By Brandy Wiegers

Earlier this year, I had an undergraduate advisee ask me if they should change from an applied mathematics degree to a pure mathematics degree if they wanted to go to graduate school. Upon further discussion, I learned that this student understood that a pure mathematics program was a better degree because of the implied quality communicated by the word “pure.” That value judgement had nothing to do with the actual educational experience but instead was based on the value we associate with the word “pure.”

This conversation got me thinking about the importance of language in communicating our values. Math departments and professional societies publicize statements communicating that we strive for an inclusive community, but even within our first descriptive words of the discipline, we are hinting at disciplinary value judgements. As a result, I’m proposing that we, as a community, use the terms “theoretical mathematics” and “applied mathematics.”

This topic is tied to the larger discussion we need to have as a mathematical community about the identity we associate with these terms. When I was first out of my Applied Math PhD I worked for MSRI and I have had multiple conversations with senior established mathematicians who told me that my applied PhD was not as real of a math degree as their pure mathematics pedigree. More directly, a famous mathematician countered my five year quest to write an applied math Math Circle activity book with the idea that they could write such a book in six months because “applied math isn’t real mathematics.” These same messages get heard by our students. They then get combined with the professional messages that raise the bar for membership into the professional community. Can you be a mathematician in high school? No, go get an undergraduate degree. Now are you a mathematician? No, go get a math graduate degree. Now are you a mathematician? No, you haven’t published. No, you haven’t done a postdoc. No, you haven’t gotten a tenure track faculty position. No, you haven’t gotten tenure.

So, math community, when are people allowed full membership into the mathematician identity?

For me, it wasn’t until I started taking on teaching and leadership roles in Math Circles that I believed I was a mathematician. For those of you who don’t know me, I started working in Math Circles my last year of graduate school and have helped create national support for those who want to do this outreach work. In running Circles across the country I find it very important for students, their teachers, and their parents/guardians to create an identity of mathematical success. I want them to see themselves as people who can do individual exploration of mathematical work, creating their own discoveries rather than being told to memorize mathematical truths others have discovered. I use active learning, growth-mindset, un-grading, outreach, and all the other sexy teaching terms to focus on providing opportunities for students to find their own mathematical success. And with that, I got a definition for “mathematician” from Josh Zucker, a founding leader in Math Teachers’ Circles and Julia Robinson Math Festival: “A mathematician is someone who thinks about math problems in their free time.”

We use Paul Zeitz’s distinction that a mathematical problem is one without a clear solution pathway (as compared to a mathematical exercise). We see that through this definition, being a mathematician speaks more of a lifestyle choice than a constant need to seek the approval of others to be a member in their club. I use this context for my example because “othering” is something that Math Circle and the broader mathematical outreach community has run into over and over, and I believe their current focus on allowing programs to self-identify as Math Circles has done much to move the field forward. You can see this in how we created the Journal of Math Circles (https://digitalcommons.cwu.edu/mathcirclesjournal/). Aiming for inclusivity, Dr. Emilie Hancock and I designed the journal requirements to allow anyone who shares our Math Circle core values in their mathematical outreach work to be able to publish in our journal. We publish papers from those who (1) explore worthwhile mathematical tasks, (2) foster problem-solving habits of mind, and (3) build communities of mathematical thinkers and problem solvers. Summer Math programs have a different structure than a weekly Math Circle, but their shared focuses provide plenty of opportunities to learn from one another.

Math Circles are where I gained identity as a mathematician, and they also reinforced for me how important it is for us to be precise with our language as we welcome others into the mathematical fold. I encourage us as a community to move towards language that invites students to study any form of mathematics that sparks their interest. This paradigm shift will be slow and we will be clumsy about it, but making a linguistic change will help us to signal that anyone who “thinks about math in their spare time” is welcome.

Acknowledgements. I would like to thank the discussion group from the Center for Minorities in the Mathematical Sciences DEI REU Workshop that was held in May 2021 (https://minoritymath.org/reudeiworkshop2021/). I also thank Dr. Allison Henrich for the support to get it written down. 

Dr. Wiegers is the Director of the Office of Undergraduate Research, Applied Mathematics Advisor, and Associate Professor at Central Washington University. Check out her REU, https://www.cwu.edu/reu/CCREU.