Just got back from my month long research visit to the Boston area. I wrote last month about how hard it was to re-immerse myself in my research and writing for this visit, even though I desperately wanted to do just that. Well, I did manage to get back into my projects, and made some solid progress. I did a lot of computational work, worked with my group to get our SageMath code to the finish line (thanks so much, David Roe), and have big parts of a rough draft of a paper put together. I love the Letter of Recommendation column in the New York Times, which is about things which are under appreciated. Honestly, I can’t say Boston is under appreciated in the math world, but I wouldn’t have expected some of the aspects that I loved the most. So here are mini-letters of recommendation for some especially worthwhile parts my visit:
Having nothing to offer anyone. One of the best parts of this trip was the fact that, on a day-to-day level, I was really of little use to anyone at MIT. I don’t mean to say that nobody was interested in the math I was doing; it was more that I had no local knowledge or responsibility. I couldn’t answer questions for students, give directions to the cafeteria, or anything else. I had no meetings, my input was not required for any decisions. I love being helpful and involved in my department, but having nothing to offer to anyone was liberating. My time opened up miraculously.
My glare-y picture of a piece of this beautiful installation.
Hanging out with Sol LeWitt’s Bars of Color Within Squares. This polished glass and epoxy terrazzo floor installation was commissioned by MIT and installed in 2007, the year that Sol LeWitt died. I had seen several of LeWitt’s algorithmic or instruction-based pieces before, and those pieces always made me think of aspects of math and computer science–how a person who writes an algorithm is in relationship with people who actually carry it out, and watching a piece of art emerge from a complicated process or plan. The scale of his pieces are often part of the joy, too. This floor is in an atrium open to the public, and I made many detours to stroll through, because just hanging out with the bright colors and being in direct contact with this giant piece of art made me feel good.
Talking face to face. Before I went to Boston, I wrote two carefully crafted emails to people there, explaining who I was, what I was working on, what I wanted to know, etc. These were pretty short emails but took me a long time to write, just because I didn’t know the people I was writing to very well and I was trying hard to be clear and undemanding. Nobody answered me, and I was struck by a sort of social and mathematical angst—should I write again, or did they not want to deal with me? When I got there, I pretty quickly saw both of these people in person and they were totally friendly. Through flukes of technology and email volume, neither of them knew I’d even written to them. So, the long and anxious process of writing those emails and ruminating on them came to nothing, not because people didn’t want to talk to me, but because that’s how email works sometimes. There are a lot of ways to miss your target from a long distance, and the stakes feel high when you are contacting someone you don’t know well. It saved the day that I was able to just show up and talk to these people in person.
Talking in person is just so efficient! In one of the cases I mentioned, I was looking for some mathematical clarification, advice on a project, and some ideas for possible journals. I had read a paper that this person was involved with, and had interpreted the results in one way, but after a short chat I was able to understand that the set up of their paper was slightly different than I had realized, and that our computational tools could actually solve a problem that they posed. He also was able to suggest several journals and tell me some concrete changes to make to the paper I was working on. I wouldn’t have been bold enough to send a draft (especially one in such an early stage), but in person I could just show him some parts of the paper and my computational data on my computer screen and we could talk about it easily. He didn’t have to spend the time writing an email back to me and making sure the tone was right, and I didn’t have to then dither about whether I should ask for clarification on various points. I could just ask, and a 20 minute in-person conversation was worth hours and hours of emails.
Bjorn Poonen answering questions after his talk, Number field fragments and Fermat’s last theorem
Great talks in the land of 10,000 seminars. I have mixed feelings about seminars. I really like hearing about math, but I think that a lot of talks aren’t really designed to communicate as much as they are to impress. So I had some ambivalence about going to a ton of seminars. But as far as I can tell, there is an algebra or number theory seminar every day in Boston, and some days there are several, so I didn’t want to totally miss the chance to soak up some new and exciting math while I was there. And I did go to some great talks. Maybe my favorite was the Simons Collaboration Seminar that Bjorn Poonen gave during my visit. Bjorn, Andrew Sutherland, Jennifer Balakrishnan, John Voight, Noam Elkies, and Brendan Hassett have received a multi-institution grant from the Simons Foundation for Arithmetic Geometry, Number Theory, and Computation. There are a number of goals for this collaboration, and Bjorn gave a talk on one thread—an idea for a possible new proof of Fermat’s last theorem using objects called number field fragments. The math involved is hard. However, it is perhaps more manageable than the current proof. This talk just made me excited about math. Bjorn is a really clear, excellent speaker, and, even though parts of it were beyond me, I both got a lot out of the talk and came away very impressed. It was such great fun to hear about new possibilities for a problem that has been central to mathematical culture for so long.
