Testimonios, a new publication from MAA/AMS, brings together first-person narratives from the vibrant, diverse, and complex Latinx and Hispanic mathematical community. Starting with childhood and family, the authors recount their own particular stories, highlighting their upbringing, education, and career paths. Testimonios seeks to inspire the next generation of Latinx and Hispanic mathematicians by featuring the stories of people like them, holding a mirror up to our own community.

The entire collection of 27 testimonios is available for purchase at the AMS Bookstore. MAA members can access a complimentary e-book in their Member Library. AMS members can access a complimentary e-book at the AMS Bookstore. Thanks to the MAA and AMS, we reproduce one chapter per month on Math Values to better understand and celebrate the diversity of our mathematical community with folks who are not MAA members.

Early Life

I grew up in the countryside in Bayamón, Puerto Rico, in a neighborhood called Buena Vista. The place was beautiful, with rolling hills and plenty of space to play outdoors. I was the fourth of six children; I have three sisters and two brothers. My mother, Flora Braña Santana, was the ninth of ten children. Her parents did not allow her, nor her siblings, to attend school past the fifth grade because they were needed to help with the farm. She later became a seamstress. My father, Germán Cordero Rodríguez, was a tall, strong young man. After second grade his parents asked him to get a job to help the family and he was not allowed to return to school. He later became a truck driver and drove an 18-wheeler truck moving cargo throughout the island. Despite their lack of opportunity to get an education and the lack of financial resources, they emphasized the value of education. They saw it as the key to a better future. Growing up, my siblings and I liked going to school because it was the only outing we had most of the time.

School was the only place we had to learn about other countries and cultures. It was our way to leave our small town and “see’’ the world. My family never took a family vacation—indeed, when we would read stories at school about a family going on a vacation, we wondered what that must feel like. We were a family of eight, and we did not own a vehicle large enough to fit all of us. The only vehicle in the family was the one my father purchased and used during the day for public transportation. He would have a neighbor drive it six days a week, taking people from the neighborhood into town for a fee. On Sundays, his only day off from work, my dad would go out with his friends. When summertime came around, we were not very happy because this meant staying home all the time. The happiest day in the summer was the day before classes would start. This was a great holiday, especially for the girls. We would set up our school uniforms on top of one of our two beds, and all four sisters would sleep in the other bed together so the next morning we could all get dressed quickly for school. When I tell this story to my children, they tell me over and over, “that’s not normal, mom.”

First school years. Throughout elementary, middle, and high school, my teachers were very supportive and encouraging. I feel fortunate that I started my education by attending the neighborhood public school where we were all Hispanics (Puerto Ricans), and all came from a low socio-economic background. Our talents and determination distinguished us from each other and not the race or color of our skin, nor the size of our houses.

From first grade to ninth grade, I attended the neighborhood school, called Escuela Segunda Unidad de Buena Vista; it later became Escuela Segunda Unidad Cacique Majagua. Almost all students (at least 90%) were provided free breakfast and lunch.

Moreover, we were given free shoes and a school bag at the beginning of the school year for several years. It was interesting that the shoes were the same for boys and girls—they were not very attractive! However, we needed them, so we were happy to get them. I had two excellent teachers in mathematics; from fourth to sixth grade, I had Ms. Solonida Hernández, and from seventh to ninth grade, I had Ms. Idalia Figueroa. They were smart, caring, and inspiring. My third-grade teacher, Ms. Sara Vargas, was the first to show me the beautiful and fun side of mathematics. Besides mathematics, I also loved my Spanish classes, and I developed a love for literature. My seventh to ninth-grade teacher was Ms. Elba Rodríguez; she was very passionate about the literary works that we would analyze in class. I looked forward to going to her class every day. Well, actually, I loved going to all my classes. I remember the joy of learning English with Ms. Marta Álvarez in seventh to ninth grade. I remember when she received a set of the SRA Reading Laboratory®, which was a program to learn how to read in English. It consisted of a set of cards with stories and questions to answer after reading the stories. It was designed by levels of different colors. She offered me to use it, and I was so excited that I went every day during lunchtime to take the tests. This was not required, but I enjoyed reading the stories and seeing how far I could go with the program. I was so thrilled every time I would advance to a new color. I now realize how much those cards helped me learn English.

