Testimonios: Dr. William Yslas Vélez

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.

Marriage and Partnership

Bernice and I met when we were 18 years old. We were children, naïve. Our backgrounds were surprisingly similar. We both had families in Magdelena de Kino, Sonora, Mexico, and as children, we both spent part of the summers in that town. On our first date, we went to a wedding shower at El Rio ballroom, where we danced boleros, corridos, and cumbias.¹

We married when I came home from my first tour to Vietnam in the U.S. Navy. I was at sea for most of our first married year, and this made for an extended honeymoon. I could not write about my life as a mathematician without also describing the joy and support that I received from Bernice and the family. Entering the mathematical community could have been like entering a not-too-friendly country, whose language I could barely speak. Instead, I walked in with an arsenal of support.

Every married couple goes through hardships and ours was no different. With large extended families, there are many personalities and viewpoints. The children adopt behaviors of the dominant culture, which have to be begrudgingly accepted. However, we overcame problems and walked through life as lovers and partners. Bernice brought complementary skills to our marriage, which made my life more beautiful, more meaningful, and more delicious. We now spend our time together cooking, still listening to the Mexican music of our youth.

Bill’s Early Life

I was born in 1947 in Tucson, Arizona, and I grew up in the loving embrace of the Mexican-American community. I found out much later that we were poor, just like the rest of the community that surrounded us. I did not internalize this poverty, surrounded as I was by the richness of Mexican culture. I was well cared for and loved. More than anything else, I was well educated. In my home, a song of education played constantly. We were the only family in the neighborhood that valued books. We had a set of encyclopedias and another set of books on nature.

My mother, who was very proud of the fact that she graduated from Tucson High School despite the then-current attitude that women did not need such an education, would often say to us, “Lo único que les puedo dejar es una buena educación.” ² My two brothers, Manuel and Gilberto, and I internalized this inheritance and we all graduated from the University of Arizona (UA). Though we led very different lives, we all passed on this song of education to others as teachers of English, music, and mathematics.

My parents were both born in Sonora, Mexico. My father, Emilio, was born in 1908 in Magdalena de Kino, and my mother, Julia Yslas, was born in 1910 in San Miguel de Horcasitas. At that time, the border between the U.S. and Mexico was fluid and people moved back and forth between Sonora and Arizona. There were families on both sides of the border and children would be sent to live with relatives on the other side of the border for extended periods. As a child, I would spend a good part of the summers living in Magdalena de Kino, and I had the great pleasure of mingling with cousins from both sides of the family. Before my father died, we would travel to Magdalena de Kino about twice per month. The ritual was always the same. We would first arrive at my paternal grandparents’ home where we were received with love and affection, always arriving with gifts of food and other goods. My father would stay with his family and my mother and the children would then drive on about five blocks to stay at my maternal aunt’s home, which was part of their hotel, El Cuervo. As children, we would roam the small town of Magdalena de Kino freely, visiting with many different family members. It was an idyllic life.

We were wild children. Life was safe and we could roam freely. Living in the Arizona Sonora desert gave us a world to explore on our bicycles. An empty lot in front of our house was the gathering place for the kids. We would have neighborhood water fights with an arsenal of weapons. We played kick-the-can and hide-and-seek. In the evenings, adults would sit on their porches to try to catch some breeze. Food was enticing. Is there anything better than a fresh homemade tortilla with butter? My mother had a hard time keeping up with us as we passed by the kitchen to pick off a freshly made tortilla.

On our trips to Magdalena de Kino, we would bring back a variety of firecrackers. A palomita, a triangular-shaped firecracker, four inches on each side, placed inside a mailbox would rip out the rivets and open it up for airmail. We found Josefina’s (my sister) baby buggy in the open lot (or maybe one of us placed it there). This reminded us of covered wagons going across the prairie. We attacked the covered wagon with flaming arrows. Several explosions were heard when the stagecoach caught on fire. This confirmed our suspicions that the wagon train was part of a cavalry resupply unit. No dolls were harmed in this egregious incursion into our sacred empty lot.

