By Matthew Pons

I was chatting with a group of students recently. We were talking about not letting our performance on coursework cause us to doubt ourselves and our value as human beings. I didn’t think that much of it at the time, but a few days later I received a thank you note from one of the students saying that the conversation had helped her, especially with final exams approaching. This caused me to take some time to reflect.

I think a lot of us connect our performance (in whatever aspect of our lives) to our value or self-worth, a practice Francis Su argued we should help the students we work with to dispel. We may try to convince our students that their self-worth should not be tied to their performance, but why don't we apply that care to ourselves? As I reminisced, I found myself focused on the two primary aspects of my professional life—teaching and research—and how I have worked to separate my performance from my value.

Regarding teaching, the process happened without any active work on my part. For much of my life, I knew I wanted to teach. I had great role models to borrow methods and ideas from, and as I began my first teaching position, I worked hard (and still do) to develop clear lessons that demonstrated key concepts with an abundance of examples, made connections to older material, provided motivation for future topics, and enticed the most motivated students to delve a little deeper. At the end of each semester, I was nervous about course evaluations. But I had supportive department chairs and other mentors who helped me parse out the comments that had substance from those that did not. Over the course of my first few years, I learned how to be proud of the work I put into a course, I learned to listen to my students when they had legitimate criticisms, and I managed to not base how I felt about my performance on the comments written by students or their performance. I think the key feature here was the support I felt from my colleagues.

On the other hand, as I thought about research, I realized that the connection between my performance and my value encompassed my entire relationship with mathematics and there was a lot to unpack. As a student, I generally did well on exams and other assessments, and so my performance did not have a negative effect on my self-worth. The support I felt from professors and my classmates played a nontrivial role in how well I did. My first big hurdle came in graduate school and passing general exams. (I have shared that experience elsewhere, so I will refrain from repeating it here.) Even in this challenging setting, I knew I was supported and, while I did fail one exam, I was successful on my next attempt. As I began my research career, I did start to connect my progress and my value. It was hard and I floundered at times, going months with no progress on my thesis. I seemed to always get stuck when reading research articles and could not make the leaps the authors claimed to be true. And I felt isolated for the first time in my mathematical life because I couldn’t rely on my classmates to share ideas as I had in the past. I had a great advisor, but I knew it was my job to solve the problems before me. Even with all of that weighing on me, I always found a way to move forward eventually, and I assumed this was how research was done. This “truth” about the process had a very negative affect on my confidence and how I interpreted my value.

After finishing my dissertation, I began a tenure-track position, and my relationship with research continued in the same way for many years. However, around my seventh year I noticed that I didn’t get stuck as often when reading new articles. This revelation helped me immensely. Yes, I surely knew more than I had as a graduate student, but my research capability seemed vastly different, and I couldn’t pin down exactly how or when the change had happened because I still felt inferior. So, I decided to analyze the situation, interrogating my doubts and fears. This led me to reshape my thoughts about mathematics research and exploration. I posed a number of questions to myself.

“Why do you feel like a failure when you can’t prove your latest conjecture?”

“Why do you feel like a failure when you get stuck with an idea?”

“Why do you feel embarrassed to reach out to a colleague to discuss ideas?”

What I realized was that getting stuck is part of the process. It is a frustrating part of the process sometimes, but I can’t control that.  The actual “truth” about the process is that we are human and it is natural to attach our emotions to our work. What we can control are our thoughts and emotional reactions to the process, and I had to develop a way to combat the negative thoughts.

Here's how I currently handle unkind thoughts I have regarding mathematics. When I feel like an impostor or inferior because I’m not making progress on my latest project, I read my old work. I remind myself that I am capable and that it isn’t some miraculous feat that I proved results in the past. I take pride in what I’ve accomplished. When I’m feeling isolated, I look for gratitude. Sometimes, this is as simple as being grateful that I had the chance to think about my work. I also take time to be grateful for the colleagues I have who love talking about math. When I feel stuck—really stuck—with a set of ideas, I return to basics. I make sure my foundation is firm or explore a new perspective on ideas I’m familiar with. Basically, I try to learn something. This is the key for me. I can’t prove a new theorem every time I sit down to do research because it takes time for ideas to come together. But I can learn something every time I come to my research, and that is how I measure my progress—by what I learned during the session—not by my productivity. Progress is often slow, and that is OK, but I can learn every day.

My relationship with mathematics isn’t perfect. I still get discouraged at times, but it doesn’t linger because I have developed an active practice of being grateful for what I do accomplish. It’s my perspective that has changed. I still have papers rejected and I still get negative reviews, but these outcomes have been separated from my value. I am proud of the work I put out, and I must trust that eventually it will reach its intended audience. The process I am interested in is the process of doing mathematics, not the process of publishing mathematics. It helps me to keep that perspective in mind. I hope it helps you, too.