From tenth to twelfth grade, I attended the high school closest to my home, which was called Escuela Superior Miguel Meléndez Muñoz. A quick look into the performance of the students at the school recently shows that it is on the top 50% of high schools in Puerto Rico, yet the percentage of students achieving proficiency in math is 35–39% (which is approximately equal to the Puerto Rico state average of 36%) for the 2016–17 school year. The percentage of students achieving proficiency in reading/language arts is 50–54% (which is higher than the Puerto Rico state average of 48%) for the 2016–17 school year.

Despite the overall school performance, I felt that it prepared me well for college in Puerto Rico. I especially liked my science teacher, Mr. José Manuel Erazo, who taught me biology in tenth grade, and chemistry in eleventh grade. In eleventh grade, I took Algebra II with Mr. Joselín Alonso, and that was when I truly fell in love with mathematics. Since there were few subjects taught at the school, and I was close in age to my sisters Olga and Lilliam, I took two classes with my sister Olga—Biology in tenth grade and Algebra II in eleventh grade. With my sister Lilliam I took two classes too—Geometry in tenth grade and Chemistry in eleventh grade.

With my baby brother, Germán, I took the Agriculture class when I was in twelfth grade and he was in tenth grade. We were members of the Future Farmers of America (FFA), and I loved participating in the events sponsored by the FFA at my school. One of the events was public speaking. I participated in the local competition and won first place at the statewide competition. My speech was titled “The Role of Women in Agriculture.” In my address, I included anecdotes of my mom and her two sisters working on the farm. I recalled that after the Q&A session with the judges, one of them said to me: “you are missing your true calling; you should be a lawyer because I assure you that you will not lose a case.’’ I guess I appeared pretty confident as I defended the role women had played in agriculture, contributions that had not been recognized in the male-dominated culture of agriculture. Looking back, I think how lucky I was that all my teachers looked just like me during my first twelve years of school—they were my first role models.

Road to mathematics. For as long as I can remember, mathematics came effortlessly to me. Having two older sisters who would often talk at the dinner table about what they were learning in school motivated me to advance in school, especially in mathematics. On the other hand, being the fourth of six children allowed me to help my two younger siblings with their schoolwork. Helping them with mathematics came naturally to me. One day, when I was in eighth grade, I attended a college algebra class with my cousin, who was a sophomore in college. The instructor was introducing the quadratic formula, which I had not studied before. The explanations seemed very logical to me, and I solved all the problems he assigned the class. Before I realized it, my cousin and several of her classmates were surrounding me, and I was explaining to them how to solve the problems.

A few years later, when I was in tenth grade, my uncle decided that he wanted to take the General Educational Development (GED) test. However, since he had only gone to school until the fifth grade, he needed to learn all the mathematics he would need to pass the exam, so I offered to teach him. We met daily for several weeks and it was challenging helping someone who had never encountered mathematical abstraction. He was curious about many things, including how the variable ‘x’ could have many different values. I remember one day, after solving a problem whose solution was x= 5; he asked: “but before you said x was nine; how is that possible?’’ After many long hours working together, he took the exam and passed it the first time. After this experience, I was convinced that helping people learn and enjoy mathematics would be my lifelong endeavor.

Undergraduate Education

I started college at the University of Puerto Rico’s two-year campus in my hometown (called Colegio Regional de Bayamón, CRB), which was about an hour commute from home. I knew I liked mathematics the most of all subjects, so I decided to major in mathematics. However, I did not know the career choices for someone with a degree in mathematics, besides teaching mathematics in the K–12 setting. My oldest sister had learned about a new field of study people were going into those days: computer science. She explained to me all the benefits of pursuing a degree in computer science would offer. While I was tempted, and for two days changed my major to Computer Science, the day before classes started I decided my passion was mathematics, and I switched back to mathematics. The first math course I took in college was precalculus. Most of my science major classmates were registered in calculus because they had already had precalculus in high school, but I had not. So, I enrolled in the two-semester precalculus sequence. (I could have taken the one-semester five-hour course, but instead, I wanted to take my time with the basics. This is one piece of advice I give young people: “don’t rush through the important things. Take your time to learn the basics, and later you can catch up,’’ Which I did.)

