Quotations in Context

In the Convergence article series “HoM Toolbox, or Historiography and Methodology for Mathematicians,” on the page “Introduction - How Do We Know About the Past?”, Amy Ackerberg-Hastings reminds the reader that sources of historical information can be broken into primary, secondary, and tertiary sources. Articles aimed at an audience of fellow scholars in a given field will be careful to emphasize primary sources. In contrast, it is an unfortunate fact that many of the mathematical quotations circulated on the internet or in publications aimed at a general audience tend to come from tertiary sources; that is, they rarely are drawn from direct examinations of the works of the attributed authors, and in fact such quotations are often shared without any mention of the primary sources in which they originally appeared.

Because mathematical quotations are so often drawn from tertiary sources, it is not surprising that frequently they have been changed in the course of passing through many hands. Sometimes the name of the original author is lost and the quote becomes misattributed to a different author. In other cases, the wording may be changed, becoming a misleading paraphrase of the original author’s intent. Even if the author and quotation are accurate, words stripped from their original setting can appear to mean something very different than when they are viewed in the context of the surrounding material.

Finding the original source of a mathematical quotation can be described as
creating a bibliographic trail, akin to this path around Prescott Fields at
the University of Maine at Farmington. Photo by UMF, supplied to Maine Trail Finder.

In 2006, I started writing a regular column called “Quotations in Context” which appeared in the biannual CSHPM/SCHPM Bulletin of the Canadian Society for History and Philosophy of Mathematics. Each column examined one or more related quotations, tracking them to their first appearances in primary sources whenever possible. These past columns, revised and updated, will now be available as a resource here on Convergence. These columns contain interesting details that might be included by teachers where appropriate in the mathematics classroom. They also represent a way to prompt students to think about and discuss the potential problems that arise from too much reliance on tertiary sources.

For mathematics educators who wish to involve their students in historical research, these columns could also be viewed as examples/templates of a usefully-bounded student project. A growing number of archives of primary historical materials have become available online, not just to scholars in specialized fields, but as well to teachers, students, and the general public at no cost: the Cambridge Digital Library, e-rara, Google Books, the HathiTrust Digital Library, the Internet Archive, the Linda Hall Library Digital Collection, and the University of Michigan Historical Mathematics Collection, to name only a few. While there still exist some barriers, such as language, to the exploration of these materials, it nonetheless remains quite possible for more advanced students to take quotations they have found in tertiary sources and successfully track that information back to their primary sources; in addition, even if students are unable to find the original source, they could still gain valuable experience by writing a detailed explanation of their work tracing the quotation back as far as they were able to go. Researching a single quotation could also help familiarize students with the vast online archives available to them; in particular, such a task could serve as preparation for more significant research projects.