I would like to dedicate this article to the memory of my mother Sally Gomez, my father John Gomez, and my brother Johnny Gomez.
Lemoore. About forty miles south of Fresno, California, in the Central Valley is a small town called Lemoore. This town is but one of many little towns that comprise the majestic farm-field tapestry of the valley. My grandparents, parents, aunts, and uncles all worked portions of these vast fields for many years as field workers picking plums, grapes, apricots, and peaches.
I lived at the dead end of a street which spanned six blocks. My house was uniquely nestled between a corn field and the cheese manufacturing factory, Leprino Foods. Because of the house’s close proximity to the factory, the constant noise and agitation of diesel trucks shuffling about could be heard all hours of the day. Though my street was only six blocks long, it was regarded as one of the bad parts of Lemoore, primarily because of the gang activity in the area.
In my family, I have two brothers, Johnny and Eric, and a sister Gloria (Johnny passed away in 2015). I am the youngest of the family. After being in the Navy for three years my father, John Gomez, worked in a mill called Continental Grain and kept that job for forty-two years until his retirement. My mother, Sally, stayed home and ran the entire household. When she was growing up, she had to drop out of high school to help take care of her younger brothers and sisters. Thus, she had a plethora of experience in helping others and maintaining a household.
My oldest brother Johnny and I were seventeen years apart in age. By the time I was born, he had already moved out of the house, so I saw very little of him growing up. However, the times in which I did see him usually were not the best of circumstances.
My brother Johnny. Without a doubt, Johnny was one of the most influential forces that launched me on my trajectory to eventually become a mathematician. This attribution of influence is not because he was a pristine role model with infinite pearls of wisdom and prophetic advice. On the contrary, his life became a living example of the kind of life I did not want to lead. Exactly the opposite.
Many of my early memories of Johnny revolve around going to the Kings County Jail with my mother and sister to visit him. He was in and out of jail for much of his life. I can vividly recall how one of my first visits to see him deeply and profoundly impacted me. When I was around eight or nine years old, my mom, sister and I went to visit Johnny in jail. As we entered the visitation room, we saw Johnny behind the glass partition, seated and waiting for us to take our seats. I remember looking at my mother’s face as she looked at Johnny. I could instantly read the complete heartbreak and the immense disappointment she had for him. It was during this time that I decided to follow a path which was in the exact opposite of my brother’s path if for no other reason than to spare my mother any more heartache and pain. Thus, I decided to embrace education and stay out of trouble.
Skateboarding. Admittedly, it was sometimes challenging to remain on my self-selected path of embracing education and staying out of trouble. On my street was a gang called XIV (the fourteeners), which seemed to be based on one of the more notorious gangs in Los Angeles. Around my sophomore year of high school, I seriously considered joining this gang on my street. Some of my friends had joined, and I became attracted to the gang’s stature and cohesion. But fortunately for me there was a very welcomed diversion and that diversion was skateboarding. Though I had ridden a skateboard since the sixth grade, I began to take the sport very seriously in high school. During the school day, I concentrated hard on my academics. After school, I practiced skateboarding with equal intensity. Skateboarding became my primary outlet from academics, an avenue to forget all of the daily worries and focus on improving my skateboarding skills.
From skateboarding, I sustained a myriad of collisions with the concrete; numerous sprained ankles, two broken bones, a sprained back, and many scrapes and head gashes. Hopefully I learned something from all of these injuries! Skateboarding gave me the necessary structure and the motivation to constantly improve at something. It allowed me to experience the triumph and satisfaction of learning a trick after countless failed attempts. It taught me to cultivate a deep sense of concentration and focus on something of interest—a quality that was crucial once I found my passion in mathematics.
Undergraduate experience. In my household, the idea of going to college was never discussed or mentioned. No one in my family attended college (although my brother Johnny was always fond of saying that he was a graduate of Penitentiary State!). College was an idea I only saw on the television. In high school, I took college preparatory classes, but there was never any intention of attending college. Taking such courses simply reinforced the idea that I was embracing education and attempting to extract the most I could from my small-town public high school. I took the usual advanced courses in English, biology, chemistry, and math. The highest math course I took in high school was precalculus. I had no idea what I was doing, nor did I have any interest in the subject.
In my senior year of high school, I decided to enroll as a full-time student at the local community college, West Hills Community College, after graduation. I had no other plans and going to West Hills allowed me to stay close to my friends who were also enthusiastic about skateboarding. During the time I started college the campus was quite small, comprised of a main building and a few portable buildings. I actually preferred to attend College of Sequoias which was another community college further away from home. It had more course offerings, but was over thirty minutes away by car. My father said there was no way the family could afford all that gas as well as the prolonged use of the family car. Thus, I enrolled at West Hills Community College, which allowed me to walk to class and back home. These walks were actually quite useful because I used to lecture aloud to myself on scientific topics while walking home. I did a lot of homework at the community college library since it was difficult to concentrate at home.