Tragedy hits home. On August 9, 1978, just one week before my sophomore year in college would start, my family experienced a tremendous loss. On the evening of August 2, my father returned home from work and, after having dinner, went to do mechanical work on the truck he drove at the time, just like he had done many other times before. The truck belonged to his cousin, and my father worked for him as a driver for many years. He knew the truck very well; earlier, he noticed that there were some issues with the brakes. As usual, he would try to figure out and solve the problem himself. As he was working under the truck that was propped up with a regular car jack, the truck dropped on him, smashing his legs and carrying him for some distance down a small hill. My youngest brother was inside the truck assisting with shifting gears. My brother did not know how to drive at the time, and my father was not an experienced auto mechanic. After one week in the hospital, my father passed away, and our lives changed forever.

University of Puerto Rico at Río Piedras. After two years at the Colegio Regional de Bayamón, I transferred to the University of Puerto Rico’s main campus in Río Piedras (UPR-RP). Getting to campus now meant approximately a two-hour commute in each direction because transportation from Buena Vista to Río Piedras was complicated and unreliable. Of course, we did not have the resources to buy a car. In my senior year, my sister Olga and I decided to rent a room in a house in Río Piedras. It made going to school so much easier. That year, we took a graduate topology course together. That was one of the best courses I took at the UPR-RP, and not just because my sister was in it!

When I was a senior in college, my abstract algebra professor at the University of Puerto Rico, Dr. Carol Knighten, asked me about my plans for graduate school. At that time, I had not even considered graduate school. With my father passing when I was a sophomore in college, finishing college and starting a new job was necessary. Dr. Knighten told me, however, that I should consider graduate school and get a PhD because I would have better and higher-paying career options. There were two hurdles to cross to follow Dr. Knighten’s suggestion: first, to pursue a PhD in mathematics, I would have had to leave Puerto Rico because there were no PhD programs in mathematics in Puerto Rico at the time. Second and equally important, I did not have the financial means to do so. However, Dr. Knighten recommended that I apply for a National Science Foundation Minority Graduate Fellowship, which I did. I received the fellowship and was able to take care of the financial hurdle.

Although my mother worried about me leaving, she was supportive of my plans to come to the United States to pursue a PhD in mathematics. Had Dr. Knighten not approached me about pursuing graduate school, I guess I would have never thought about it and would not have had the satisfying career I’ve had as a mathematician and an educator. Never underestimate the power of words of encouragement. I graduated from the University of Puerto Rico (UPR) with High Distinction.

The Cordero sisters. The oldest of my siblings is my sister Nilda. Nilda, who started college at the age of 16, obtained a bachelor’s degree in biology from UPR after transferring from the CRB. She later completed a master’s degree in Chemistry at the UPR and was a high school teacher at a public school in Bayamón for 30 years. Olga, who is two years younger than Nilda (and a year older than me), completed a bachelor’s degree in mathematics at the UPR after transferring from CRB. After she finished her undergraduate studies, she worked for an engineering/architecture firm in San Juan, Puerto Rico.

The year I decided to come to the U.S. to pursue graduate school, Olga decided to follow and went to the University of Iowa with a Graduate Fellowship provided by the university. She transferred from Iowa after her master’s degree and received a PhD in Statistics from Utah State University. My youngest sister, Lilliam, who is one year younger than me, studied computer science at the CRB. By the time Lilliam started college, the two-year institution had become a four-year college.

As I mentioned earlier, my parents did not even complete elementary school, yet all four girls studied STEM careers. Besides our love for STEM, we also loved literature, art, and music. We would talk for hours about all the things we were learning in those subjects at school. During my senior year in college, my teacher in literature thought I was a Spanish literature major and was quite disappointed when she learned I was not pursuing a degree in literature. Unlike the girls in the family, my brothers pursued interests outside of STEM. My oldest brother went to vocational school (and studied woodworking), and my youngest brother studied business in college.

Graduate Education

I started my graduate studies at the University of California at Berkeley. It was a big cultural surprise moving from the little town in Puerto Rico where I lived with my family to Berkeley, California, where I would live with roommates. The biggest shock was the university environment. It seems that all the graduate students at Berkeley came from very top universities from all over the world and knew so much more math than I did at the time. I felt an extreme sense of estrangement and alienation, and the demands of my studies, plus the challenges of living in a place so different from where I came from, made it hard to connect with people.

