Testimonios: Dr. Anthony Várilly-Alvarado

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.

Family History

Dr. Anthony Várilly-Alvarado

Brazil has a special place in my heart: I owe my existence to a chance encounter in 1976 between a Costa Rican woman in her late twenties pursuing a master’s degree in education, determined to make a better future for herself, and an Irish math PhD student who was following his advisor on their sabbatical at the Universidade Estadual de Campinas. After marrying in late 1978, my parents moved to Moravia, a suburb of San José, Costa Rica, where my mother had lived all her life until she went to study in Brazil. I grew up in a house built on the same modest plot of land owned by my great-grandfather; my father, Joseph, still lives there today. My mother lost a six-year battle with cancer in 2002.

My maternal grandmother, Abuelita Julia.

Her name was Jesusita, although most friends and family knew her as Susy. Jesusita de los Ángeles Alvarado Blanco, to be more precise. It is an unusual name, even by Latin American standards. My maternal grandmother, Julia Blanco Rojas, had been told she would have difficulty conceiving; she prayed and promised God that if she had a child she would name him Jesús. When my mother was born, Julia pivoted. My grandfather, Augusto Alvarado Montero, the oldest of five children, had many jobs in his life, including stints in his late teens picking bananas for the United Fruit Company on the Atlantic coast. He made good money doing this 1 much of which he sent home to help pay for the education of his siblings. He never got to go to college.

My maternal grandfather, Abuelito Augusto.

I didn’t meet either one of my maternal grandparents. Julia died of ovarian cancer in 1965, when my mom was 15; Augusto followed in 1973, from a stroke. Julia had a second child, my uncle Enrique, but he died young, and so by age 24 my mother’s immediate family was gone. 2 She had already completed a bachelor’s degree in science education at the Universidad de Costa Rica 3 and taught high-school chemistry at the Liceo Vicente Lachner in Cartago. A government scholarship allowed her to go to Brazil and get a master’s degree; she jumped at the opportunity, and began learning Portuguese in preparation for the trip.

A picture of me as a baby being held by my mom, in 1981.

Picking up Portuguese as a Spanish speaker is not too hard. My father Joseph, however, did not speak Spanish in 1976. But he is a quick study, and he loves to learn new languages. His path to Campinas was in some ways even more unlikely than my mother’s. He grew up in Dungloe, a small town in northwestern Ireland, the son of a policeman(and my namesake) and a homemaker, Nan Varilly (née Boyle). He is one of five siblings, all of whom worked hard to move up the socio-economic ladder from rather humble beginnings. By age 12, my father was out of the house, attending a boarding school in Letterkenny on a scholarship. Unable to attend Trinity College in Dublin 4 on account of being Catholic, 5 he studied mathematics at University College Dublin. There, he found a home and was well-supported by mentors like Seán Dineen. At age 21, he left his native Ireland for the United States, where he enrolled as a PhD student in mathematics at the University of Rochester. On Dineen’s advice, he began working with Leopoldo Nachbin, a Brazilian mathematician who had been in turn a student of Laurent Schwartz. When Nachbin asked him if he wanted to go to Brazil in 1976, my father gladly accepted the offer. 6 Shortly after I was born, my parents decided to tear down the old house in Moravia where my mom had lived, and build a new house together. They timed their project just right: following some ill-advised monetary policy by then-president Rodrigo Carazo Odio, Costa Rica experienced a serious bout of inflation; the price of a sack of cement increased seven-fold during construction, forcing my parents to scale back their plans. By the end of the project, they were left with little disposable income. My mom often credited the guayaba and cas trees in the backyard for helping myparents get through the economic crisis, but I never understood exactly how. 7 I remember her being emotional when we had to cut down the cas tree in 1987; I was too young to understand the mixed feelings she felt towards it.

My parents when they met.

My father with my paternal grandparents in 1947.

The struggles my parents experienced as they navigated the difficult economic turmoil of the 1980s were invisible to me. I was a happy kid; I loved to kick a ball around, though I was no good at it, and I collected Bazooka Bubble Gum tattoos. I entered kindergarten at the British School of Costa Rica in 1985, four years after the school began operating, and I graduated from it in 1998, having completed an International Baccalaureate (IB) Diploma. The British School is a small private school; my parents were determined to give my siblings and me the best education they could, and they wanted us to all grow up bilingual. Through most of my childhood and teenage years, my parents spent over half of their income on our education. It was a privilege and a sacrifice that we neither understood nor squandered. My mother had a few maxims she drilled into all of us. The most important one was perhaps Papito, lo que tenga que hacer en esta vida, hágalo bien, 8 but a close second was Papito, cuando yo me muera no hay herencia, sólo su educación.9

A picture of most of the family in our kitchen. It was my mother’s birthday, circa 1986.

