Introducing Dan Kalman
“Wow! That is so cool!” That’s what I have felt so many times after discovering an unexpected or surprising mathematical result. Generally, these results are not what accomplished research mathematicians would consider deep. Indeed, almost every paper I have written is based on undergraduate mathematics and involves methods that never stray far from the standard curriculum. But these topics are so rich and interconnected that opportunities for new discoveries abound. It has been my great good fortune to uncover a few of them. Having made a discovery, I invariably want to share it. And it is another aspect of my great good fortune that I enjoy writing about discoveries almost as much as I enjoy making them (and talking about them).
One is sometimes asked, where do you get your ideas? For me, it has almost always been pure serendipity. Over and over again, some intriguing mathematical puzzle has unexpectedly dropped into my lap. Inspiration has come from preparing for classes, ideas and work of my students, suggestions of colleagues, and applied projects from my aerospace industry days. Here are some examples: I am trying to understand why a co-worker (a software pro) had coded an application in a certain way. In a sudden flash of insight, I realize that his programming approach can be extended to an entirely different problem. (Doubly Recursive Multivariate Automatic Differentiation) After giving a lecture to students, I receive an email message from an attendee pointing out a wonderful extension, complete with a reference to one of Euler’s papers. (Another Way to Sum a Series: Generating Functions, Euler, and the Dilog Function) My father is telling me about all of the references to numerology in a book he is reading. I mention number theory as an area of math that is somewhat related, and as an example describe a long-standing open problem. To my surprise, he instantly offers me a solution. (A Perfectly Odd Encounter in a Reno Cafe) Although there is not room here to do them justice, I must at least mention two other aspects of my mathematical meanderings: teaching and collaboration.
It is a great pleasure to be able to share some of my favorite articles in this MAA Virtual Special Issue. In light of the comments above, no one should be surprised that it is quite an eclectic collection. I hope that readers will derive as much enjoyment from these papers as I obtained in their development and writing.
Dan Kalman’s Chosen Articles