Why passing my oral examination felt like a failure, by AJ Stewart

Thump, thump, thump, thump,…. Is that my heart? Why am I so nervous? I shouldn’t be nervous. It’s just a question. Come on, AJ. You know the answer. What is it? I know I know this. Why can’t I come up with something? Just say anything. Say something.

The voice of one of the professors on my committee shook me out of my anxiety.

“I think we should move on.”

I turned away from the chalkboard and saw four emotionless faces distributed throughout the room. I was about 45 minutes into my oral examination. It only got worse from there.

Often, part of finishing a Ph.D. program involves an oral examination. This oral exam is conducted outside of any class structure and is usually the last formal examination of graduate school. Professors ask the graduate student questions from their research area, which the student must answer in the moment. My oral exam was my chance to prove to myself that I belonged. To get rid of the nagging sense that I didn’t measure up. It wasn’t about my mathematical knowledge. It was about my identity. My very existence.

I had clung to my mathematical ability as the thing that would give me everything. It was the thing. The only thing. It was how I would raise myself up. And without it… well, I didn’t want to think about that. I never felt confident. Of course, if you were in a class with me, you wouldn’t doubt my confidence. I was always working, always answering questions, always looking ahead. But this never came from a stable place. It was a sign of my insecurity. I felt like a fraud. And rather than slip into the background, I made sure everyone knew I was smart. Deep down though, I had a doubt. Was I a mathematician?

It was no longer just an exam. It was a trial. I would be judged, and my committee would determine the truth. Was I just a conman from Florida who had sweet-talked his way out of the swamp and into the ivory tower? Or was I a talented researcher? When I stepped up to that chalkboard, it felt like a matter of life and death.

It started off fine. I was setting up the assumptions for the most recent paper that my advisor and I were working on. I needed to define Witt vectors as well as some of the canonical maps used in their construction. But when I was asked to describe what I meant by “lifting” an element from Z/p^{n-1}Z to Z/p^{n}Z, my mind went blank. If someone had asked me the same question the day before, I would have scoffed. But in that moment, I froze.

“I think we should move on.”

This was the beginning of a series of questions that made it clear that the committee didn’t care what I knew but was more interested in what I didn’t know. I knew about line bundles of projective space over complex numbers but faltered in the characteristicpcase. I could state the Riemann-Roch Theorem and use it in various applications, but I couldn’t complete a proof of it. Most of my answers were interrupted with other questions that either expanded or deepened the solution I was presenting.

It was a miserable experience. I said “I don’t know” more times than I could count. I felt like a failure. All of those hidden feelings of insecurity overwhelmed me. When I left the room to let the committee deliberate, I was despondent.

After five minutes, the committee came out, and my advisor said, “Congratulations!” I had passed. It didn’t feel like a success though. The minute they all left, I went back into the room, curled up on the ground, and cried. I just cried for about an hour.

Was I a mathematician? The voice in my head said, “No.”

My committee was doing their job. They were there to measure my mathematical ability. But they never asked about any of the other skills that were integral to my mathematical identity: how I connect with students, find interesting applications of mathematics, support my colleagues, or lift the spirits of first year graduate students.

To them, these things weren’t part of being a mathematician, and therefore were absent from the assessment. Their system of measurement was based on their knowledge, their identities, their values, and their world view. In order to succeed, in order to measure up, I needed to be one of them. But I wasn’t. I’m not. I never will be. I don’t want to be.

When I look back on the experience of my oral exam, I realize that I was measuring myself against people. People that accomplished great things. People that I idolized. But people that also supported my own toxic behavior. I didn’t know how to both be myself and be a mathematician. I thought that these two things were mutually exclusive.

I was wrong.

Everyonecan be a mathematician. One’s identity and mathematics are not mutually exclusive. People all over the world dance and play music. When they dance, they are dancers. When they play music, they are musicians. Why should we limit the title “mathematician” to only those privileged few that suffer for their knowledge? I felt like a failure after my oral exam because I didn’t live up to standards. It has taken me a long time to realize that it was the standards that failed, not me.

I think we should move on.

Mathematics has spent too long defining strict boundaries–demanding that people live up to some set of standards to be called a mathematician. Mathematical expression is more than just a written formula. It’s an action, a feeling, a part of humanity. Math is for everyone, just like music or dance. When a person finds a creative way to solve a problem or can explain a complex idea simply, they are a mathematician. And if you feel like I felt during my oral exam, like a failure or like you don’t belong, know that you are a mathematician, in the best sense of the word.

:-D AJ Stewart was born and raised in Florida, where he spent a lot of his time fishing, snorkeling, and catching reptiles. His childhood was hectic, and he never felt school was important. After barely graduating high school, he spent years cooking in restaurants until he finally decided to attend the local community college. He excelled in math and left Florida for California where he got his B.A. in mathematics from Humboldt State University. After completing his undergraduate degree, he moved to Oregon and got his Ph.D. from University of Oregon with a focus on algebraic geometry, birational geometry, and Hodge theory. His current research is in nonlinear algebra, applied algebraic geometry, algebraic statistics, and data science. He hopes to focus more of his future research on quantitative justice. He is currently an instructor at Seattle University (which was his first job after Ph.D.) but will be moving to Washington D.C. in Fall of 2021 to work in Congress as the 2021-22 AMS Congressional Fellow.

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