Early Education

When I was in ninth grade, on a totally ordinary morning at school, my math teacher, Paul Murray, changed my life. Right before the beginning of first period, he intercepted me on my way to class, catching his breath, and asked me to follow him. He explained that that day was the first round of the Costa Rican Math Olympiad and that the school wanted to send five students from tenth grade to it. But one of the designated team members had not shown up. “Wanna go?” Being a goodie-two-shoes, I explained to him that I did not have permission to skip class. He rolled his eyes, pointed to a bus, and said, “Just get on the bus with the rest of the team, will ya? I’ll take care of the rest.”

At eight years old.

I was good at math as a kid. Part of me felt like I had to be since my dad was a math professor at the University of Costa Rica. But I had never thought much of it. That morning, when I got to the first round of the Costa Rican Math Olympiad, something changed. I remember struggling for the first time. There were only 30 questions, for three hours, and they were multiple choice! But I had never seen problems like these. They required you to think in a way that school had never really challenged me. Some questions I could tell I simply didn’t have the background for, but other questions were within my reach if I only spent time toying and struggling with them. It was exhilarating.

Throughout my childhood and adolescence, I was obsessed with astronomy. My contact with the subject came mostly from books at the University of Costa Rica’s library and the odd purchase of Astronomy magazine, of which only a few copies could be found throughout the country, at ridiculous prices; I never owned a telescope. There was no visible professional community around the subject in Costa Rica, and this reality slowly eroded my dream of becoming an astronomer. I began drifting towards subjects more grounded in reality, like civil engineering, even though my heart was not in them. Math Olympiads, together with a role model and coach in my dad, rekindled my love of abstract subjects, of the pursuit of knowledge as its own end. I have been lucky and privileged in this regard, having been raised by supportive parents who nurtured and respected my hopes for the future.

International students in the United States often pay full tuition in college. Under ordinary circumstances, my parents did not make enough money to pay these kinds of sums, but by 1998, circumstances were not ordinary. My mother was being treated at M.D. Anderson Cancer Center, without U.S. health insurance. She would fly to Houston once a month for treatment. The hospital gave her many financial breaks, and the British School gave my brother and me a significant scholarship so we could keep attending school and finish out the IB program, but the financial strain on the family was immense. I had originally set my sights on studying abroad in England. But the fees for overseas students were simply out of my family’s means. So I started looking into American universities, armed with AltaVista, the leading search engine of the day. It soon became clear that some universities awarded need-based financial aid, even to international students. All of them, however, were very difficult to get into: Harvard, Princeton, Yale, MIT, etc.

I’ll never know exactly what the admissions officers at Harvard saw in my application. I filled it out by hand, wrote my college essay in 45 minutes, and in the page dedicated to summer activities (usually packed by most students with summer camps, internships at companies and research labs, sports and musical pursuits), I wrote “Not Applicable” and left the rest of the page blank. To be sure, I was a good student, very academically inclined, but so are many other thousands of applicants. I had written a small paper on triangle geometry for the extended essay component of the International Baccalaureate, which I attached to my application. Perhaps it helped? I thought I bombed the in-person interview, though I later came to realize that my interviewer, Renata Villers, a Harvard alum, must have gone to bat for me in a serious way.

Higher Education

Freshman year at Harvard.

Junior year at Harvard.

College years. I arrived in the United States on September 9, 1999, aged 19 and eager to study mathematics. My first semester at Harvard was rough. I felt like I was drinking out of a fire hydrant the whole time. I took Math 25: Honors Calculus and linear algebra, which wasn’t the hardest class offered to freshmen (that was Math 55), and for the first time in my life I really struggled with math, but not in the “fun struggle” kind of way. I began doubting if math was for me after all. The professor, Kalle Karu, was phenomenal, so I figured I was the problem. I confessed my anxiety to my parents, who encouraged me to keep at it, to give my dream of studying math a chance until the end of the year. At the beginning of my sophomore year, my doubts hadn’t gone away, so I began the year by taking some applied math courses, as well as physical chemistry. I loved those courses, but in the end, they made me realize how much I missed proof-based mathematics. By the fourth semester of college I was back as a math major, and I took abstract algebra from Barry Mazur and topology from Curt McMullen. Both were awe-inspiring instructors (and world-class mathematicians, though I didn’t fully grasp this at the time). They rekindled my love for the subject.