Growing up in Poverty

Growing up, we lived in a house that my father had built. My father, a mechanic, also had a garage built adjacent to our home. When I was about seven, our family went through financial hardships. My father’s garage was sold to a good friend, Cristóbal Redondo. In order to save our home, most of our home was rented out to a family. We kept two rooms of the house, plus a small trailer that had one bed, where my father had always slept. We had no running water in the two rooms, no heating, and no cooling. We used the bathroom and shower in the garage next door. One room served as a bedroom and the other room as the kitchen and dining room. There were six of us, my parents, my three siblings, and myself. Next to our two rooms was a concrete floor, perhaps 10 feet by 12 feet and over it were grape vines. This concrete floor was separated from the adjacent street by a three-foot-tall wire fence. When the weather permitted, we slept on cots under the grape vines. The sun was our alarm clock. Despite this poverty, my siblings Josefina and Manuel were sent to piano lessons every week. I never learned to play a musical instrument and Gilberto was fortunate that a children’s mariachi group was started in his school and he learned to play the string instruments of a mariachi group.

When I was in seventh and eighth grades, home dance parties were very popular. For me, at that age, there was nothing more wonderful than holding a girl in my arms and swaying to the music. At home parties, there were no teachers around to monitor the rule of maintaining a distance between dancing partners. Since kindergarten, there was always a girl I was attracted to and these parties gave me an opportunity to dance with that girl.

I mention these dance parties as an indication of my ignorance about our poverty. How could I have asked my friends to come to our home? I couldn’t invite them in. There was no room. My guests had to sit in this small outdoor floor, which also acted as our bedroom in summer. Worse, what if someone had to go to the bathroom? They would have to go to the garage next door. Apparently, I was blind to the poverty that I lived in. My life was so rich with music, with freedom and wonderful Mexican food.

After selling the garage, my father rented a gasoline station from my maternal uncle, Augustín Islas. I started to work there when I was eight, pumping gas and fixing flat tires. My father died when I was nine. My brother Manuel, who was thirteen, took over the management of the gasoline station and was responsible for its day-to-day management. He hired one of our maternal uncles, Francisco Islas, to work at the station during the day, and after school, Manuel would take over and close the station at 9 pm. Manuel would buy old cars, hire a mechanic to fix them and then sell them. He was always looking into how to bring in a bit more money.

When I was a bit older, I began taking over the late afternoon shift and would work until 9 pm. During the summers, I would walk the half mile to the gasoline station to open it at 7 am and I would work until 9 pm. My pockets served as the cash register, right-hand pocket for coins, left-hand pocket for bills to make change. There were no credit cards then. Gasoline sold for 17 cents per gallon. Teenagers would show up with their 22 cents to buy gas for the evening. The business was slow. Fortunately for me, I was a voracious reader and passed the time reading books. In the seventh or eighth grade, I submitted over 120 book reports.

My mother was serious about education. I have no idea how she managed it financially. All of my brothers and I attended Catholic schools, first All Saints Catholic School until eighth grade, then Salpointe Catholic High School. She worked three jobs. One of those was selling Stanley Home Products. She would arrange a demonstration party at someone’s home, display goods, and take orders. Stanley Home Products would send my mother large quantities of three-cigarette packages to hand out at these demonstrations. Cavalier cigarettes were the brand. All of the neighborhood kids smoked Cavalier cigarettes.

On Mexican American Culture

I grew up in a very diverse environment. We lived at the corner of 34th Street and 7th Avenue. On 34th Street, between 6th Avenue and 8th Avenue, there were at least three Anglo ³ families, one Yaqui family and another Tohono O’Odham,⁴ but the majority were Mexican American. At All Saints School, at least a third of the students in my class were Mexican American and there was one African American student. In grade school, all of my teachers, except for one, were nuns. Perhaps it was this Catholic environment that made overt racism a rarity. However, high school was different. There were still many Mexican Americans there, but I felt that the school was trying to make me into a “white boy.” I reacted against this by more fiercely embracing Mexican culture and adding my mother’s maiden name, Yslas, to my name.