This is Maya, an awesome ambassador for Clover.
Everything at Clover. Of course mathematicians turn coffee into theorems, but we also occasionally need other fuel. This is where Clover comes in. This local chain started as a food truck and now has restaurants all over the city. They serve all vegetarian food, and most people I talked to agreed that their signature chickpea fritter sandwich is a true wonder. Except one person who thinks the breakfast popover sandwich is the real secret to their success. Anyway, I probably ate 10 meals at Clover while I was there and I loved every one. I also found my favorite Clover server, named Maya. Short story: One evening she was cleaning the juicer and had set it on the counter in an unusual place. The shift manager bumped it and it fell into a bucket on the floor. The manager didn’t see the juicer fall and was looking around confusedly for the source of the noise. Maya was trying to help me and play it cool and not laugh or call attention to the fallen juicer, and watching her juggle all this was utterly charming and hilarious and made my day. She deserves a letter of recommendation for just being awesome.
Girls’ Angle mentors Elise McCormack-Kuhman, a sophomore in Mechanical Engineering at MIT, and Jacqueline Garrahan, a Masters student in Applied Math at Northeastern.
Visiting Girls’ Angle. Girls’ Angle is a non-profit organization (I wrote about it a couple of years ago here) that headed by Ken Fan that, among other things, runs an amazing math club for girls in grades 5-12. Undergraduate and graduate students mentor the club members and help them investigate the mathematical world. The club meets on Thursday afternoons near MIT campus. I visited last week’s meeting, and was really impressed with the students and mentors. I dropped in on several working groups and saw at least two pre-high school students working on potentially unsolved problems of their own devising. I was asked not to describe the problems, so that professional mathematicians do not swoop in and finish them off before the girls are able to, a request I am very happy to honor. But I was just so impressed with the girls’ mathematical abilities and their understanding of how mathematics works—thinking of questions to ask, generating data, forming conjectures, and finally creating a rigorous proof. Also, it was great to talk to the mentors about their experiences with Girls’ Angle. Feeling a little down on the current numbers of women in mathematics? Visiting this club, meeting all these incredibly talented and interested girls and women doing math together, makes me hopeful that this can and will continue to change.
Sitting in on Mathematics of Social Choice. Another thing that I often feel down about is the difficulty of changing anything through legislation in a nation of gerrymandered state and federal congressional districts. Moon Duchin and the Metric Geometry and Gerrymandering Group at Tufts University have taken on the mission of studying the applications of geometry and computing to US redistricting. Through a series of workshops across the country, they have taught a huge number of mathematicians and members of the general public about the mathematical aspects of redistricting, and mathematical techniques for addressing fairness and identifying unfair districting plans. I attended their Madison, WI workshop in October (which was awesome). I was especially interested to learn about a framework for identifying extremely gerrymandered districting plans that involves randomly sampling many possible plans, and using real voting data to determine what election outcomes would have been under these plans. A single plan can then be placed in context–does it give an outcome that falls within the big part of the bell curve of outcomes, or is it an outlier, giving results that are by comparison extremely beneficial to one party? Moon was recently hired by the Governor of Pennsylvania to use this framework to analyze the districting plan proposed by the state legislature to replace the famous “Goofy kicking Donald Duck” plan that was declared unconstitutional by the Pennsylvania State Supreme Court. Last week, I was lucky enough to be able to sit in on Moon’s Mathematics of Social Choice course at Tufts, on the day when she was teaching about this framework and process. I was totally excited about this, and I’m sure the students were too, but they probably didn’t know as well as I do how rare a classroom experience like this is. Maybe because we as math professors teach a lot of math that is far from our research, it is not all that common to hear a math professor talk in an undergraduate class about her own work. Add to that getting to hear a first-person account of her personal role in using this work to help create a more fair and just world. As if that wasn’t enough, by the way, this is happening RIGHT NOW, and it is also accessible to non-math majors.
Moon teaching Mathematics of Social Choice.
It was really energizing to see the possibilities of social change powered by mathematics, and to see how Moon shares this with her students. Not only is the topic very important to me, but it is also sort of career-affirming to see this synthesis of social engagement, mathematical innovation, and thoughtful pedagogy. I want to bring this all together, but I often feel that I’m not quite there, and I wonder if it’s actually possible. Apparently it can happen, and I am grateful that I got to see this in action in the classroom.
Now that I’m all energized, it’s time to get ready to go back to my own classroom. Next up for me: rewriting my Calc 2 syllabus. Thoughts about any of these activities, or what you would do with a month of math-cation? Things I should plan for next time? Let me know in the comments.