Looking back at freshman year, I think the problem was one of time. I worked in the dish room of Annenberg Hall, the freshman dining hall, doing shifts on Monday, Wednesdays, and Thursdays, from 4:30 pm to 8:30 pm. By the time I got home, I was physically exhausted and had a hard time focusing on homework. Like many other international students and students from underrepresented backgrounds, I took on the campus job that paid the highest hourly wage. More savvy students took on library desk jobs, where they essentially got paid to do homework. I changed course my sophomore year when I became eligible to be a course assistant in the math department, though I lamented leaving Annenberg Hall; the staff there worked fantastically hard though their efforts seemed barely noticed by the surrounding students. But if I wanted to be able to rise to the same mathematical level as my peers who didn’t have campus jobs, I realized I needed to take on a job that was more compatible with school work. I was fortunate to find such a job.

Harvard taught me a lot of things; it was a humbling experience, to say the least. Its pressure-cooker environment is not for the faint of heart, but meeting people who are much smarter than you in what you consider your strongest suit is both disorienting and good for you. It made me realize that I liked to do mathematics because I loved the subject, not because I was decent at it. I learned that in the long run hard work will take you much further than innate talent. I also learned that meritocracy is a myth, having graduated in 2003 in the same class as Jared Kushner.

My family in Ireland, taken in 1994.

My mother died on July 8, 2002, the summer between my junior and senior years of college. That fall, my brother Patrick started college at MIT. Through sheer determination and will power, my mother beat the life expectancy cancer sentenced her to by more time than any of us thought possible. At her funeral, several of her co-workers remarked to me that she had lived to see her dream of making sure her children went off to college.

If I could go back and have a do-over, I would approach college much differently. I was hard-headed, and I almost never went to office hours (this was a serious mistake). I loved working with other people, which was great, but when the time came to apply for graduate school, there were very few professors who knew me well enough to write a strong letter of recommendation. I’ve now chaired the PhD admissions committee in the Rice Math Department for six years; so I know that letters of recommendation are probably the most important part of an application. You need letters from professors who know you well, who can speak to your potential for completing a good PhD thesis. It all worked out in the end for me, but this is part of where a bit of luck and the privilege of coming from a top ranked school with good grades have played an important role in my life.

Graduate school. When I started graduate school at UC Berkeley in fall 2004, I had no idea what research was like in math. Research Experiences for Undergraduates (REUs) were not widespread in the early 2000s, and in any case international students were not eligible for National Science Foundation (NSF) stipends. Still, there were hurdles to be overcome before starting on research. For me, the hardest one was the advanced oral exam. I do well on written exams, but I freeze up on oral exams. To this day, when I am asked a question during a talk, I have to pause for a moment, breathe in and out a few times, and force myself to stop thinking that I am not thinking about an answer. My oral exam was rocky, to say the least. I passed it, though only because about an hour in I was certain I had failed, so I calmed down and was able to finally start thinking clearly.

Towards the end of my second year in graduate school, I proved my first research-level result. It was a small proposition, something I needed for a project. I remember the moment distinctly: I proved something that people didn’t know already. It was a modest contribution to the sum total of human knowledge, but it was a contribution, and I was the author! That was the moment I finally believed I can do this! From there on out, I worked really hard on my thesis and a couple of side projects. Not everything panned out, and there were moments of intense frustration, anxiety, and anger at myself. I was extremely fortunate to have a strong group of friends in graduate school, including Dan Erman, Bianca Viray, and David Zureick-Brown; we supported each other through thick and thin. I also met some wonderful people who were a little older than me, at the postdoc stage, mostly at conferences, like Damiano Testa, Ronald van Luijk, and Mauricio Velasco. I learned a lot from them, and we collaborated in projects. There is no need to go at it alone. I learned this lesson serendipitously.