While in Puerto Rico, I would often visit my professors during office hours. At Berkeley, I felt very intimated by them, not just because of the language barrier but also because they seemed intimidating. I was fortunate that my first year I took Complex Analysis from a new visiting professor who had just joined the department, Dr. Gustavo Ponce, who was originally from Venezuela. I thoroughly enjoyed his class and decided to take other courses in complex analysis. The next semester I had a course with Dr. Donald Sarason, who later became my master’s thesis advisor.

After completing my master’s, I moved to the University of Iowa where my sister Olga was studying mathematics. When I moved to Iowa, I felt more comfortable talking to my professors. In my first semester, I took an abstract algebra class with Professor Frank Kosier. He was very entertaining in class and seemed very approachable. When discussing a theorem or concept, I noticed that sometimes he would write the letters “BS” next to it. Being the careful note-taker I was (and not knowing what it meant), I would also “designate’’ some results and concepts as such. After a couple of weeks of lectures, I decided to go to his office for some clarifications. I started by saying how I was familiar with most of the theorems and concepts we were studying but just had a question about why for some results he added the letters “BS’’ next to them, and for some others, he did not. He looked at me puzzled, paused for a moment, and then blasted into laughter. He then said: “Minerva, if you don’t know what BS stands for, I’m afraid I can’t tell you what it is.’’ When I shared this experience with a couple of classmates, they laughed and finally told me what it meant. I felt so naïve.

The second semester, Professor Norman Johnson was my abstract algebra instructor. One day I was in his office during office hours, and the writings on the board caught my attention. There were many geometrical figures all interconnected. After he explained his research, I was fascinated by the subject and read several papers he recommended. I wasn’t sure how to approach him about conducting research for my doctoral dissertation under his guidance. Luckily, after achieving a near-perfect score in the doctoral written exam in algebra, he approached me and asked me to work with him for my dissertation. Since his research was at the intersection of algebra, combinatorics, and geometry—three subjects I loved—it was very easy for me to agree to work with him.

Teaching mathematics in college. At the University of Iowa, I was given the opportunity to teach as a graduate teaching assistant. I was terrified at first of standing in front of a room full of undergraduate students and having to teach in English. I remember one day in class, one of my students asked a question. I did not quite get what he was asking, so I asked him to repeat his question. After a couple of times of me asking and then not understanding his question, he said, “Oh, never mind.” I asked him to repeat what he said, and very frustrated, he said again, “never mind.” I had no idea at the time what “never mind” meant. Instead of interpreting it as a single phrase meaning ‘don’t worry about it,’ I had understood it as two separate words. Fortunately, my office-mate helped me understand the intention the student might have had.

Despite these issues initially, I immensely enjoyed being a TA, and in my classes, there was always laughter and good camaraderie among my students. I tried to share with my students the difficulties I was experiencing as a student myself in a ‘foreign’ country with a different language. I found the students to be quite receptive and encouraging. A comical situation I experienced when I was a graduate teaching assistant at the University of Iowa in charge of teaching a section of Calculus I, was when I was discussing how to use the first and second derivative of a function to draw its graph. I did an example and could tell that the students did not grasp the ideas well. So, I decided to do another example. After I completed that example, I asked the class if they would like to see another example, and they said yes. As I started to work on my third example, I could hear the students talking in the back, and a few were giggling. I turned around and asked what was going on. One shy young lady said, “I think you’re doing the very same example for the third time.” It was hilarious.

Tragedy strikes again. My mom was one of the kindest, most positive people I have ever met. When she was little, she was one of the few children in her class to have shoes, and since all the kids walked to school with no shoes, she would hide her shoes before getting to school and go shoe-less with them. When she was 54 years old, she felt something on her chest and went to the neighborhood clinic doctor. The doctor told her she was fine and dismissed her. Two months later, she could still feel it, so she went back. And, at 54 years of age, she had her first mammography test. It turned out she had stage IV metastatic breast cancer.

After the diagnosis, she underwent radiation and chemotherapy, but it was too late; a year and a half later, she passed away. Sadly, I attribute her misdiagnosis and untimely death to the dismal quality of healthcare available to the working poor.

We buried her on December 31. I was still in graduate school and it was so hard to find the motivation to keep going with everything. She had been my strongest supporter, and receiving my PhD was going to be my greatest gift to her. But now, she would not see me graduate. I went into a deep sadness and was not interested in doing anything, not even mathematics.

