This issue marks another changing-of-the-guard for the Monthly. Paul Halmos' act will be a tough one to follow, but the new team of Associate Editors (see inside front cover) and I will do our best. As always, the Monthly is looking for fine expository writing on mathematical topics. We want reviews of evolving fields of research, new insights into old mathematical truths, elegant ways of dealing with complex ideas in the classroom, and other celebrations of the beauty of our subject. From time to time I'd like to offer some thoughts of my own, and I'll do that in 'The Editor's Corner.' I don't want to be Cornered into a fixed commitment, so the column will appear only irregularly. In this first effort I offer some thoughts on Riemann's Hypothesis (RH). Most professional mathematicians are aware that RH exists and that it is an extremely important unsolved question in pure mathematics, particularly in number theory. I want to share with you a very simple way of stating the problem; one that could be explained to a bright class of tenth graders. Then I'll have a little to say about some of the ramifications of RH, and finally there will be some news about exciting recent developments in the field. First, how might we explain the problem to high school students? Here's one way. Beginning with the set of all positive integers, let's discard those that are divisible by the square of any integer larger than 1. Thus, we throw out 4, 8, 9, 16, 18, 20, 24,..., etc. We are left with the list of the squarefree positive integers,