We do not choose our families. But we do have a lot of say on who we let mentor us. Mentors really matter. You need many of them: no one person has all the answers and all the advice that is appropriate at all stages of your life and career. I have had many people I gladly count as mentors. Among them, my thesis advisor, Bjorn Poonen, and my postdoctoral advisor, Brendan Hassett, really stand out. I knew I wanted to work with Bjorn ten minutes after I, as a prospective student, met him. I asked him about his research, and in order to answer me, he asked three questions back, to calibrate the state of my mathematical knowledge, without judgement. Once he knew what level to pitch his answer, I was blown away by what he told me. At the time, I didn’t understand that I was drawn to Bjorn because he is a fantastic communicator. I love the area I work in, but I could have been happy doing many other things. Your relationship with an advisor is lifelong and is particularly intense during graduate school. Making sure the match between people is right is much more important than pursuing some specific subject. When picking a mentor, you should pick the person, not the subject.

One thing that helped keep me sane through graduate school was a stable personal life. Throughout graduate school, I lived with my girlfriend, Sarah, a wonderful, caring, ambitious and supportive human being, who helped me navigate the ups and downs of graduate school. There was a semester early on where we had to live off of my $1,200 month stipend in the Bay Area (rent was $950/month), while Sarah looked for a job. Although at our poorest, I remember those months as some of the happiest of our relationship. We got married in 2010, though as sometimes happens, we grew apart and divorced a few years later. This of course was a difficult time, but I was already a tenured professor, and my work could absorb the personal shock to the system.

Postdoctoral years. When I finished graduate school, I had some good offers for postdocs. One of them was at University of Georgia (UGA), another was at Rice. I happened to be visiting Atlanta while deciding where to go; a conversation with Danny Krashen helped me sort things out. Danny was trying to convince me to come to UGA. All I remember is that at one point he said, “OK, the truth is that there is no better mentor for you than Brendan Hassett [at Rice], but […]” I honestly don’t remember the end of the sentence. That moment crystallized things for me. I knew in my heart of hearts that Danny was right and that Brendan would be a great, if demanding, mentor. I took the job at Rice the next morning, on my way back to California. Years later I told Danny this story, and he gave out a big laugh. He told me something similar had happened to him earlier in life, and he was happy to have (inadvertently) paid it forward.

Some of Brendan’s best advice came early on: “don’t stall, keep moving,” meaning prove the best results you can, but don’t hold off until things are optimal before releasing them to the world, at least not when you are a postdoc. Also, be proactive in your search for new research problems to work on. The other piece of advice was “don’t move away abruptly from what you know, work by analytic continuation,” meaning take advantage of what you know already, and move towards where you want to be slowly, writing papers along the way. I can very easily trace a path between a paper I wrote on Zariski density of rational points on del Pezzo surfaces over number fields and a paper constructing pluri-canonical forms on moduli spaces of special cubic fourfolds (there are four papers in between). It’d be hard to find a conference with talks in these two topics. Related to this, don’t spend six months learning an entire subject from the ground up because you might need it for a paper. Chances are you’ll eventually realize the idea won’t work, you’ll have six fewer months to write papers before you apply for tenure-track jobs, and no new paper to show for your six months of work.

Brendan also taught me a lot about being a professional mathematician, about having long-term goals in mind, and problems of various sizes around those goals. I also learned a lot about taste from him (although this word was never used in our conversations). I learned that just because you have a hammer, and you see some nails in the distance, it may not be worth your time to go hammer those nails unless you have a good reason to do so. Our time is finite, and everyone succumbs to finitude. As you get older, you get more picky about the problems you work on, not because other problems are not interesting, but because each choice of a project closes doors on other choices. I cannot improve on David Foster Wallace on this point, so I will simply quote him wholesale:

Day to day I have to make all sorts of choices about what is good and important and fun, and then I have to live with the forfeiture of all the other options those choices foreclose. And I’m starting to see how as time gains momentum my choices will narrow and their foreclosures multiply exponentially until I arrive at some point on some branch of life’s sumptuous branching complexity at which I am finally locked in and stuck on one path and time speeds me through stages of stasis and atrophy and decay until I go down for the third time, […] it seems unavoidable—if I want to be any kind of grownup, I have to make choices and regret foreclosures and try to live with them.10

My own outlook on life is nowhere near as gloomy as DFW’s. I feel only gratitude for the privilege that I do something that I truly love that I get to share with students and colleagues. I have forfeited many other careers, some much more lucrative than my own. But I have no regrets about my choices. I once asked Ryan Hynd what he would do today if it were his last day on Earth. Without missing a heartbeat, he said, “same thing I had planned on doing this morning. And if that’s not your answer, then what the hell are you doing with your life?”

