Testimonios: Dr. Victor H. Moll

Dr. Victor H. Moll; Illustration created by Ana Valle.

The Early Years

I am not sure when, but part of my family came to the south of Chile from Germany as a nineteenth- century immigration policy by the Chilean government. [1] What I do know is that in the 1950s it was an established tradition in medical schools in Chile that upon graduation, doctors would serve in small towns before applying for jobs in Santiago and other large cities. My father, Victor Hugo Moll Strassburger, graduated in 1955, married Ema Lucy Becker Correa, his girlfriend since his first year of medical school, and took his first job in Cabildo, a small mining town north of the capital. In Chile you start medical school right after high school, so they dated for a long time. He was the only doctor serving several small villages.

My parents, 1954.

I am the oldest of three. My sister Ana Maria, my brother Ricardo Antonio and I were all born in Santiago, since the capital had hospitals with better facilities. My parents’ families all lived in Santiago, so we often visited them. The few memories I have from that time always involve relatives coming to spend time with us, with my grandmother Clara Moll Strassburger directing the group. Those visits by relatives always involved lots of cooking and among my favorite sweets were calzones rotos, [2] which is a deep fried cookie full of powdered sugar. After my father’s untimely death in 1963, my mother and the three of us stayed in Cabildo for one more year.

My fourth-grade class, Cabildo 1964.

So I spent my early years in Cabildo, starting my formal education in Escuela de Hombres, Número 5. This was a typical elementary school in a small town, probably with students of different ages in the same room. My teachers were Angelina Guzmán and Maria Eugenia Palacios. The photo above shows my fourth-grade class, I am the fifth from right to left in the middle row. Through social media, I have been able to reconnect with some of my classmates and with my teacher Ms. Palacios who sent the picture.

After my father’s early passing, we moved to Quilpué, a town near Valparaiso. The privilege of being the family of the town doctor had ended. My mother, then 33 and a widow with three young kids (I was seven and the oldest), had to learn how to survive. She remarried Sergio Labarca very soon after that. She used to tell me, that without a doubt, this was one of the best decisions of her life. My siblings and I gained a new father, in the complete meaning of the word. It was his opinion that education was the most important gift parents can give to their children. He found one of the best schools in the region (and one of the most expensive ones). Most of the small income our family was receiving, with both parents working, went to pay for education. Therefore, I started fifth grade at The MacKay School. My sister and my brother went to similar types of schools. This was a British school founded in 1857 to serve the community of immigrants coming from England as part of the business activities around the port. Before the opening of the Panama Canal, Valparaiso was a major port for ships going from Europe to the West Coast of the United States. It was here that my teacher, Maria Eugenia Pardo, noticed that I had some talent for mathematics. I still remember that she was very happy when I was able to show that any angle inscribed in a semi-circle was a right angle. This was seventh grade, a period in which mathematical education in Chile was being guided by abstraction and axiomatic mathematics was taught even at this level. For me, there were some inherent life complications being from a working class family and being a student at a fancy private school. The economic standing, naturally associated from being the son of a doctor, had ended. Somehow mathematics became my refuge.

I finished my secondary education at the public Liceo Coeducacional de Quilpué. It was a very stimulating time: the country was going through very interesting social changes in the early years of the 1970s and being in high school at that time offered many experiences that built character. Many of my classmates left the country after the coup d’état and are scattered all over the world. We still get together via electronic gatherings, which sometimes have to be early in the morning in order to accommodate those with very different time zones. Some years ago I had an interesting experience when I was invited to give a talk about my academic path by the office of the mayor of Quilpué. The chance to give a presentation to high school students about my academic life made me uncomfortable. The school had decreased in quality and was beginning a slow recovery period. For many years, the Chilean public had been convinced by authorities that private schools are always better than public ones. This had the consequence of depriving public schools of funds needed to function, leading to a deterioration of what was a very good school at the time that I attended. The beginning of recovery began when the mayor’s office decided to aim towards students interested in arts. During the time of my invited lecture, I met with many students, and tried to convince them that it is possible to be interested in science and not fit the stereotypes (they assume that if you liked mathematics, you had to be a nerd). I was lucky that two of my best high school friends, Kenna Meneses and Juan Francisco Carrasco, came to my presentation and vouched for my stories. At the end, they seemed to like what I was telling them. Although, I had returned to my high school with mixed feelings, having the opportunity to talk to the students made it all worth it in the end.