Growing up we understood that we were second-class citizens. The movies portrayed Mexicans as bandits. The movie about the Alamo had a profound impact on me. The white North Americans were the heroes, and the Mexicans were the bad guys. However,all of my family were Mexicans, and I could not internalize that message. I rebelled against this view of ourselves, and I reacted with a racist attitude towards white dominant North American culture and people. They didn’t want me and I didn’t want them. I was an angry young man, and my mother worried about the crowd that I was hanging around with. “Dime con quien andas y te digo quien eres.” ⁵

Not only were Mexican Americans looked down upon, but even within our culture, there was discrimination. We were darker and more Indian-looking than many of our cousins.⁶ My paternal grandmother was fair-skinned and had blue eyes as do several of my cousins. Women at that time were told to wear sun hats so that they would not become darker. Added to this, we were poor and had no father. My mother worked three jobs to maintain a home while all of my aunts were stay-at-home moms, as was the norm then. She was often criticized for not being home.

Many minority youth experience alienation from the dominant culture and, like me, react by not wanting to participate in a culture that demeans them and does not value their background. I never had a Mexican American teacher through high school. In my undergraduate and graduate studies, I remember only one Mexican American teacher, and that in a humanities class. What did that say about the relevance of education for my community? Over the decades, we have lost so many talented minority students because they could not see themselves on a path leading to college. These students saw too many exit signs along that path, and for many, their high school experience simply obliterated the roads that led to further education.

How did my mother do it? She provided my brothers and me with the best possible education available in Tucson. The financial hardships were significant in sending us to Catholic schools, but what is even more challenging was that somehow she guided us into this educational pathway. We all knew that she worked hard outside the house, but we also knew that she would stay up late into the night washing our clothes and ironing our Levi's jeans. As I grew up and began to loosen the anger that I felt towards Anglo society, I also gained respect for my mother, my family, and for our culture. This respect began to impact my actions. What would my mother say if she saw me doing this? That thought guided me. I was proud of our family and the respect that they had for education. This pride was an important tool for me that provided the extra impetus to forge ahead in times of difficulties. As I wrote in the dedication to my PhD thesis, “… si me he avanzado, es porque soy Yslas-Vélez. Arriba la familia.” ⁷

Higher Education

I did not display any particular talents in high school. I was never the best student in a class. I thought I was very well prepared for college though I had not the slightest idea what career to follow. I have written about my four-year career in college and I only want to mention how our wedding occurred.

We planned to marry in May 1968, just after graduation. By February 1968 plans were well on the way for this wonderful event, but then the U.S. Navy intervened. I was ordered to report to Long Beach, CA on March 27, 1968 to be processed for sea duty. By April, I was on board the USS Yorktown in the Tonkin Gulf. Fortunately, I had enough units to graduate, but all wedding plans were cancelled, invitations thrown away. In June 1968, President Nixon had a troop withdrawal of 5,000 troops and the Yorktown was ordered back to homeport. I called Bernice by short-wave radio as we sailed back to Long Beach. She had three weeks to plan a wedding. Family and friends jumped in to prepare the traditional wedding food: birria (a prepared beef), beans, rice and tortillas, enough to feed over 400 guests. I arrived in Tucson the night before the wedding, we were married and that night we began our return to Long Beach, but I was soon out to sea again.

In mentioning the following set of events to a mathematician, he remarked that I should have been the poster child for failure. I started graduate school in 1970, having just returned from Vietnam serving on aircraft carriers. It had been two years since I had completed my undergraduate degree. I earned many Cs in advanced math courses, I was married and our first child, Ana Cristina, was born in the third week of that first semester. I was a teaching assistant, teaching two courses per semester. The salary of $3250 per year was not enough to live on, but I also had the GI bill, which provided educational assistance for veterans and service members. I was fortunate that my brother-in-law, Francisco Redondo, would have side jobs on some weekends, and I would work as a laborer for his masonry crew.

Not only did I not fail, I thrived. The five years in graduate school were among the happiest in my life. I was learning a great deal of mathematics, I was married, I had two children to come home to, (Andrés Antonio was born on March 25, 1974), and I owned a house. When I returned from Vietnam, I returned with a little bit of money (you don’t spend much out at sea). Bernice, who had taken over our finances, suggested that instead of paying $75 per month in rent, we should look for a house to buy, which we did, and the payments were $135 per month. It was a fix-up special. The week after we bought it, my two brothers and I put up a new roof. I also used my masonry skills and built brick walls to line our flower gardens and I also learned how to do basic carpentry.