Tenure-Track and Beyond

In late 2011, I applied for tenure track jobs. There was a job opening at Rice, and even though it was a dream to stay there on a more permanent basis, it is highly unusual in mathematics for an institution to hire one of its postdocs into a tenure-track position. On a late Friday afternoon in mid-November, David Damanik, then the head of the appointments committee, knocked on my door and asked me if I was interested in interviewing for a tenure-track position at Rice. I’m not sure I kept my cool, but I immediately told him I’d love to.

“Good. How about Monday?”

This was a bit shocking and caught me unprepared. I mumbled something about teaching two classes on Monday.

“OK. Tuesday then?”

Realizing I could not delay the future much longer, I took the date. The interview went as well as it could have, though I didn’t hear back about an offer until February. I was not the top choice for the job, and that’s OK. I’ve never felt like I have a chip on my shoulder for that. Every year, hundreds of people apply for each available tenure-track position at a research-intensive university. I was under no illusions that I was somehow the department’s top choice for a position, though I did feel like I could rise to the challenge of the job. The top choice candidate could only take one job; thankfully, they didn’t want the job I dreamed of taking.

With my partner, Carey.

I earned tenure in 2016, and in 2019, ten years after setting foot at Rice as a newly minted PhD to take on a G. C. Evans instructorship, I was promoted from Associate Professor to Full Professor. Never in my wildest dreams did I imagine that that’s what the future held in store for me when I first arrived in Houston.11 Although I have worked tirelessly to get to where I am today, I recognize the luck and the privilege that have smoothed out my journey, and the sacrifices my forebearers made so that I could have opportunities to thrive. With a seat at the table, I now have the chance to help others thrive. I do not intend to waste the chance.

Chalkboard with a glimpse of my research. Photo courtesy of Anthony Várilly-Alvarado.

Today I live in Houston with my partner Carey, a smart, thoughtful, kind, and independent person I am happy to share my life with. We have both suffered loss in our previous marriages, and this perspective, afforded by failure, pushes us to make sure we don’t fall into the same traps of the past, or revisit mistakes. Before the COVID-19 pandemic we used to enjoy the arts and music scene in Houston, and we traveled together extensively. The pandemic brought a lot of our activities to a screeching halt, but we have found new hobbies together.

Research

Most of my work to date is in an area called arithmetic geometry. I study Diophantine equations through a geometric lens. Perhaps the most famous Diophantine problem is Fermat’s Last Theorem, which states that the only solutions to

x n + y n = z n; n ≥ 3

are those for which xyz = 0 (i.e., at least one of x, y, or z must be zero). A decade before Wiles gave his spectacular proof of this result, arithmetic geometers already had good reasons to believe that Fermat’s Last Theorem is true: for each n, the Fermat equation defines an algebraic curve on the projective plane, and the general theory of curves already showed that, for each n ≥ 4, there could be at most finitely many solutions to Fermat’s equation. For a detailed explanation of how this is the case, I invite you to watch my talk at the 2020 Joint Mathematics Meeting titled The Geometric Disposition of Diophantine Equations.12

I’ve spent the better part of the last ten years studying equations that give rise to geometric objects called K3 surfaces. One of the most incredible surprises of my life has been a collaboration with people coming from electrical engineering, government security, and coding theory, to develop a geometric framework behind efficient systems for cloud storage, using K3 surfaces! I never expected that my knowledge reservoir on algebraic surfaces would be helpful in applications. Most projects I’ve worked on had applications internal only to mathematics when I began them, but now I’ve found that people from many kinds of applied fields can use these tools. I am currently working with earth scientists, using algebraic geometry to understand micro-layers of the earth’s mantle from earthquake data! Theoretical mathematics has a lot to contribute to the world, but you have to understand it at a deep level in order to make the connections to the world around us.

With my Dad.

With my sister, Paola, and my dad.

I have the rare privilege of having a father who is also a mathematician. He works on non-commutative differential geometry. Our work within mathematics is quite distant, but we share a common basic language that allows us to explain to each other our recent papers. In 2017, we finally converged in a conference, the Mathematical Congress of the Americas, in Montreal. And in 2020 he came to Denver to watch the lecture linked to above, which was an invited address of the American Mathematical Society at the Joint Math Meetings. I feel incredibly lucky to be able to share this connection with him.

