When It All Started
It’s Saturday evening and the sun is about to disappear from the horizon. I hear the sound of dominoes, clashing with each other. A table is set, my sister and cousins are shuffling the dominoes and we all get ready to play. Sometimes for hours. When (if!) we got tired, we would switch to Monopoly or card games. Regardless of the game, there was one constant: I always enjoyed counting the game points/“money’’ at the end. In a sense, this is where it all started for me. These are the earliest memories I have about numbers and mathematics.
My parents, however, tell a different beginning. They share stories about how I could not speak until after I was two years old but then quickly learned how to speak, read, and count in a very short time; well before starting kindergarten. They tell stories about me extrapolating that if 1+1 is 2 then 10+10 is 20 and 100+100 is 200 at a very early age. Some years later, when I finished second grade, a teacher suggested I skip third grade and jump directly to fourth grade as I had the mathematical skills for it. My parents agreed and I skipped third grade. Unfortunately, I have no recollection of any of these events.
School and Early College
El Triángulo de las Matemáticas. Almost all of my childhood memories start in seventh grade. They are mostly about how I would spend my evenings playing outside with my friends and cousins as, at the time, my parents did not have the resources for me to attend after-school clubs or camps. The memories that do involve math have to do with when we played board games. As a matter of fact, throughout most of middle school and high school, I enjoyed mathematics but never really felt passionate about it. I had the same teacher from eighth to eleventh grade and while I was doing well, the math discussed in class was very mechanical and I never felt engaged or challenged in these classes.
It all changed when I entered an after-school math club El Triángulo de las Matemáticas  during my late years in high school. It was led by Mr. Jorge Haddock, who was also my math teacher during my high school senior year. We met every week to work on cool math problems. The thrill I felt after struggling and then solving what at the time felt like very hard problems was an indication that I wanted to keep engaging with mathematics. I felt like I would enjoy doing what Mr. Haddock was doing (and I did not know any mathematicians other than my school teachers), so I decided to apply to college as a math major with the goal of becoming a high school teacher.
Remembering mom and dad’s sacrifices. My transition to college, in 2007, required a big adjustment. I had just turned 17 when I moved out of my mom’s house to live in a tiny college apartment with my best friend in the western part of Puerto Rico. We were both attending the University of Puerto Rico at Mayagüez, a state university known for their engineering programs. As happens to many college freshmen, for the first time I had to take full care of myself (e.g., having to cook, clean, manage finances, set my own schedule, do my coursework, etc). It was then that I started to understand what a big sacrifice it must have been for my parents to take care of me and my sister and provide us with the best possible chance at a college education.
For instance, in order to pay for our house, Dad entered the military and completed missions in several international destinations. He left home to stay in deserts, camps, and other non-desirable places. Mom held the fort down while Dad was away and then she went back to college in her thirties to complete her bachelor’s degree, while working full time and taking care of me and my sister. I realized that if my parents were so strong to go through really difficult times to chase their dreams, I should try my best to do the same.
Summer research programs. It was Spring of 2009 and one day, out of the blue, my phone rang. I picked up and a strange but energetic voice said “Hello Alexander, how are you?… Can you read these papers?’’ Somewhat in shock, I said: “Yes.’’
Some months before the call, a faculty member told me I should apply to summer Research Experiences for Undergraduates (REU). I applied to a dozen of them, despite the fact that I was underprepared for them. I had only taken an introduction to proofs class and while I worked really hard at the applications, I wrote what I can now confirm were very poor application essays. Not surprisingly, I didn’t get accepted to eleven of them. Yet, a twelfth, Dr. Frank Morgan’s SMALL REU group needed something special. They needed more than a mathematician. They needed a bilingual mathematician.
In that same year, Frank Morgan had arranged to spend the summer at the University of Granada in Spain and bring his REU group with him. I have never asked him, but my guess is that the idea of having at least one bilingual student was too tempting for him to ignore. So, he looked at my application and called me to talk about the program. When he asked me if I could read some papers and tell him what I thought, I did what I needed to do. I spent hours reading the papers, although I could barely understand what was written in there. A week later we spoke and he officially accepted me into the program.
