You think you've got problems.

Introduction. My life, like that of any other’s, has its share of problems. I consider myself fortunate, however, to have more problems than most. In the past several years I’ve dealt with war, gambling, and drugs to name but a few. In writing this article I intend to dump some of my problems on you. The problems that I refer to are mathematical, but accessible to a wider audience (so keep reading). Several problems will be surveyed, with an overview of their origins and a brief discussion of the processes involved in their solutions. Computations will be kept to a minimum and there will be plenty of visuals to aid you in understanding the major ideas. Some of these problems have led to publications, others to presentations at conferences; some are still works in progress. Hopefully, you will find these problems interesting in their own right. At least, this article will shed a little light on what kind of problems some mathematics professors experience outside the classroom.