In addition to doing research in Maths, I have been teaching at university since I was myself an undergraduate: in different roles, about different topics, and to different types of students. I was a Teaching Assistant at Instituto Superior Técnico and MIT, a lecturer at Cornell University and Fordham University, and this year I'm supervising and lecturing here in Cambridge. It is very exciting to teach and interact with Cambridge's highly motivated and math-loving students.
The most unusual course that I've ever taught was Math and Politics, a course aimed at both math and non-math students which covers topics such as voting systems, fair division algorithms, and game theory. An example of a result that we proved rigorously in this course is the (in)famous Arrow's Impossibility Theorem, which tells us that perfect democratic voting is impossible, not just in practice but also in principle. More specifically, it states that no voting system that satisfies three fairly reasonable properties: 1) not being a dictatorship, 2) if each voter prefers candidate A to candidate B, then the group as a whole prefers candidate A to candidate B, and 3) if voters have stated their individual preferences regarding candidates A, B and C, and candidate C later withdraws, then the group preference between A and B is independent of whether the results are tallied up before or after candidate C drops out of the race.
I find a lot of joy in giving back to the community and I am fortunate to have come across opportunities to do this in ways that involve maths and personally resonate with me. I have taught math to young children in an after-school program, lead maths workshops to secondary school teachers, and given outreach talks/public lectures to a variety of audiences (two of them in bars!), with topics including rubber sheet geometry, the size of infinity, maths in origami, and a history of the sphere packing problem. But one of the outreach experiences that impacted me the most was teaching maths in prison.
During a sabbatical semester at Princeton, I joined the Teaching Prison Initiative, an all-volunteer organization which aims to reduce recidivism rates by increasing inmates' access to college education - there are studies that establish the causal relation. Some of the program's students end up earning a two-year college degree while still in prison (the graduating ceremonies inside the prison are very moving), and the credits earned for the courses taken can also be transferred to a regular university, where they can complete a four-year degree upon release.
I came into the prison one evening every other week, to do my part of team-teaching a college entry-level algebra course (graphing functions, solving equations, interpreting word problems, etc.). The conditions were sombre and there were many rules to follow - what not to wear, what not to bring, what not to do -, but in the classroom the mood was different. Everyone was happy to be there, most were very motivated to succeed in the course, some were genuinely interested in maths ("why does dividing by zero give you infinity?", "what is a proof?"), a few wanted to go on to study more maths or computer science.
Mostly we talked about algebra, but sometimes they shared with me glimpses of life inside. The library is a collection of books, not a place where you can study. The common room is crowded and the TV is always on, but you can elect to stay in your cell to do homework - standing up, using the top bunk as a desk. Many things can make you miss class: your unit is under lockdown, your name has not been added to the right list, or you've been transferred to another prison, in which case you are forced to abandon the course altogether. But what stayed with me was their attitude: hope, humour, gratitude, and a strong desire to help each other succeed.
For the future, alongside my regular research and teaching, I hope to continue to find ways to share Maths with more people: for education, social justice, equality, inclusion, or simply for the joy that it brings!
Ana Rita Pires