Undergraduate Studies

After graduation and with the knowledge that the best option for a high school student with interest in mathematics was to join an engineering school, I did so. In March of 1973, the beginning of the fall semester, I began my studies at Universidad Técnica Federico Santa Maria, one of the most prestigious engineering schools in Chile. The core part of the curriculum was common to every student, including three mathematics courses. It was there that I realized that my background was not optimal. Many other incoming first- year students had seen calculus in high school. This was all new to me. And then came the coup, September 11th, 1973. Learning integral calculus with a curfew was challenging. All of my undergraduate education was during the new regime.

The geographical isolation of Chile, coupled with a nineteenth century immigration policy that allowed only Europeans mostly from England, Germany, and Yugoslavia to immigrate, created a more homogeneous society than some of our neighboring countries. I am not sure of all the details, but I believe that this is how my ancestors came to the south of Chile. This centralized immigration policy and the lack of travelers from other countries produced a relatively racially homogeneous population. I have no early memories of African, African-American, Asian, or other immigrants being part of our town. To me, the racial distinctions were weaker than the economic ones. More than that, the concept of class was very strong. There are even Chilean terms to describe the distinction between having class versus having money. Growing up, I never felt discriminated because of racial issues.

Liceo Coeducacional de Quilpué in 1971.

Although I took mathematics courses at Santa Maria, I began my career in college on a track to become an electronic engineer. In the university educational system in Chile, you choose a career at the moment you enter college. There is no concept of having a major. When I arrived, studying mathematics had been closed as an option to all incoming students, even though this had been an option in previous years. Fortunately, in my third semester as an undergraduate student at Santa Maria, I managed to transfer to become a mathematics student. There were only two other students in the mathematics program.

Liceo Coeducacional de Quilpué in 2014.

There are many differences between the Chilean and American university systems. From the point of view of this story, the most important one is the fact that in Chile students choose a career at the end of high school. If you want to be a lawyer, you go directly to law school. No time to warm up. If you do not like it or do not do well, you have to retake the entrance exams and apply again. If you are a student with some talent in mathematics, the most natural choice is to go to an engineering school. So I did. For some bureaucratic reason, at the end of my second year, I was allowed to transfer internally. This saved me from applying to university again—my parents would have been supportive, but not happy if I had to start again. The mathematics degree was a five-year program and during the last three years it had only three students. We had mostly mathematics courses, some courses in English (my father’s plan to put me in a British school paid off) and once in a while we registered in some physics courses. Classes were obviously small, sometimes in the instructor’s office. This is where I learned some analysis and to like espresso. There were lots of independent studies courses. Essentially, it meant that the instructor would choose a book and the students would lecture each other. During some semesters we would take classes at the nearby Universidad Católica. This gave us a chance to learn material not offered at Santa Maria.

This was a period of transition in the life of the country. Among the instructors, there was a single PhD in mathematics, which was unique mostly because the university was not in Santiago: the center of everything. He was the renowned Roberto Frucht, an expert in graph theory. At a moment where I was thinking of abandoning mathematics and studying something else, a second PhD came to the department. Luis Salinas C. came back from Germany, rescued me back to the subject that I loved and became my advisor. Many times in my life I have been lucky and having him return to Chile then is among these lucky times. My last three semesters I took all of my courses with him. I owe him more than words can say.

Things have changed in Chile since my days as an undergraduate. Many Chilean mathematicians came back to the country. They have created a wonderful educational structure and Chilean students travel to the best institutions in the world to study and many renowned mathematics departments have faculty from Chile.

Graduate School

Upon completion of my undergraduate studies I was hired as a faculty member of the Departamento de Matemáticas of Universidad Santa Maria. At that time (1978) it was not required to have a PhD to teach in a university. Yet my undergraduate thesis advisor, Prof. Luis Salinas C., was always talking to me about going abroad for a graduate degree. A real opportunity to go abroad developed with the visit to Universidad Santa Maria of Prof. Eugene (Gene) Trubowitz from the Courant Institute of New York University in July 1980. Since I spoke English (having been a student at The MacKay School) it became my role to be in charge of his visit. I still remember walking on the beach, with conversations that usually started as “Victor, suppose A is a normal matrix of size n.’’ To make a long story short, I joined the PhD program at NYU in September 1980 with financial support from my school. Since I was late in the application process and had not been aware of the required forms, I went to the American Embassy in Santiago with a telegram from Gene that essentially said “Come to New York, we will fix the paperwork here.’’ As you can imagine, the first time I showed up at the embassy carrying only this telegram I was denied a visa. The next time, it occurred to me that if I spoke English to the guard my chances might improve. They did. I got a tourist visa and left for New York. The paperwork was fixed after my arrival.

