HoM Toolbox, or Historiography and Methodology for Mathematicians: Introduction – Some Closing Thoughts

Amy Ackerberg-Hastings (MAA Convergence)


This article was designed to share the basics of historical practice with the wide range of people who might want to research and write the history of mathematics: instructors and students in history of mathematics courses; students contemplating graduate studies in mathematics and its history as well as academics and professionals considering a new direction in their careers; and experienced historians of mathematics looking for new ways to express and evaluate their own theoretical approaches to historical interpretation. The article should also provide benefits to those whose main goal is to become more knowledgeable readers of the history of mathematics or audience members in history of mathematics conference sessions.

We have asked a number of questions along the way, including:

  1. What is history? Why should we want to research and write it well?
  2. How do we know about the past?
  3. How do we create history based on what we know about the past?
  4. What is the history of the history of mathematics?
  5. How can we articulate our own philosophies of the history of mathematics?

None of these questions have a single correct answer, although some possible responses are supported by a stronger body of evidence than others. One thing all five questions have in common is that they require us to identify methods, techniques, and approaches essential to understanding how and why the past unfolded in the way that it has—the “tools” of the history of mathematics. Although your metaphorical toolbox should be much fuller as a result of reading this article, there will always be space for adding more tools via the many theoretical approaches to historical interpretation that are applicable to the broad, global discipline that is the history of mathematics.