In my first year at West Hills Community College, the placement exams recommended I take trigonometry. My first math class at the college level was trigonometry! This was exactly the right starting course for me. It was during this time that I really started to take mathematics and science very seriously. I realized that doing a whole bunch of problems thoroughly and clearly greatly helped me solidify my understanding of topics. I also found that explaining the idea aloud to myself really helped me in absorbing ideas.
My time at West Hills was an exceedingly pleasant one. I had a few inspiring professors at the college. For example, my chemistry professor, Dr. Robert Holmes, was one of the few instructors with a PhD at the college and was a very encouraging person to me. He was eloquent, highly scientific, and very serious. After earning top marks in his chemistry course he gifted me a chemistry book as a form of encouragement to continue. This inspired me to major in biochemistry once I transferred to a four-year university.
I also took a history course that was highly influential in my future interests. For the final paper in the course, I had to write about an event that changed world history. I chose the topic of the development and use of the atomic bomb. During my research for the paper, I began learning about some of the scientists associated with the bomb. This in turn led me to read about some of the key contributions Albert Einstein made to physics. Soon after, I became extremely interested in the many wonderful ideas in physics. It was during this time that I began to realize the full power of mathematical thinking—its ability to describe nature. It motivated me to want to learn about general relativity and quantum mechanics. I was completely overcome by the magical beauty of how equations could so simply describe physical processes. I was particularly struck by just how geometric the universe actually is. But if I was going to delve deeper into the physics, I had to learn much more mathematics.
After two years at West Hills Community College, I transferred to the University of California at Santa Cruz. Initially, I was a biochemistry major. The transition from community college to the university was incredibly difficult for me. In fact, after the first semester, I seriously considered dropping out of college. I could not keep up with the fast-paced environment and much higher demands of homework. Most of all, I grew very disheartened by laboratory sciences. I found the labs too tedious, and I had no intellectual investment or scientific curiosity for the laboratory exercises. I missed the purely theoretical aspects of mathematics.
Realizing I would be much happier if I switched my major from biochemistry to mathematics, I changed my major. Finally, I could really spend time learning more advanced mathematics beyond calculus and try to learn some physics. I fondly remember leaving math classes with great excitement regarding all of the mathematical ideas I was learning. As a math major, it felt absolutely wonderful. I was able to think about mathematics all the time. Professor Arthur E. Fischer and Professor Anthony J. Tromba, both highly influential professors at UC Santa Cruz, completely convinced me of the incredible beauty and versatility of differential geometry. Their lectures were very enthusiastic, riveting, and inspiring.
After graduating from UC Santa Cruz with a BA in mathematics, I stayed in Santa Cruz and worked for the UC Santa Cruz math department as a grader and a math tutor. In addition, I took a couple more math classes, and then I enrolled in the master’s program at UC Santa Cruz. After writing my thesis and taking the algebra qualifying exam, I obtained a master’s in applied mathematics. After completing my degree I took some time to consider the following question: Should I go further and get a PhD? During this time of contemplation, I returned to West Hills Community College because I accepted a position as an adjunct instructor there. It was also a great chance for me to thank the institution where I got my start. Had it not been for the existence of West Hills Community College, I would not be writing this article now.
Am I Capable of Earning a PhD in Math?
Earning a PhD. As part of my decision on whether or not to earn a PhD in mathematics, I felt that it was important to go to a different institution so I could see how other places did mathematics. I wanted to study Einstein geometry under Professor Charles P. Boyer. Charles Boyer was one of the leaders in that area, having discovered a new technique of constructing special types of Einstein geometries. Einstein geometry is a type of geometry that obeys an equation discovered by Albert Einstein in his modern theory of gravitation-general relativity.
After numerous thorough discussions with friends, I decided to accept University of New Mexico’s offer to enroll in their PhD program. Part of the attraction in attending UNM involved a generous stipend sponsored by the New Mexico Alliance for Graduate Education and Professoriate (NMAGEP). This was a fantastic program that not only supported me with an additional stipend, but also provided numerous conferences and workshops for graduate students from underrepresented groups that focused on navigating the challenging road to becoming a professor. Looking back, this program was instrumental in helping me to think about what it meant to be a professor.
After postponing my fall enrollment at UNM, I arrived there in January of 2003. It was refreshing to be studying mathematics once again, and I was growing increasingly optimistic about my future career trajectory. But this optimism was cast into the shadows. In the early fall of 2003, it was determined my father had stage four colon cancer. By the time the malignant mass was found, it was too late for any procedure or radiation to prolong his life. He passed away in September of 2003. Days before he died, quitting the PhD program was weighing heavily on my mind. If I withdrew from the program, I could return home and help out my mother. My sister planned on moving back to Lemoore from Palm Springs with her family. I felt like I was abandoning my family if I remained committed to the PhD program. The afternoon before my father passed away, I was sitting next to him, telling him my final goodbyes. By this time he was extremely frail and life seemed to be visibly evaporating from him. But somehow my father was able to conjure a sentence: “Don’t let this mess up your schooling.’’ In that single sentence, the decision for me to complete the PhD was solidified. I simply had to finish now.