In March 1975, I had completed my thesis and as a gift to myself I bought a skill saw and a sander. I built a living room set out of pine lumber: sofa, love seat, and end tables. This set was indestructible, and I called it my first approximation to a couch. Later I found springs from an old couch and created the second approximation. After 15 years or so, Bernice got tired of it and I came home one afternoon to find out that she had sold the set for $200.

Overcoming Naysayers

I have often heard that being married in graduate school and having children makes graduate school much harder. I found it to be the opposite. On the day that our daughter was born, I did not turn in a good homework set for my algebra class. The next class day the instructor walked into the classroom and handed back the homework. When he came to mine, he wadded it up in a ball, threw it at me across the room and yelled, “You will never be a mathematician.” Such an incident can be devastating to a person, but I went home that night and held a baby in my arms. I felt that my family was a place of refuge. Later, that same professor looked at one of my solutions and asked me to take his course in algebraic number theory the following semester and to think of working with him. He became my thesis advisor.

I took his course in number theory and I did agree to work with him. I became a number theorist, yet I only took a one-semester course in number theory; I did take supporting courses in group theory and function fields though. Henry Mann, my thesis advisor, took a real interest in me. I would talk to him regularly and in the course of our conversations, I would discuss my family situation. I was born in Tucson, half of Tucson was related to me. Every weekend there was a baptism, birthday party, a quinceañera,⁸ or a wedding; and every other Thursday a funeral. I was also the family plumber. Besides my family commitments, I taught two classes per semester for the five years that I was a teaching assistant. I was pressed for time.

Henry Mann had us over for dinner one evening in my second year. As we drove home that night, Bernice mentioned that Mrs. Mann had taken her aside for a talk. She told Bernice that if she wanted me to be good, she had to learn to leave me alone. Bernice was quiet for a bit and then her quiet, confident voice came out of the darkness, “You will never be good.” Mathematical research is important and it is fun. But so is having a family that loves you. I recall that I read a biography of a mathematician, perhaps it was Hilbert. The biography mentioned that when Hilbert heard that a graduate student had married, he would have nothing more to do with him. I think that was a common attitude back then that mathematics should take over your mind and your body. I bought into it and worked so hard.

Graduate Research

Looking back at my research career I made a mistake. I never had a research program. I just loved working on problems. One of my best research tools was the question, “What are you working on?” I wrote several papers based on that question. Of course, I failed more often than I succeeded. I found out that I was not clever enough for this research style. That does not mean I was a failure. I earned a PhD in number theory and in the process participated in the mathematical adventures of a community, sometimes forging a trail myself, but mostly enjoying the scenic views provided by the rest of the community.

My advisor suggested that I work in the additive theory of groups and number theory. I studied his book on addition theorems and concluded that you had to work a great deal to make little advances. It did not appeal to me. Don Lawver, one of our faculty members, came to Mann and asked him if he knew the answer to a very simple question. Here is the set up. Let F be a field of finite dimension over the field of rationals, f(x) an irreducible polynomial over F, and K = F(θ), where θ is a root of f(x). Let O_F and O_K be the rings of integers in the two fields and P a prime ideal in O_F. A classical result in algebraic number theory shows that the prime ideal factorization P in O_K is obtained from factoring f(x) modulo P, except for those P that divide the discriminant of f(x). Lawver’s question was how does P factor when f(x) = x ^p – a, where p is an odd prime and P is a divisor of p in O_F. In this case, P divides the discriminant of f(x) so the classical theorem does not apply. The case for p = 2 was well-known. Mann suggested that I investigate the question of how prime ideals factor in extensions of F when a root of the irreducible polynomial xⁿ – a is adjoined to F. This turned into my thesis problem.

While working on my thesis, I bumped into the irreducible binomial, x⁶ + 3. When a root of this binomial is adjoined to Q, the field of rationals, it yields a normal extension with Galois group S₃, the symmetric group. I mentioned this to Mann and this gave rise to a joint paper where we characterized all such normal binomials and their Galois groups. It turns out that Olga Taussky-Todd, a classmate of Mann in Vienna, had obtained this result many years before.

