. Finally, we mention, Louis Antoine de Bougainville, mathematician, explorer, and student of D'Alembert who wrote a sequel to L'Hospital's "Analyse des Infiniment Petits". Bougainville was present at the Battle of Quebec and when Cornwallis surrendered at Yorktown. He also circumnavigated the globe. We discuss some of the contents of his text book and recount several of his adventures.
Jim Tattersall received an undergraduate degree in mathematics from the
University of Virginia in 1963, a Master's degree from the University of
Massachusetts in 1965, and a Ph.D. degree in mathematics from the
University of Oklahoma in 1971.
On a number of occasions he has been a visiting scholar at the Department of Pure Mathematics and Mathematical Statistics at Cambridge University. In 1991, he spent six months as a visiting mathematician at the American Mathematical Society. In 1995-1996, he spent eighteen months as a visiting professor at the U.S. Military Academy at West Point.
He was given the Award for Distinguished Service (1992) and the Award and for Distinguished College Teaching (1997) from the Northeastern Section of the MAA.
He has served as President of Canadian Society for the History and Philosophy of Mathematics, Archivist/Historian of NES/MAA, and Associate Secretary of the Mathematical Association of America.
His book on number theory was published by Cambridge University Press.