Conclusion and Advice

Some advice is peppered throughout the narrative above. Rather than rehash it all, I’ll offer some further pointers for different stages of an academic career.

Undergraduate years. Less is more: fewer math classes, done excellently. This is a marathon, not a sprint. Early on, take proof-based linear algebra, abstract algebra, real analysis, and if possible a course in point-set topology (not all at the same time, of course!). Go to office hours. Connect meaningfully with your professors. Always ask why. To quote Ravi Vakil: “What is a group?” is not a great question. A better question is “Why is a group?” Whenever you meet a new definition, play with it through examples and ask yourself: why would anyone think it’d be a good idea to formally codify this concept?

Graduate school. The first year will be brutal. Hang in there. When you get over the hurdles of written and oral qualifying exams, your world will be turned inside out: up to this point, the pressure to get things done has been external, framed by structured coursework, homework, exams, etc. Now it’s up to you to generate some internal fire to work on a research project. Think of it like a full-time job. Make sure you put in 40 hours of work per week. Above all, don’t go through it alone: find a group of friends who can act as a support network. Read and criticize each others’ work. When you look for an advisor, choose the person, not the subject.

Postdoctoral years. This is a hard, lonely time, with new mountains of responsibility. A good match with a postdoctoral mentor is key, but keep in mind that they are not your thesis advisor. Work hard, but take personal days regularly. Write all the papers you can, at the sweet spot intersection of interesting, feasible and within (or just beyond) your reach. Lean on your mentor to help choose projects.

Tenure-track years. Keep your eye on the ball. Minimize committee work. Keep writing papers. Enjoy the flow. Otherwise, why are you doing this?

Tenure. Keep moving. Time to give back. You will be busier than ever before, but in a good way. Mathematics requires community. You are now in a position to effect changes in that community, and by doing so, improve it. Do so.

Related to this last bit of advice, and perhaps most counterintuitively: be a bit selfish during your development as a mathematician. We Latinx people have strong family cultures, and often seek out opportunities to give back to a community that has given us so much. You will do so, in due course. First, get a seat at the table. From there you will be able to help more people than you ever dreamed of.

 

1 This is not to say that the working conditions were good; see the chapter A la sombra del banano in Carlos Luis Fallas’s novel Mamita Yunai, originally published in 1940. (Yunai is a transliteration of Uni(-ted), the way in which most Costa Ricans referred to the United Fruit Company.)

2 My mother had a stepsister, my aunt Nelly, who was 15 years older. For reasons that were never clear to me, they were not close in the 1970s. Whatever the rift was, time helped heal the wound, so I grew up with an aunt and older cousins whom I’ve always been fond of.

3 My mom was never one to complain much, but I do recall a certain amount of bitterness when she talked about her college years: textbooks were both difficult to find, and often unaffordable, so she had to work off of her lecture notes as the sole course materials. The situation today has partially improved—textbooks are not as hard to find.

4 Trinity College alumni include George Berkeley, Edmund Burke, Samuel Beckett, William Hamilton, Erwin Schrödinger, Jonathan Swift, Oscar Wilde, and many others.

5 The restriction was counterintuitive: only after 1970 did the Catholic Church stop forbidding believers from attending Trinity College without special dispensation.

6 Keen readers will note that the Mathematical Genealogy Project lists Gérard Emch as my father’s PhD advisor. This is correct; things didn’t work out in the end with Nachbin, and my father switched advisors halfway through graduate school.

7 After showing my father a first draft of this testimonio, he explained: each night for some time, he and my mother would collect the windfall cases and guayabas and sell them to the local grocer. This would pay for the next day’s bus fares to their workplaces.

8 “Whatever you have to do in this life, do it well.” My father would usually abbreviate it this to “whatever you do, do it well,” although his favorite version, following Robert Heinlein, is “anything worth doing is worth overdoing.”

9 “When I die, there is no inheritance, only your education.”

10 This little reflection is embedded in A supposedly fun thing I will never do again.

11 As it happens, Houston already had a special place in my heart, even though I had never been to it: attentive readers will recall that my mother was treated at M.D. Anderson Cancer Center (without U.S. health insurance!) for the last few years of her life.

12 A link to the talk is provided here: youtube.com/watch?v=GnE2lFJ1x-Y.