As I’d wager is true for many mathematicians, I was ‘good’ at math growing up. From learning to add and subtract in elementary school all the way through AP Calculus, nothing but A grades. Though I earned my fair share of B’s (and even a few C’s) on assignments in my undergraduate math courses, I still had the idea that, overall, I was ‘good’ at math. Adjusting to grad school was a bumpy road, full of twists and turns, both in the classroom and out, but I managed to make it work. Or, at least, that is what I had told myself prior to the winter break of my first year. It was the Friday before spring semester started and, more importantly, the day of my first attempt at the Preliminary Exam for Real Analysis. As the phrase ‘first attempt’ implies, I failed the exam that day. To this day, I still remember going to get the test results from the Graduate Studies Director in my department; we had to get our test results in person, in their office — no finding out via a bulletin board posting with anonymous IDs or being notified over email. “On Vector Spaces, you did well. On Real Analysis, you did not do well.” The latter of those two matter-of-fact sentences felt like a devastating blow at the time. In some ways, it was devastating, as something that I held to be my identity was shattered; after all, *if* I was ‘good’ at mathematics, *then* I wouldn’t have failed an analysis exam.

Due to the fact that spring semester courses started just two days after the exam, I was already in the swing of things when I got the results, which was both a blessing and a curse. On the one hand, it meant that I couldn’t afford to dwell on the results once I got them because I had so much to focus on with coursework and TA duties, so I just pushed along somehow. On the other, it meant that I didn’t have any room to process what had happened immediately afterwards. In the following weeks and months, I did some periodic soul searching. Time and again, my introspection landed on the question of belonging and whether this was the place for me. Eventually, I started to ask others (both older grad students and professors) this question, and the answers that I got revealed a pattern that was surprising to me at the time. No matter how exceedingly smart or immensely determined a person seemed, they always had their own tales of when mathematics presented a challenge to them that seemed insurmountable or shifted the way that they viewed their connection to mathematics.

Following a dozen or so of these conversations, I learned a couple of lessons. The first was that there was a name for what I was feeling: imposter syndrome. The state of mind that one doesn’t belong in a position that they are in or that they somehow tricked the world into seeing them as something that they are not. Lesson number two was that imposter syndrome is perfectly normal to go through, especially after a major setback. And the third thing I learned was both the most important and hardest to swallow: sometimes in life you fail, and that failure is okay. Mistakes are great as they provide moments for us to grow and blossom as individuals; failing gives us a chance to look critically at our personal habits and approaches to math (and life in general).

By the time it got to the day of the retake, I had stopped asking if I was ‘good’ at mathematics because that was never really a question that needed to be asked (or answered). Instead, I asked myself if I enjoyed mathematics and wanted to continue studying it. Since the answer to both of those was a resounding yes, the next question I asked was what I needed to do in order to ensure that I could keep doing what I loved. This ultimately meant adopting completely different study habits and making passing that second attempt at the exam my number one priority. This shift in perspective led to me passing the real analysis preliminary exam and every other written and oral exam I had on the path to candidacy status in my PhD program.

Throughout my graduate studies, I took on several leadership roles, ranging from being a peer mentor to an officer in the student chapters of various professional societies within the math department to even being the president of the entire graduate student body at my university. Whether meeting one-on-one with a new mentee or giving a welcome address to hundreds of incoming graduate students at orientation day, I always make sure to leave off on this adage, “Success, both in life and in graduate school, isn’t about never getting knocked down. It’s about standing up one more time than the number of times you get knocked down and finding the strength to do so, both from within and from the community of learners and scholars, friends, and family around you.”

*Michael Bush is currently a Ph.D. candidate at the University of Delaware, where he has already earned an MS in Mathematics. For his bachelor’s, he attended The College of Wooster, where he double majored in Mathematics and Physics. He has been inspired and mentored by numerous mathematicians, including his current thesis advisor Constanze Liaw and his research advisors at Wooster, Jennifer Bowen and John Ramsay. His previous work in physics was mentored by John Lindner and Cody Leary. Currently, his area of research lies in complex and functional analysis with applications to differential equations.*

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