June came, I packed my stuff and flew internationally for the first time in my life. Once we arrived in Granada, we settled at the Carmen de la Victoria university residence, overlooking the imposing Alhambra Castle. At the time, I found it all very impressive. Then, reality struck. During the first couple of research group meetings, the other three participants in the program (all coming from prestigious institutions) were talking about densities, manifolds, and isoperimetric curves. I could not understand much of it. By the third day, I felt hopeless, so I started packing and decided I was going to head back home.
Before making it official, I spoke with Frank and told him I was lost. We sat down and discussed the background needed for me to work on a particular case of the research problem we were working on. More than anything, our conversation gave me hope that I could at least attempt to work on a problem. I spent the next four weeks working on it and the problem became part of my first math publication. From that point on, Frank became a big advocate for me and later recruited me to join the Notices of the AMS editorial board when he was Editor-in-Chief.
The following summer, I applied and got accepted to the Mathematical Sciences Research Institute Undergraduate Program (MSRI-UP) in Berkeley, CA. This time I was better prepared to work on a research project and had a good experience throughout the program. It was uplifting to do research mathematics in such an amazing place and with an excellent group of peers. To top it off, my research advisor was Dr. Edray Goins, who became a mentor and role model for me.
Graduate School: Learning from the Hard Times
Finishing my undergraduate degree was my second biggest academic accomplishment at the time (getting the SMALL REU problem solved was the first). I feel blessed to have experienced many other positive moments in my life that fill me with joy every time I think and reflect back on them: getting married, getting my PhD, co-founding Lathisms, getting the job I had desired, among others. While these moments have carried and continue to carry me through life, they aren’t the moments that made me stronger. Difficult times are the ones that have taught me how to be resilient.
I rarely talk about these difficult times, but was recently reminded of the power of sharing these moments, particularly, for a younger generation that might look at us and see “awesome mathematicians who rarely struggle.’’ So, here are some of my most difficult academic moments.
First year of grad school was HARD. It was an early week in January and the beautiful Notre Dame campus was covered with snow. Temperatures had ranged from single digits to below zero for the past week and I was in my on-campus graduate apartment. I had been inside for about 300 straight hours. I was tired, without energy, and frankly a bit depressed. “How did we get here?’’ I thought.
A year before that, after the two REU experiences, I was sure I wanted to become a math professor. After a long and stressful graduate school application period, I received a handful of offers and decided to enroll in the mathematics PhD program at the University of Notre Dame. “I am only one degree away from my goal of becoming a university professor,’’ I thought at the time.
The first two weeks of the semester were a slap in my face in many ways. I had the privilege to be raised in a place where I was part of the majority; now, at Notre Dame, there were no Black, Latinx, or Native American faculty in the math department. Overall, there weren’t many people of color in the department and more generally, in the university. It felt isolating and it was a sudden introduction to the racial disparities and lack of a path for a graduate education that many people of color face in the United States.
A second shocking issue was classwork. I was not sure what type of mathematics I wanted to study and was unsure about my background, so I thought it would be a good idea to take four courses in my first semester. I enrolled in Real Analysis, Complex Analysis, Algebra, and Topology. Very quickly the semester turned into a stress-inducing machine. Reading notes and books, doing weekly homework, studying for exams. I was spending a lot of time (and doing well) in Algebra and Complex Analysis, but was really struggling with Topology and Real Analysis. In an unhealthy pattern, I would spend most hours of every single day of the week doing course work. Despite this, I kept struggling with Real Analysis. The professor’s teaching style, which would have him talk for the whole hour while writing very few things on the board, was not working for me. I obtained less than 40% on both the midterm and the final exam. By being one of the three students who “stuck with it’’ for the semester (out of the initial 12 or so students), I obtained an A–. But my course average, just like my energy and desire to continue learning from the professor, was much lower than 40%.