Mann said that I had to learn p-adic methods. Modern mathematics is written in this language. He did not use this language because his thesis advisor, Furtwangler, had a fight with Hensel, who developed p-adic methods. Mann, being Furtwangler’s student, would not use p-adic methods. Later on Mann suggested that I look at his own doctoral thesis. In order to solve my thesis problem, I had to completely understand the results of his thesis. With a German dictionary at my side, I plowed through his thesis. He had left one case unsolved, and this case was critical for my work. Using p-adic completions, I resolved this last case, thus completing his thesis, and was able to move forward with my problem. I still remember the conversation that we had on this. I mentioned how I solved the problem by showing that a particular root of unity existed in the p-adic completion. He completely understood. The year after that, he included p-adic methods in his algebra course.

Professional Career

In the summer of 1974, I was offered internships at Jet Propulsion Labs, Sandia Labs and Bell Labs. I selected Bell Labs in Murray Hill, NJ because Bernice and I had never been east of Tucson. Family and friends were concerned about this decision. If the children got sick, “were there doctors in New Jersey?” Others thought that Bernice should stay in Tucson with the children. “Was there food we could eat there?” “Where would we buy tortillas?” The question of our separation was never considered between us. It was an adventure. We bought an old tent-trailer and set off for a 3000-mile camping trip from Tucson to New Jersey with our three-year old, Ana, and six-week-old baby, Andrés. Storms caught us in Kansas. Having to get up in the middle of the night, turn on the camp stove to heat up Andrés’s bottle was a nightly chore. When we returned home, we mentioned these incidents of hardship at a family gathering. One of the nanas of the family recounted her trip from Arizona to Sonora, Mexico when she was a 17-year old, traveling in a horse-drawn wagon with her sick child. That stopped our complaining. We had a wonderful time that summer as a family. Bell Labs was an amazing experience and I wrote a paper on a number-theoretic conjecture of Ron Graham.

When I completed my PhD, I did not want to be a professor. In fact, I did not apply for any jobs. Sandia Labs in Albuquerque, New Mexico, called me and asked if I would be interested in a position there. I visited and they hired me. I worked on the Command and Control of Atomic Weapons for two years. It was very interesting. In Albuquerque, the Society for the Advancement of Chicanos and Native Americans in Science (SACNAS) was just getting off the ground, and I joined many Chicano and Native American scientists in helping to form this organization. I later served as its president.

Many of us learn to deal with racism that occurs in our lives. We just push on. Institutionalized racism is much more difficult to deal with and academia is replete with it. It can be difficult to uncover this kind of racism, but it is there. In the late 1980s, I applied to work at the National Security Agency (NSA). In an exit interview, I was told that if I worked at NSA I could not have contact with foreign nationals. I replied that I worked at a university and this was impossible to comply with. The interviewer asked, “besides the university?” I am a Chicano, living 60 miles from the Mexican border, with relatives still living there. How could I avoid such contact? In the end, I said that I could not comply with this rule and I was turned down. I was a Vietnam veteran, had held a security clearance while I worked at Sandia Laboratories, yet this was not enough. It is perfectly fine for Chicanos to give their lives for this country, but it is not fine to devote our lives to work for this country.^9,10

After two years at Sandia, I found that I missed the teaching. I called Larry Grove, one of my professors at the University of Arizona (UA) to ask if there was a position available there. The department head called and asked me to give a lecture. I was hired and began as an assistant professor there in 1977. For the next ten years, I was lost in thought. There was a strong group in algebra and number theory. Dan Madden, who had been hired the year before me, had common mathematical interests and we investigated number-theoretic questions together. I worked so hard, though work is not a good description. It is not work when you love what you are doing. I didn’t worry about tenure because I knew I would get it. However, like so many minority scientists, I felt out of place in the department, especially in the beginning.