It is hard to describe my early days in New York City. I came from a relatively small town without much foreign influence, where everybody looked like part of the same family. This was the time before the 1985 economic boom in Chile, when the country essentially became a 51st state. I made many mistakes in those early days. Perhaps the worse one dealt with housing. NYU owned a group of buildings nearby and studios were assigned to incoming graduate students. The first time I went to the housing office, they told me about this option and I realized that rent was about 40% of my total income. Immediately I refused the offer, much to the consternation of the person in charge. I did not understand why she kept explaining to me that these studios were my optimal choice. Needless to say, my off-campus living accommodations during the first year of graduate school ended up being inferior. Someone should have grabbed my hand and told me to sign the dotted line. It takes time to learn the American system.

The schedule at Courant was such that classes would meet once a week for two hours. For me this meant that at the beginning of being in New York, before making friends, I had no human contact from Thursday night until Tuesday night. It came as a great surprise when one day after class, in the elevator going down, this person said to me, “We seem to be in two classes together, would you like to have a cup of coffee?’’ He was Fred Schiafando,
who turned out to be a friend for life. Lectures at Courant moved fast, and soon a group of students decided to get together to study. Social life improved from that point on.

Coming from an educational system with lots of classes I was surprised when at registration I noticed that taking four classes meant eight hours of contact. Naively I asked, “What I am supposed to do with the rest of my time?’’ The response was absolutely correct: “Try to catch up.’’ I was lucky to have Prof. Henry McKean as my instructor for complex analysis. His style of lectures and his point of view of mathematics as a whole made a profound impression on me. Being his PhD student has been one of the biggest honors of my academic life. At the beginning of my second year, I met a first-year graduate student: Lisa Fauci, who later became my wife. My life with her has been great since then.

Professional Career

After graduation, I took a postdoctoral position at Temple University in Philadelphia. Recently, cleaning my office, I found a copy of my job application: it was one-and-a-half pages long. It is remarkable how things have changed. During the next two years I spent a lot of time on the trains between Philadelphia and New York. I also attended a class on elliptic functions that Henry McKean gave at Courant. I worked out all the possible details and years later Henry and I coauthored a book. [3] In 1986, Lisa and I applied for jobs together and both took jobs at Tulane University in New Orleans, Louisiana. Our unspoken plan was to be in New Orleans for a short time and then move back to the Northeast. We never left.

New Orleans humor.

First off, New Orleans is a great place to live in. New Orleans is not your typical American city. It is humid. Most of the time things do not work properly. Sometimes, the driver of the street car stops the ride so they can get themselves a cup of coffee and will turn around and will tell you to take your feet off the seats. Music is one of the city’s biggest priorities and soon became always present in our home. My kids, Alexander and Stefan, had a chance to become students at NOCCA (the New Orleans Center for Creative Arts) as jazz musicians. You should come visit, but come first when there are no big parties happening, which does not leave too many open days! One of my favorite events in the city is Jazz Fest, it takes place during two weekends in April-May. It was a fantastic feeling watching my son Stefan play piano on the Blues Stage. Such is life in New Orleans.

Weiss award photo, New Orleans, 2011.

It has been great to be at Tulane University. Among the many positive aspects of working at Tulane, I must say that the existence of a great child-care program, with a dedicated group of teachers that educated our kids while we worked in peace, is one of the best benefits that I have had. In addition, the undergraduate students that I have had a chance to work with have made my job a very enjoyable one. Among the many students, I would like to single out Roopa Nalam, who worked on a research project with me involving integrals of special functions, and Kirk Soodhalter, who wrote a thesis on some interesting aspects of modular forms. Roopa went on to complete an MD-PhD program and now is an Assistant Professor at the Baylor College of Medicine. Kirk completed his PhD in mathematics at Temple University (in numerical linear algebra) and is now an Assistant Professor at Trinity College in Dublin. I am very proud of the two of them. These two students are part of a large group of students who have enriched my academic life. Some years ago I was awarded the Weiss Presidential Award for Graduate Teaching. Since this award is chosen among faculty nominated by students, this had a special meaning to me.


MSRI-UP research group, Berkeley 2014.