With all my family and friends back at home, I was alone, stressed, and tired. Qualifying exams were coming in January and temperatures were ranging in the single digits. I decided to quarantine myself in my apartment to study for the qualifying exams for twelve straight days. This is how I ended up inside for about three hundred straight hours, exhausted, and depressed. By the end of it, I took my qualifying exams and felt like I had not only dumped all the stuff I had just studied, but that I also left all my humanity there.
As soon as I turned in the exam, I knew I was out of energy and motivation and needed help. After taking a week-long break, I reached out to my community; I talked to my girlfriend (who is now my wife), advisors, counselors, and colleagues. The consensus was that I needed to make changes; otherwise I would not survive graduate school. I started exercising and playing sports, stopped prioritizing coursework over my own physical and mental health, and reduced the coursework to a manageable load and in areas I was more interested in. Fortunately, I really enjoyed Katrina Barron’s Algebra class and so I started taking more courses in the area. Not surprisingly, I ended up getting my PhD in algebra (under the direction of Matthew Dyer).
Withdrawing from differential geometry. The lessons I learned during my first-year graduate experience helped me get through the remaining years of my graduate career. For the most part, years two through four were fairly positive, in part, thanks to the advisor and area of research I chose. But there was one more experience worth pointing out. For the first time in my life, I had to acknowledge that I was going to fail a math course. I had a 3.90-ish GPA in high school and college and had never really failed a course. Even graduate Real Analysis, with the low scores I had, I was fairly sure I would pass as every other student was in the same boat. Then I met differential geometry. After the first two weeks of classes, it was clear to me that either I devote all my time and energy to that class (mostly to pick up all the needed background and then to catch up in the class) and relive what I lived through during my first year or I was going to fail the course. I had it clear at the time. There was no way I would go back to the unhealthy habits of year one. Hence, I accepted I was going to fail and decided to drop the class.
Job search. Going into my fifth year, there had been one question I was dreading to ask my advisor. “When do you think I will finish the program?’’ After a year struggling to get myself to ask it (and afraid of the potential answer as I had guaranteed funding for exactly five years) I did ask him. Matthew, quickly asserted: “If it all continues well, you can finish this year.’’
I felt so relieved. I could finally finish and fulfill my goal of getting a PhD and becoming a professor. Yet, one more difficult process lied ahead—the job search. Looking for jobs in academia is a nine-month process. First, drafting your documents (in August at the latest), then searching open positions, submitting applications (early winter), getting interviewed (January), doing on-campus interviews (February/March) and finally accepting a position. It’s a draining process, to say the least.
I was inexperienced in the process and had no training about it. So, I asked my colleagues what they planned to do and many said they would apply to 100+ jobs. I then did the same. It wasn’t until a year later that I realized this was a terrible idea, at least for me. How can one really research 100 places, gather information about their positions, the type of department they are, what they are looking for and then tailor every single one of the applications? I don’t find it possible.
Not surprisingly, I received 80+ rejections. Well technically less, as many of the places never actually contacted me with a formal rejection. Fortunately, I seemed to have been an exciting candidate to some liberal arts institutions, as I got visiting offers from Swarthmore College, Haverford College, and Williams College, and a tenure-track offer from Hobart and William Smith Colleges. After visiting these places, I decided to decline the tenure-track offer and join the Department of Mathematics and Statistics at Swarthmore College. It was a risky move, but it ended up being one of the best decisions I made. The year I spent at Swarthmore confirmed that being a professor is the perfect job for me and a year later I obtained a tenure-track position at Villanova University. The three years I have spent at Villanova have been professionally and personally fulfilling.
As a Latino who grew up in Puerto Rico, I benefited from a culture in which building and fostering communities was always important. Yet, the somewhat individualized experience I had in graduate school and some solitary experiences at the Joint Math Meetings made me wonder if it would always be like that. Thankfully, it has not.
Meeting Erik, Darleen, and Pam at USTARS. The Underrepresented Students in Topology and Algebra Research Symposium (USTARS) was the first conference I attended in which I felt I belonged. Instead of being the single or one of the few people of color in every single event of the conference, the whole conference was centered around us. More importantly, there was a concerted effort to create a supportive and welcoming atmosphere for the graduate students involved in the conference.
