Coping Strategies and Mindfulness

Along with my research this summer I’ve been doing some meta-research: being careful to keep close track of my mental states, the better to remember and internalize ways of working through the most frustrating and draining parts of doing research.

One thing I’ve realized is that sometimes I need to give myself a break even when I’ve already convinced myself I “don’t deserve it”–haven’t been working hard enough. Some times that worry is more true than others, of course. But a related consideration, more important than I initially realized, is that there are lots of things that aren’t “sitting down and thinking hard about your problem” that are still mathematical work, and those can get to an overwhelming point where I need to take a walk, too.

In particular, there’s a website, MathOverflow, that serves as a place for research mathematicians to ask and answer mostly highly specific, technical questions that pertain to their research. The website has been up for about nine months now, and it’s become a wonderful resource in a lot of ways. There’s a core group of experts on a decent range of mathematical subfields who are fairly heavily involved, and many more people than have research-level questions to post there lurk and learn a lot from the answers to research and “softer” questions posted.

But many people have seen MathOverflow and wished there were a website like it for the rest of us, students of all ages and professionals in math-related fields who have serious questions that wouldn’t be appropriate on MathOverflow. It’s a great idea whose time, I think, has come. But as I’ve found out in the last few days, when it gets down to the finer details of hashing out what kind of group a community wants to be, and in this case how to avoid going the way of so many forums that are overrun with spam, bad answers, and lazy students, the going gets tough. There are philosophical differences and practical issues and hypothetical discussions of what practical issues might come about later. It’s exciting to get into, to see the great lumbering machinery of a good brainstorming session driving forward. But as I’ve found ou, it can be exhausting, and it’s work. You have to deal with people along with all the math and the policy questions, and that’s a lot.

So it was easy to take time away from the time I was spending not doing research to work on this exciting new project. But in doing that, I convinced myself I wasn’t “working,” and got to a point where I was actually working pretty hard but not allowing myself to acknowledge that because it wasn’t the work I’ve been doing on my research problems on a day-to-day basis.

One nice nighttime walk in the mountain air and watching an enjoyable romantic comedy with friends and fellow researchers later, I’m settled, happy and ready to dive into both math and the math-community-making project again.

It’s a simple point that seems all to easy to let go of if you don’t keep it actively in mind: the “er” part of researcher is someone to whom attention must be paid, no matter how stubborn said researcher is to set all but the problems aside.

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I’m enjoying the fact that the primary purpose of this summer for me is to work on math–that at this stage in my education and mathematical life, I don’t have to worry so much about what comes of that work. The doing, for now, is enough.

I’ve approached and retreated from the frontiers of frustration several times over the past few weeks, defined and redefined what the heck I’m actually trying to do with these problems, bashed through lots of calculations to find that they are mostly inconclusive but suggest new directions. Doing math the last several years, I’ve learned to take at least a minute or two to savor the feeling of making a new discovery–since, most often, it turns out to be wrong, sometimes only in details and sometimes more fundamentally. Lately I’ve been waking up in the early hours of the morning with some regularity with thoughts that my proofs are wrong. Sometimes I actually get up to work through the details or check them out–and sometimes that even helps me be assured that I was, in this case, actually right.

Research is frustrating for everyone almost all the time, it seems. But right now, even with the frustration, it’s just so refreshing to not have the problem set and lecture grind. And to be able to spend time away from research problems reading up on interesting areas and techniques in mathematics and immersing myself in the culture and history of mathematics, as both profession and area of inquiry, a little bit more.

I’m reminded why I wanted to study math in the first place, and that I want to continue to study it, wherever that may lead in the end.

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Phase I

So, everyone in my group has met with our professor several times, and we’ve all nominally started working on our problems–figuring out what we want to figure out about them, making conjectures and figuring out they are false after several hours of calculation, writing computer programs to search efficiently through ~2^49 matrices for counterexamples, etc. It’s a good day when I discover and can prove a formula for one case of the objects I’m counting.

There’s a lot of literature review, too. I find the process comparatively relaxing–when I’m reading papers on what has already been done in the area surrounding my problems, I often feel like I’m building a mathematical toolbox and intuition that will help me approach the problems I want to work on. Diving in head first and tackling the problems naively can be fun, but it’s also daunting, emphasizing how much one doesn’t know when one starts work on a problem.

Right now, I don’t feel like I have any traction on any of the problems I’m working on–so I’m mucking around: testing small cases in the rare event that they exist (the numbers associated to everything I’m working with grow super-exponentially! Unfortunate for my concrete-cases-loving, pattern-seeking brain), looking for recurrences (and then discovering that they do worse than the naivest of upper bounds I can establish), and brainstorming other angles I can take on the problems. All this is towards the goal of actually defining what those problems are, of course! I’m not in a comfortable place where I have a list of calculations or concrete angles I want to try out–still casting around. Which is sometimes one of the best parts of research, but also, for me, the hardest research skill to develop.

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Hallo!

Hello to anyone who might be reading this!

This is (er, hopefully will be) a blog about my experience doing math research at Eastern Tennessee State University this summer. This blog is part of a WISE Words project to document the summer experiences of several female undergraduates in the sciences through blogs like this one.

I’m doing this research as part of an REU–Research Experience for Undergraduates. That means a few things concretely: I’m here with some other undergrads who will also be doing math research with the guidance of the same professor, and I get paid a really sweet stipend. REUs are, briefly, programs held at various universities across the United States, largely funded through NSF grants for the specific purpose of encouraging undergraduate research. They are held in a variety of STEM fields, from mathematics to physics to biomedical research to aerospace engineering. Of course, there are many other programs through which undergrads can do summer research at their own universities, other universities, in industry or government, etc. Things that are called “REUs” are united by the vision the NSF has articulated for undergraduate research programs of this sort. I’m not entirely sure what unifying features “REUs” have specifically that may distinguish them from other programs. If you’re interested, try the NSF’s publications on stimulating undergraduate research and desire to attend graduate schcool.

We’ll be doing research on some problems in probability, graph theory, and combinatorics. Here, it seems that students work in groups of 1-3 (inclusive), and may work on a few different problems over the course of the nine weeks of the program. Some might contribute to a few different problem groups simultaneously, and can move around as changing interests and fancies dictate. I’m thinking that will prove a good way to minimize the inevitable frustration of doing research, often getting nowhere for days or weeks at a time or following false leads to dead ends.

Otherwise, the structure of the program is yet to emerge: how we work is mostly up to us, and we’re still getting settled in. Being able to do research sitting around in your apartment with a pen and paper is rather a nice feature of research in pure mathematics, and it gives us more flexibility than many lab-based students might have. (Though, of course, computers are often used even in pure math, and can be useful for  generating conjectures, studying small test cases, and developing intuition about a problem).

I’ll save the good stories for later, for color. I doubt anyone will be reading this, but if you are, please leave a comment with any questions you might have about REU experiences, research in math, etc. Already, the REU students have gotten to talking about what we’re worried and excited about starting this research gig, so I intend to bring up any issues that come up in discussion that I think might be of interest to others just starting research. I’m also sharing an apartment with the two other girls in the program, so, pursuant to the general goals of WISE Words, I’ll share anything specific to women in mathematics that might come up.

Be well,

Katie

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