Working with students and young faculty. Over the years I have also had opportunities to work with undergraduates outside of Tulane. One day, I was asked by my friend and colleague Prof. Ricardo Cortez if I wanted to go to a conference of the Society for the Advancement of Chicanos/Hispanics and Native Americans in Science (SACNAS) in Portland, Oregon. I had to admit that I had never been aware of this organization. For me, one of the highlights of the conference was to meet Prof. Ivelisse Rubio and Prof. Herbert Medina. After I gave my talk, they told me about the Summer Institute in Mathematics for Undergraduates (SIMU), an undergraduate Research Experience for Undergraduates (REU) program at the University of Puerto Rico at Humacao, and asked me if I was interested in being the senior leader. This meant being in charge of 12 students doing research for about seven weeks. I still remember their voices telling me “This is a lot of work.’’ I accepted. My family and I spent a great time in Puerto Rico. They were at the beach and I was working. Even though the workload was enormous, I still believe that the SIMU model is one of the best for undergraduate programs. The students were exposed to research-level mathematics, which opened new avenues for them intellectually, but also were told how to approach the graduate school application process, how to present a paper at a conference, what is expected of them as members of the community, and many other aspects of being a mathematician. I loved it. Luis Medina, now professor at the University of Puerto Rico at Rio Piedras, was my student at SIMU. After that, I was lucky that he chose to come to Tulane University for graduate school. We still maintain a scientific collaboration. I am very proud of him. The SIMU model was later adapted by the Mathematical Sciences Research Institute (MSRI) at Berkeley, California in their Undergraduate Program (MSRI-UP). Participating there was a wonderful experience again, as I was surrounded by intelligent students and assisted by graduate students and postdocs. Many of the students participating in this program are now faculty members at a variety of schools.

In recent years, I have been involved in wonderful programs whose mission is to engage faculty—who work in schools with a high teaching load—in research. The programs that I have participated include PCMI (at Park City, Utah) as part of a special program in Random Matrices and the second one at ICERM as part of REUF (Research Experiences for Undergraduate Faculty). These are exceptional programs and I would like to encourage the mathematical community to participate in these programs. I am certainly planning to continue doing it.

Math interests. My mathematical work these days started when a former graduate student, George Boros, told me that he could evaluate an integral. I have told this story in detail in “The evaluations of integrals: a personal story,” Notices AMS (2002) 311–317 and “Seized opportunities,” Notices AMS (2010) 476–484. George’s comment transformed my research. In fact, the evaluation of definite integrals will take you into many interesting areas of mathematics, and you should try it.

Research Experience for Undergraduate Faculty (REUF) research group, Rhode Island 2018.

The basic question is this: given a function f, defined on an interval [a,b] (with -∞ ≤ a < b ≤ +∞) one wants to evaluate ∫ab f(x)dx in terms of special values of a class of functions. This is familiar from elementary courses. On the other hand, students are often told that the function f(x) = e–x^2 does not have an elementary primitive, but there are methods to see that

As a freshman, I was told that this exponential function does not have a primitive. I vividly remember my reaction: “Maybe you do not how to integrate it, but I will figure it out.” Needless to say all of my efforts went nowhere.

In one of my luckiest academic moments, my former student George Boros told me that he could evaluate

in terms of some elementary radical and a complicated polynomial Pm(a) in the variable a. He had a mechanism to evaluate the integral of a rational function by doubling the degree of the integrand and, by some symmetry reduction in certain special cases, he was able to cut the degree in half. That gave him a complicated expression for Pm(a).

At the beginning, not being particularly impressed with evaluating integrals (prejudice comes in many forms), the only part that I thought might be interesting was that his procedure vaguely reminded me of Landen transformations for elliptic integrals. I started trying to evaluate this example by other methods and failed. My not knowing about hypergeometric functions ended up being a good thing. One can prove George’s result in an elementary manner using these functions. The work on this integral took us through an almost magical trip visiting many parts of mathematics which appeared to be disconnected. Many roads of this mathematical trip are mysterious. For instance, the integrals above are the (Taylor) coefficients of

expanded as a power series in c. Very strange. George’s proof uses a theorem of Ramanujan and to this day, I do not know how he thought of this. Since George passed away in 2008, the mystery will remain. For a long time I have looked for a different proof, using this double root. It should teach us something new about this problem. So far I have not had luck in this regard. It is needless to say that my original impression of George’s problems was wrong. I am glad that I did not dismiss him right away and decided to pay attention to his methods. My current students continue to surprise me like this. I do my best to listen to them. It is one of the privileges of the business we are in.

[1] In the nineteenth and twentieth centuries, Chile established immigration policies that encouraged European immigration.
[2] This literally translates to “ripped underwear.’’
[3] Henry McKean and Victor Moll, Elliptic Curves: Function Theory, Geometry, Arithmetic, Cambridge University Press, 1999.

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