The Winter of Our Discontent–and Our Sweep Map Inversion

It’s been quite a winter. I was finally able to resume the math research that I had been neglecting over the semester’s frenetic final month. But even before I had become swamped with the work of writing tests, grading homework, and quelling student anxiety, my research progress had been slowing. Bogged down in endless iterations as I tested an algorithm and continuously revising computer code for that algorithm, I hadn’t made any new discoveries in quite some time. So this winter I decided to give the algorithm a rest and start playing-yes, just playing–with some different cases. Almost immediately, I stumbled upon an example that seemed to violate the conjectured bijectivity of the functions (called sweep maps) that I work with. It looked to good to be true–and it was. A silly misordering on my part had led to this erroneous “discovery,” but my mistake ultimately led me to a deeper understanding of the sweep map as well as to possible inversion strategies for the new cases I was looking at. Moreover, these insights invigorated my psyche, giving me the energy boost I needed so I could research on.

When I wasn’t researching, I was thinking–not about math, but about life. I have never been one for sappy end-of-year reflections, but last fall I began reflecting on just how I got to where I stand today. This was prompted by some conversations with an old friend, one whom I had met as a freshman undergrad and whom I had not spoken to in a long time. As I talked to him, the past six years flooded back into my mind, and I recalled a former self who was barely recognizable.

Searching for the reason for this change, I went digging through the paraphernalia of my undergraduate days. As I flipped through old issues of the campus paper for which I used to write, I was confronted with names belonging to people who had once been close friends but who now seemed like strangers, with words attributed to me but that I hardly remembered writing. Then I began digging through envelopes filled with everything from award certificates to old homework to mundane correspondence. I could not escape the realization that I had once been energetic and successful, blessed with opportunity and with a circle of supportive friends. I had been happy.

And then came grad school. It began jubilantly enough. I had been once again blessed with a great opportunity, this time the chance to earn a master’s degree in math, all funded by a teaching assistantship. I was eager to indulge my passion for math and prepare for my dream career. But my personal life was unraveling fast, and I was struggling to balance this fact with my new world of grad school, a world that I was surprised to find that I felt uneasy in. My life, my background, even my personality did not seem to fit that of the stereotypical grad student at all. I was reluctant to engage with the other students–and even more reluctant to seek help when coursework became challenging. I was ashamed–ashamed of what I was going through, ashamed to no longer be a straight-A student, ashamed to be different. I was isolated–isolated from the other students, from the faculty, and from my old friends, for I could not let them see how I had changed. Where I had once joyfully looked forward to the future, I was now operating in survival mode, just trying to make it through the next assignment, just trying to make it through whatever challenge was waiting at home. That is no recipe for success. Success requires enthusiasm, engagement, networking.  I knew that; I had been a master of it as an undergrad. But I was far too emotionally exhausted to do it this time. And so while I completed my master’s degree last May, it was not with the level of excellence I was used to. It was small wonder that I put together a half-hearted Ph.D. application proposing to do research in a field in which I had no background, even smaller wonder that that application was rejected.

So where to now? Well, first I must address some people, starting with my friends from undergrad days. I am sorry that I have been too caught up in my own pain these past few years to be the friend you remember, the friend you deserve. I would like to thank all of you for always standing by me, even if our relationships have been relegated to cyberspace recently. For those of you to whom I have not spoken in some time, I hope we can rekindle our relationships, for none of you have ever left my heart. For those of you who knew me only as a graduate student and saw me only as I was angry and overwhelmed, I am sorry that you never got to know the real me, and I want you to know that I was never angry with you personally. I hope that we can begin to develop the relationships that I know we can have.

As I write this, many new things are beginning. A new semester has started at Champlain College, and I am getting to know a fresh crop of calculus students. I can’t wait to see how they grow both as students and as people over the semester. Meanwhile, I nervously await admissions decisions from Ph.D. programs, hoping that at least one will say yes so I can get back on the path to my dreams. I can now say that I am ready to complete a Ph.D. My research has allowed me to prove to myself that I have something to contribute to the cannon of mathematical knowledge. I also now know that I-my entire person, with all my experiences–belong in grad school. My life has calmed, my personal growth continues, and my pain and shame is melting away. The winter of my discontent, to paraphrase Shakespeare, is thawing. My dream of becoming a math professor is regaining its strength, and despite the roadblocks it has faced, it will not be stopped. Today, I get back on the road to that dream.




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My name is Erin Milne, and I am a mathematics student and teacher. I earned my master's in math from the University of Vermont, and I received my undergraduate education from Lyndon State College. My goal for this blog is to make mathematics interesting, useful, and non-frightening, as well as to inspire other low-income and first-generation students to continue their education. I hope this blog will be helpful, inspiring, and thought-provoking for high school and college students facing the same challenges that I have faced.

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