In that place, I started building a community. I attended a talk by Darleen Perez-Lavin, which led me to also meet Darleen’s collaborators Pamela E. Harris and Erik Insko and which later resulted in a research collaboration between all of us. Since then, Pam, Erik, and I have worked on numerous research projects. Through the connections I made there, I also met Mohamed Omar, Alicia Prieto-Langarica, Gabriel Sosa, and many other individuals who have been influential in my career.
The biggest lesson I learned is that building community does not happen by chance. It requires planning, purpose, and commitment from the individuals involved. And once you build communities, they can be life-changing. Thus, I have decided to get involved in projects which, in one way or another, are centered in building community.
Lathisms: Latinxs and Hispanics in the Mathematical Sciences. During a conference, Pamela E. Harris, Alicia Prieto-Langarica, Gabriel Sosa and I discussed the idea of showcasing the contributions of Hispanic and Latinx mathematicians during Hispanic Heritage Month (HHM) as a starting point for building a stronger and more connected Hispanic and Latinx community in mathematics.
Shortly thereafter Lathisms (Latinxs and Hispanics in the Mathematical Sciences) was born. During the first year, we showcased one mathematician per day during HHM. They are featured in the poster to the right. Since then Lathisms has created a podcast, listserv, and continues to showcase Hispanic and Latinx mathematicians on its website. With support from the American Mathematical Society (AMS) and Mathematical Association of America (MAA), the project has reached thousands of schools and many universities.
Villanova: DREAMS Program, Co-MaStER. One of the nicest things about Villanova is that the faculty in the department have a great rapport with each other. Yet, our connection to math majors is not as robust. To bridge the gap, I co-created two programs: DREAMS (Discovering Resources and Exploring Advanced Mathematics and Statistics) and Co-MaStER (Community of Mathematicians and Statisticians Exploring Research).
DREAMS’ goal is to introduce students to intriguing problems in mathematics and statistics that could potentially lead to a research project and to provide graduate school information and advice, along with mathematics career perspectives that demonstrate the value of advanced studies in math. Co-MaStER is a research program where we gather research projects from different faculty in the department, send them to students, collect students’ applications and pair interested students with appropriate research projects. Each research group functions independently, but once a month everyone gets together for professional development and research sharing sessions. So far we have received overwhelming positive feedback about them.
Math SWAGGER. In Summer 2020, I joined Pamela Harris, Vanessa Rivera Quiñones, Luis Sordo Vieira, Shelby Wilson, Aris Winger, and Michael Young in co-leading the Mathematics Summer Workshop for Achieving Greater Graduate Educational Readiness (Math SWAGGER), a five-week virtual summer program for underrepresented students enrolled in a mathematics/statistics graduate program. We engaged in conversations about topics that affect the life and academics of graduate students. In addition to the fact that we all learned from each other and from our stories, advice, sufferings, and successes, the early results so far point to the creation of a strong community of scholars ready to support each other through their own graduate paths.
Conclusions and Advice
Through all the programs I have been part of (both as participant and organizer), it has become clear to me that while no individual can single-handedly create a space where all members feel welcomed, heard, supported and given an opportunity to thrive, when we all come together as a community of engaged scholars with a common purpose we can create such events and spaces. When creating these spaces, it is imperative to think about who are the most vulnerable members of our communities and how can we make sure we provide the tools for such members to excel.
A second and final concluding thought, which I shared in a 2020 interview for the Meet a Mathematician series, is about the idea of being successful. In the interview, I was asked to provide some words of wisdom to the mathematics community. My response: “Don’t let others define what success is for you.’’ Success can have many different forms in the mathematical community: being a professor at a research university, a liberal arts college, or a teaching college (see Lathisms.org for many examples), teaching at the elementary, middle, or high school level, becoming a journalist or freelance writer (e.g., Evelyn Lamb), leading community centers (e.g., Amanda Serenevy), running nonprofit organizations (e.g., Jeanette Shakalli), working in industry or government, and many others. Choose what is more appealing to you and define success for yourself.
 The Math Triangle