This is the only time of year when I think folks on the quarter system, as opposed to semesters, have it easy. We’re in our second week of classes at Mudd, and even for those still savoring their last refreshing sip of summer, it is most definitely Back to School season. It’s in the air. I’m also returning to Mudd from sabbatical, so it’s a great opportunity for me to take stock and think deliberately about the upcoming school year.
I’m starting this year convinced that mentorship is universal. Mentorship isn’t a map with a specified domain and codomain. There isn’t a fixed group of mentors or mentees. Our roles may be fluid, and everyone is a candidate for both giving and receiving mentorship; it is universal. Below the fold, I’ll describe my experience at PCMI this summer and how it reinforced my understanding of the universal nature of mentorship.
The Park City Mathematics Institute is a summer mathematics institute run by the Institute for Advanced Study. Currently in its 25th year, PCMI consists of several different intensive programs that cut through a very wide swath of mathematics. There are programs for K-12 mathematics teachers, undergraduate faculty, an undergraduate summer school, a graduate summer school, and research program. In addition, there are one-week programs for high school students, and mentors of undergraduate research by minority students. With cross-program activities throughout, it is a specific goal of PCMI to increase interaction and exchange of knowledge between these constituents of the mathematics community.
I was the lecturer for the undergraduate faculty program at PCMI 2015. As the name makes clear, the undergraduate faculty program is specifically for mathematics faculty who focus on undergraduate education. This year, we studied two seemingly unrelated and
challenging subjects: Algebraic Stacks and Critical Education Theory. Algebraic stacks are very general tools for studying moduli problems, and they are both technical and abstract. They are the farthest thing most folks would consider undergraduate material. Critical education theory is radical, asking scholars to reconsider the very goals of what they do in the classroom. Over three weeks, we collectively studied both subjects, learning about fine moduli spaces and universal families, agency and praxis, representability of functors, Friere’s ontological considerations in education, and so forth. For more details about PCMI and the UFP, check out Adriana Salerno’s awesome posts on our sister blog Phd Plus Epsilon.
The “students” in UFP were professors, many of whom are senior faculty with much greater experience in teaching and research than I! Who is a teacher? Who is a student? As we discussed moduli, people brought to the table backgrounds in representation theory, algebraic geometry, and a host of subjects, to the benefit of us all. Similarly, we each came with unique teaching histories, and lived experiences, enriching our discussion of education and social issues. This really leveled the playing field, and created and environment of mutual respect and acceptance. It allowed us to discuss topics as varied as funding opportunities for undergraduate research, gender inequity in mathematics, tips for publishing in MAA journals, and implicit bias in the classroom.
We formed a close group and were able to help each other in many ways. For example, one member of the group was in her first year of a tenure-track position. She also had a medical condition which made it difficult, at times, to walk, or even sit upright. I watched how she handled this situation with grace, and learned strategies for dealing with my ulcerative colitis in the classroom. Another member of our group was an established senior faculty member. He also brought his family including children to PCMI. I watched how he managed to work out every day, bring boundless enthusiasm to our UFP meetings, while making his family a priority. And he didn’t miss out on our social events (and, um, hotel room parties) either. These are but two examples. Through formal and informal discussions, I learned a great deal about work, life, and work life balance, from them and the other members of UFP.
This experience really reinforced the notion that we can all be the source or target of mentorship. Our roles are fluid here. A mentor need not be someone with more years on the job, or more papers, or older. We each have unique lived experiences. Sharing our perspective is to the benefit of the community. Don’t be shy to ask for, or be open to, mentorship as the situation presents itself. And as this school year rolls along, I’ll be looking to my students, to my colleagues of all ranks and positions, and to the community, to help me make it through this crazy world and grapple with big questions, e.g. with war, oppression, starvation, environmental disaster, what is the ethical role of a mathematician? I’m going to need all the help I can get!