PhD. With my father’s support and my sister’s willingness to uproot her life to take care of my mother, I stayed in UNM’s PhD program. Around this time, my advisor Professor Charles Boyer gave me a graduate fellowship from his research grant which allowed me not to teach and focus on courses and the beginnings of research. To have a professional and successful mathematician believe in me and encourage me the way he did, instilled a great wave of enthusiasm and excitement in me as I moved forward with my total immersion in mathematics. I earned my PhD in five-and-a-half years (with distinction) and a new life was ahead!
The Professorial World
After I earned my PhD, I accepted a two-year visiting position at Swarthmore College in 2008. This was an absolutely incredible position with a reduced teaching load, and I was thoroughly excited to be there. But gradually I had the uncomfortable feeling that I did not belong at such an illustrious institution. Not seeing much faculty diversity at the college, particularly in the Natural Sciences and Engineering division, made me feel more like an outsider. It became clear to me just how different my pathway was in becoming a mathematician and that perhaps I was ultimately doomed to failure since my pathway was not more traditional. Impostor syndrome took a strong hold of me. To further complicate matters, my brother Johnny was on his way back to prison yet again to serve a one-year sentence. What other faculty member in their first year in a visiting position had to worry about a sibling heading back to prison? To my mind, this was just one of many other examples of why I did not belong.
Near the end of my two-year position, Swarthmore College was able to offer me an extension on my visiting position. This was very generous especially since this was around the time of the Great Recession. The college was actually pleased with my work and invited me to stay on for a few more years. This invitation was a clear signal that the college viewed me as thriving at Swarthmore. But there were three factors that led me to decline this offer at the end of my two-year visit. First, the desire to return to my family in California particularly because of growing worry about how my mother was handling my brother’s return to prison. Second, the personal belief that I was not Swarthmore material and thus did not belong. Finally, the need to secure a tenure-track job instead of staying in a visiting position. Not feeling like I belonged at Swarthmore was the main factor that ultimately convinced me I should move on. Thus, after my two-year visiting position I left Swarthmore college and took a tenure-track position in California. Before I left I met with Stephen B. Maurer (the chair of the mathematics and statistics department at Swarthmore at the time) to tell him the main reason why I was leaving. He sent me an email after our meeting which completely shifted my view about myself. With Stephen B. Maurer’s permission, here is the email he sent to me:
I’d like to address the worry that you were brave enough to broach with me today: are you really good enough for Swarthmore? It’s really the same issue as when we admit students who have no history in their families of fancy colleges, or any colleges, or any history of expectations as demanding as ours or of positions of substantial responsibility in society. Swarthmore’s belief is: people with the right underlying talent don’t have to be brought up to the top gradually through several generations. They can leapfrog to comfort in an environment of high expectations in a few years. If we are right about this—and surely we are right in some cases—then Swarthmore, and not more laid back places, is really the place to make these people shine. This goes for the students from humble backgrounds that you inspire here, and it goes for you.
I never responded to Maurer’s email because I did not know how to respond. It shook me to the core. I thought very hard about this email over the next several months as I adjusted to my new tenure-track position in southern California. I eventually came to the startling conclusion that Maurer was absolutely right! Moreover, I realized I was selling myself short. It is as if I finally let myself accept the idea that I did a successful job at Swarthmore. Within the first semester at my new position, I told Maurer that I was heading back on the job market. It turned out Swarthmore was able to offer me a chance to return but this time as a tenure-track assistant professor!
In 2012, I returned to Swarthmore as a tenure-track assistant professor and achieved tenure in 2017. My mother passed away in 2018 and so I am very thankful she lived long enough to see me achieve tenure. She was always one to express how immensely proud she was of me. Returning to Swarthmore College is without a doubt one of the best decisions I have ever made in my entire life. With the help of an extremely supportive department and surrounded by inspiring students, I finally feel that I belong at Swarthmore.
Because my pathway to being a mathematician was not along a traditional path, I assumed that my role as a professor would therefore be less valuable and ineffective. This point of view was highly corrosive. It took a lot of conversations with colleagues, friends, and family to realize this view of myself was completely inaccurate. Something that I would like to impart upon the aspiring mathematician is this:
There are countless paths to having a deep and meaningful relationship with mathematics.
However, like any journey along an arduous path it is immensely helpful to have useful resources. I cannot stress this enough, dear reader. Build a network of people you can reach out to for help, advice, or direction. Seek out feedback, viewpoints, and opinions from others in your support system. You may be surprised how open people can be in giving you effective guidance. A favorite teacher, professor, friend, and family members are just a few examples of people you can add to your network of support. Even more support can be found for example through the Math Alliance (mathalliance.org), which has a vast database of professors who are ready and willing to mentor students interested in the mathematical and statistical sciences. With a solid support system at your disposal you will be able to be inspired and encouraged to carry on even in the darkest hour. And carry on you must for one day it may very well be you who takes up the role as a mentor!