Math Monthly

Della Dumbaugh is a professor of mathematics at the University of Richmond. Her research is in the history of algebra and number theory. She says:

When Mark Warner was governor of Virginia he asked, “what do historians of mathematics study?” That is a great question. We study mathematics, the people who create mathematics, the institutions that support mathematics, the false starts in particular areas of mathematics, the politics that influence the development of mathematics, and how the larger cultural context impinges on the development of mathematics. This discipline combines technical questions in mathematics with appropriate historical questions to yield a rich perspective on both mathematics and history.

I must say that I wish I knew more about the history of math. When trying to add to the collection of theorems that are known to be true, it would definitely have helped to be more aware of their history.

Dumbaugh was named the editor-in-chief of American Mathematical Monthly, starting in January 2022. The Monthly has been published since 1894, and its editors mostly have served five-year terms. She is only the second woman to serve as editor, a figure that seems to be low, way low. Yet she is also the second consecutive female editor. Maybe that is the beginning of a streak.

Her View of the Monthly

Dumbaugh found the Monthly in a novel way: Here is a neat interview with her that explains it. Check out the part on her relationship to the Monthly:

I may be one of the few members of the mathematical community who did not meet the Monthly through the content on its pages. Instead, I met the journal through my PhD research on Leonard Dickson and his work in the theory of algebras. In particular, Dickson aimed to elevate the standard of American mathematics through quality journal publications and he served as an editor of the Monthly from 1903 to 1906. After I finished my dissertation, I turned my attention to a question about Dickson’s celebrated History of the Theory of Numbers and published that article in the Monthly.

My View of the Monthly

I found the Monthly in a more common way: as a high school student. I loved it from the beginning, have read it for decades, yet have never submitted to it. I still recall using my hard earned money, money from odd jobs, to pay for my subscription to the Monthly.

I enjoyed the articles, but especially liked two features. The problem session each issue and the reviews of other articles and books. Since this was decades before the Internet seeing these articles helped me learn about directions and areas of mathematics.

I still recall seeing the 1962 Putnam exam in the Monthly. It was the first that I ever saw. I later took the exam as an undergraduate and did poorly. Oh well.

More recently, I was struck by the article, “Calculating Intersections: The Crossroads of Mathematics and Literature in the Lives of Mother and Daughter” by a mother and daughter: Della Dumbaugh and Hannah Fenster. Read it for interesting comments about the mom and daughter relationship:

This article tells the stories of how we, Della (mom, mathematician) and Hannah (daughter, writing instructor and bookseller), arrived in our professional settings through the lens of mother and daughter. For us, the intersections of literature and mathematics inspired many of our pivotal moments.

Open Problems

Ken recently had an article in the Monthly with Bill Gasarch and also Mark Villarino, who had another that same year. What I would think of as a good paper for the Monthly has a mixture of history, survey elements, and originality of approach to an entertaining problem, framed to be accessible to a high-school student. What topics might our readers suggest?