That year I was living in Bowling Green, Ohio, where my then-husband had a visiting professorship. In February, he was giving a talk at the University of Michigan and I decided to join him on the trip to Ann Arbor. There was a terrible winter storm, and the roads were covered with snow. On the way home, we had a terrible car accident. I remember laying there in the snow, thinking I was going to join my mom.

Due to the injuries to my ribs and pelvic bone, I was unable to walk for three months following the accident. I would just lay in bed and think about dying and being with her. I felt so much pain during that time, but all that pain, all that sacrifice, was also the motivation to finish my PhD I did not want all to be in vain, even if my mother could not see me graduate in person. I knew wherever she was, she would be watching over me, and she would be proud.

Doctoral dissertation defense. The first talk I ever gave was my doctoral dissertation defense. As an undergraduate or graduate student, I did not have the opportunity to attend a conference or give a talk. So, for my defense, I practiced so many times what I was going to say and write (at the time, the presentation was given using a blackboard with no visuals) that I memorized every single word I would say. However, at one point in the middle of my defense, I noticed that the audience seemed uneasy, so I asked if there were any questions. My supervisor quickly replied: perhaps you would not mind repeating the last result and its proof but in English this time. I did not realize it, but I switched to Spanish in the middle of my dissertation without even being aware of it.

Research—Finite Geometries

My research area is at the intersection of algebra, geometry, and combinatorics. It is called finite geometries. Specifically, I study finite projective planes coordinatized by non-associative division algebras; these are called semifields. These finite geometries belong to the larger class of combinatorial (balanced incomplete block) designs.

In my work, I classified and discovered several new classes of semifields. Such an algebraic structure is somewhat less than a field in the sense that multiplication may well fail to obey the associative law. Still, the corresponding projective plane has a fairly rich collineation group. Notice that other “weakening’’ of the algebraic structure called a field have been widely investigated over the years, both from an algebraic and a geometric point of view. For example, nearfields fail to be fields if just one of the two distributive laws is missing. While the work of Zassenhaus in 1935 classified finite nearfields, there is no complete classification for finite semifields yet. In my research, I always combine algebraic methods with geometry. So, in my work, groups, rings, and polynomials always come together with collineations, subplanes, particular configurations of points and lines, etc. The challenge is always how to translate any piece of algebraic information into geometric data.

One of the research results I am most proud of is a conjecture I made relatively early on in my career about the existence of a particular class of semifields. A few years later, a group of young mathematicians in Italy proved the conjecture. Currently, I study other finite algebraic combinatorial structures, including loops, quasigroups, and nearfields. These structures are used in algorithms to encrypt and decrypt data in a safer way than using associative structures.

Professional Career

The day after my doctoral dissertation defense, I flew to California for my first job interview. I was so nervous, worrying that I might revert to Spanish in the middle of my talk, but I did not. It was an enjoyable experience. I later interviewed at another school in California and one in New York. I received two job offers for tenure-track positions in mathematics departments. However, I did not accept either position and instead moved to Lubbock, Texas, where my husband had a faculty position at Texas Tech University. There were no positions for me, but like many women with a PhD, I moved to the place where my husband had a job.

Since there were no faculty positions at Texas Tech when I moved to Lubbock, I decided to contact the school district to see if I could teach in one of their high schools. As it turned out, they needed a math teacher for Estacado High School, and I was offered a position, which I accepted without ever visiting the campus. At the time, Estacado High School was the lowest performing school in the entire school district. The campus had over 95% minority enrollment and over 90% economically disadvantaged students. Unfortunately, the school suffered from a high turnover of teachers, which, as research shows, has a very negative impact on student success. During the in-service training, I met the principal and other teachers at the school. The principal was very careful in emphasizing how much we needed to show love and concern for the students.

I was very thrilled that these were things that the school valued. Unfortunately, I was not prepared for the environment in the classroom. I loved mathematics and was so excited to teach this group of students. I understood they needed someone to teach them mathematics and show them that they cared for them; I treated my students as my friends. Very soon, unfortunately, I found myself in a very chaotic classroom due to my ignorance regarding high school effective classroom management skills.