Mathematically, I could not have asked for a better environment. But I found the social interactions with faculty draining. I have often said that just because we are serious it does not mean we should be somber. Where was the joy that we should feel in having the opportunity of being mathematicians and professors? People were very brusque with each other, and the etiquette of polite Mexican society was totally absent. At the beginning, Bernice and I hosted lots of social gatherings at our home. On one evening we had three mathematicians at dinner. Bernice would ask a question and they would answer me. They couldn’t talk to women. Such socializations were too much for both of us and we withdrew. Having one mathematician in the house was enough for Bernice.

The lack of socialization skills of mathematicians is legendary. If the mathematician looks at his own shoes when talking, he is in an introvert. When he looks at your shoes he is an extrovert. Is it their vision of how mathematicians should behave? Is this behavior genetic or learned? Do mathematicians feign such behavior to impress upon their students how deep in thought they are and how brilliant they are? I personally think this is a charade for most. Why can’t our model for a brilliant mathematician be someone like Irving Kaplansky?¹¹ When I spoke with him he would bubble over with enthusiasm.

On Being the First and Supporting Students

I was the first Chicano hired in a tenure-track position in the mathematics department at the University of Arizona (UA). Somehow this made me an expert on minority issues. I was trained to be a mathematical researcher yet expected to function as a sociologist. This is the common plight of minorities in our profession. When you are the only minority, the community views you differently. Perhaps you are viewed as being representative of your culture, like a zoo exhibit, or you are viewed as an expert witness for your culture and asked a puzzling number of questions. How do minorities prepare themselves for these encounters? This places an extra burden on us that the majority population does not have. It took me years to find my minority voice, and in this, SACNAS was a tremendous asset. It is a sign of the times that minority scientists have to come together to support each other. That is why organizations like SACNAS, National Association of Mathematicians, Association for Women in Mathematics came into existence. Shouldn’t the mathematical community ask itself why women and minorities have to expend so much energy in creating these organizations to protect themselves from the majority?

In the 1980s, I became faculty advisor to the student chapter of the Society of Hispanic Professional Engineers. I attended most of their weekly meetings and their annual conferences. I began to learn how to advise students. This was the beginning of the end of my research career. I began more serious efforts at increasing minority participation in mathematics and after a few years it consumed me. I was not happy giving up my research career, but I was not bright enough to carry out this work with students and work on research.

I was very fortunate to come into contact with Phil Kutzko and the Math Alliance. I served on the board of the Math Alliance for many years. When I was president of SACNAS, I tried to institute a program in SACNAS to help minority students apply to graduate school. We tried it for a few years, but SACNAS was too big. The Math Alliance allowed me to propose this program again and the Facilitated Graduate Application Process program is now an important component of the Math Alliance.

Passion for life has always been part of my being. I passionately studied mathematics in college and taught with passion when I became a faculty member. When I decided that the mathematics major was the best major for students I passionately promoted the mathematics major, first among minority students. Then when given the opportunity to direct the Math Center in the mathematics department, I directed this energy towards all students.

I am truly fortunate to have had a career in mathematics. I enjoyed all of it. I loved the research, the joy of teaching, and the challenges to convince students to take more mathematics. I lived an idyllic life, one that I shared with a beautiful person, Bernice.

¹ Boleros are a genre of slow-tempo Latin music. Corridos are narrative songs and poetry that form ballads. Cumbia is a musical genre that originated among Afro-Colombian populations and later was popularized throughout Latin America and the U.S.

² My inheritance to you will be a good education

³ One of the ways Mexican Americans referred to white Americans at the time.

⁴ Both Yaqui and Tohono O’Odham are Native American people of the Sonoran Desert, residing primarily in the U.S. state of Arizona and the Mexican state of Sonora.

⁵ Show me who you are with and I will tell you who you are.

⁶ My recent Ancestry results indicate that I am 25% Native American.

⁷ “If I have succeeded, it is because I am Yslas-Vélez. Long live family.”

⁸ a fifteenth birthday coming-out-into-society party

⁹ NSA Policy on Contact with Foreign Nationals, Letters to the Editor, Notices of the American Math. Soc., Vol. 42 (2), February 1995, pg. 219.

¹⁰ Names on a Wall—A Perspective on Why Diversity Matters, American Scientist, Vol. 85(2), March-April 1997, p. 200. 13.

¹¹ Irving Kaplansky (1917–2006) was a Canadian American mathematician, college professor, author, and musician.