## The Mysteries of Unit Fractions

From Egyptian Fractions to the Riemann Hypothesis

Dr. Ben Braun, Assistant Professor of Mathematics at the University of Kentucky will present the departments' final Fast Talk of the semester on Friday, November 8 at 3:30 p.m. in Olin 114.

From Egyptian Fractions to the Riemann Hypothesis: The Mysteries of Unit Fractions - Many of the deepest questions in mathematics are rooted in what seem the simplest of objects. In geometry, circles lead to the number we call Pi, while triangles lead to the Pythagorean Theorem and its failure in non-Euclidean geometry. In number theory, the desire to divide natural numbers into equal parts leads us to rational numbers, the simplest of which are of the form 1/n, called unit fractions. In this talk, we will explore some of the fascinating properties of unit fractions, starting in the ancient world and closing in the 21st century. Along the way, we will see a selection of long-standing unsolved problems that are deceptively easy to state.