In addition, one day, at the end of class a young girl asked me if I would take her home with me because her situation at home was challenging. I went to the principal to ask what the right thing would be to do at the time. He instructed me not to take the student home with me. The next day as I was finishing class, the young girl started a fight with another girl. She threw her classmate on the floor and was hitting her. Students started screaming, and a teacher from the next-door classroom called the police and they interfered. After everyone left the classroom, I sat there and burst into tears. I realized that what I wanted to do the most, which was to teach these children mathematics and show them that I care about them and their future, I was simply not good at because I did not know effective classroom management techniques. I walked to the principal’s office and told him that I was not helping these children that desperately needed help and that I had decided that that day would be my last day at the school.

For the next several months, I immersed myself in learning the ins and outs of publishing in mathematics, and I submitted a couple of manuscripts. Around that time, Texas Tech had an opening for a faculty position for which I applied. After my talk, one of the faculty members told me that my talk was the best he had ever heard in his 30-plus years at Texas Tech; it made me feel content. I received an offer and started my first tenure-track position the following fall.

Personal Life

I am very close to my three sisters, and we talk on the phone often. Three of my siblings live in Puerto Rico (Nilda, Lilliam, and Wilfredo, my oldest brother). My sister Olga lives in France, and regularly teaches at the American University in Washington, DC. My youngest brother, Germán, with whom I was very close, passed away in 2010. Now that I have been in academia for some time, have achieved full professorship, and have been working as an associate dean in the College of Science at the University of Texas at Arlington for six years, I feel that my efforts to increase the number of women and Latinxs who pursue careers in science and mathematics are more fruitful.

Reflections on Diversity

Growing up in Puerto Rico and attending school at the University of Puerto Rico has been something that definitely helped me learn mathematics. I never felt that I was less qualified or less capable of learning mathematics than my peers because I was a Hispanic woman. Indeed, both in high school and in college, I received the highest award for a graduating senior in mathematics. My sister Olga, who is just one year older than me, also received these awards. It took some time after I came to the United States to realize that people could question my ability to do mathematics because I was a woman of Hispanic origin.

I remember the first year as an assistant professor, a colleague told me I got my position because I played the Hispanic woman card. I had no idea what he meant by that. His explanation did not make sense to me. The conversation ended with him telling me that I was lucky because I was the “good kind’’ of Hispanic, because “I didn’t look it.’’ It was not until several years later that I understood the hurtful nature of his words. I could not help but feel sad for my fellow Hispanics and women colleagues like me who have dealt with this mentality all their lives. I wish I could say that I have seen the mathematics community improve, but that has not been the case.

Last year, I was selected as an IF/ THEN American Association for the Advancement of Science (AAAS) ambassador. This program aims to increase the number of girls interested in careers in Science, Technology, Engineering, and Mathematics (STEM). For several years now, I have been involved in outreach activities to bring more underrepresented minorities and women into mathematics. I have given many talks to groups of fifth and sixth-grade girls and their parents. Often, the parents only speak Spanish, and I feel very fortunate that I can talk to them and explain to them all the opportunities that their daughters have if they get interested at a young age in science, engineering, and mathematics.

A View Towards the Future

More Latinxs/Hispanics should get involved in mathematics research and mathematics education. Having a diverse group of individuals working on this will help attract a more diverse group of people into mathematics. With the changing demographics of this country and Latinos making up a larger percentage of the population, it will be imperative that we are participating in mathematics. To encourage young people in math, I show them the power and the value of mathematics.

Without mathematics, we would not have the advances in technology that exist today. For example, their cell phones would not work as well as they do if someone had not spent the time doing the mathematics required. Without mathematics, we would not have the advances in medicine that exist today. We could not even see movies and pictures so clearly as we do today without all the advances in mathematics.

Hispanics are the fastest-growing and youngest group in the U.S.—expected to comprise 30% of the U.S. by 2040. If we do not make efforts to attract Latinx students into mathematics and other STEM areas, the U.S. will not be able to maintain its current position in the technology world.

My advice to students is to take as much math in high school as possible, but not move too quickly. It is essential to learn the basics very well before moving on. With a strong background, it is easy to catch up and finish a college degree on time. The important thing is to persevere and not give up, remembering that mathematics is for everyone. You don’t have to be a straight-A student in high school or college to have a successful career as a mathematician. That’s the beauty of it.