Math Colloquium | From Ancient Egyptian Fractions to Modern Algebra, Feb. 2

The Mathematics Department colloquium series features Greg Oman discussing "From Ancient Egyptian Fractions to Modern Algebra" on Feb. 2 at 4 p.m. in Morton 115 or via Teams.

Oman is Associate Professor of Mathematics at the University of Colorado - Colorado Springs.

Abstract: The ancient Egyptians did not use conventional notation to express rational numbers. In fact, they only had notation for so-called 'unit fractions', that is, rational numbers of the form 1/n for some nonzero integer n. They expressed rational numbers as sums of *distinct* unit fractions. Fibonnaci proved that every rational number can be so-expressed, and in contemporary mathematics, there remain unsolved number-theoretic problems involving sums of unit fractions. The purpose of this talk is to translate the notion of 'Egyptian fraction' to the realm of ring theory, and to lay some groundwork in this direction. The fundamentals of the talk should be widely accessible, and technical results do not require obscure algebraic machinery.