The Recovering Mathematician

The Recovering Mathematician

For the past few years, I've referred to myself as a recovering mathematician. Let me explain.

I fell in love with mathematics about a decade ago while taking a calculus class at my local community college. Yeah, I know. Calculus. Yuck. It wasn't so much the course content that I fell in love with, though, but the way the professor explained it to us.

Nothing was presented to us as fact. Everything was questionable. Everything was a question. The math, it seemed, wasn't that the derivative of $x^n$ is $nx^{n-1}$ but how you get there using the limit definition of a derivative.

I began to pay close attention when the professor wrote the word "proof" on the whiteboard. A story was about to be told.

The Fuzzy Wurlitzer

College and I hadn't always gotten along. After high school, I spent about two months goofing off at The University of Texas at Austin "discovering myself."

I was supposed to study music, you see. I was going to be a jazz pianist. You know, like Thelonius Monk or something. But I liked minor seconds and tritones, and the piano professor at UT-Austin liked major thirds and perfect fourths.

Don't get me wrong; those are some beautiful intervals. But life isn't major and perfect. It's dirty and dissonant. And good jazz is rooted in Real Life™. And also Egyptian sun gods and trips to Saturn.

Well, the good professor disagreed. So I quit and switched my major to "general studies," where you learn nothing about everything. I spent my time skipping class to play music.

For the next couple of years, music was my mistress (may you rest in peace, Duke Ellington). I left UT and, at my mother's behest, took some classes in audio engineering at the Arlyn recording studio.

I graduated as a certified audio engineer of the studio arts and promptly started working as a live sound engineer in various nightclubs back in my hometown of Houston, where pretty much everything I had learned was useless.

I played the Wurlitzer electric piano in a duo with a drummer. He played in weird time signatures, and I forced the electrons from my Wurlitzer's pickups through fuzz and wah-wah pedals. I picked up a regular Thursday night gig with a cover band. We played things like Cannonball Adderley, Pink Floyd, and the Ghostbuster's theme song, all in the same set.

It was wild. It was fun.

Then one day, I got a call from this guy I'd gone to engineering school with. He'd landed an unpaid internship at the hottest studio in Hollywood: Oceanway. Radiohead had recorded Hail to the Thief there a couple of years earlier. Beyoncé and Beck were laying down tracks. And he was in the middle of it, putting all of his audio engineering knowledge to work getting coffee for producers or whatever.

He called me because he had met a band that needed a keyboardist for their latest album. I phoned the drummer, and he played some tracks for me, holding his phone up to the speaker because this was like 2005. It was British pop rock.

They agreed to pay for a plane ticket and put me up in their apartment for a week. I just had to pay for food. I'd never been to Los Angeles and didn't want to pass up the chance to step foot in a studio where Miles Davis and Frank Sinatra had recorded. So I agreed.

Six months later, I joined the band and moved to LA to be a rockstar. We called ourselves the Small Hours. And while we came close to getting close to making it — we played one show at the Viper room — I had more or less lost interest after a year of grinding the LA scene. And I'd fallen head over heels for a girl I met at my day job.

The Girl

I worked shipping and receiving for a company that distributed the finest smoking accessories and hippie decor in Van Nuys. Like cheap acrylic bongs and poorly painted ceramic figurines of mushrooms and dragons.

A few months into the job, I met one of the girls that worked the drill press in the shop. She had gorgeous jet-black hair and a smile that made my knees weak. But she only spoke Spanish. And three years of high school Spanish class had somehow only prepared me to say "Hola, me llamo David" and then stare blankly and awkwardly.

I started studying Spanish. I bought a bilingual dictionary and began memorizing phrases to say each day. I enlisted the help of another woman who worked in the shipping area of the warehouse — and who knew a little bit of English and wanted to learn more — to help me practice Spanish.

Eventually, I worked up the courage to ask my crush on a date. I spent hours the night before memorizing Spanish phrases. The next day after work, I approached her and began to recite: "Hola. Yo quiero saber si usted quiere ir conmigo a ver una... una... peli... Ugh! I can't remember how to say movie!"

Fortunately, I had written everything down and taken it to work in my back pocket. I pulled out the paper and finished reading from my script. To my absolute shock, she agreed.

Three — yes, three — weeks later, we finally went on that date. We saw Ice Age 2.

Nine months later, and after nearly destroying my bilingual dictionary from so much daily use, I asked Raquel to marry me. And for reasons I'll never understand, she said yes.

The Awakening

I had a hobby that bewildered Raquel. I read science books. Like, textbooks. I bought logic puzzle books to work on in my spare time.

One day she had an idea. "Why don't you go back to school and study science?"

"Yeah, I guess so," I thought. "I like physics. Maybe I'll do that."

So, after moving back to Houston with Raquel and getting married in my parent's backyard, I started casually taking classes at the local community college. I planned to knock out some core classes and then transfer to the University of Houston and major in physics. Or maybe chemistry. I didn't know. They're both awesome.

I knew I'd have to get caught up in mathematics, no matter what science I decided to study. So I took a placement test and got placed in a college algebra class. It was fine. I passed without too much trouble. Then I took trigonometry and pre-calculus. I was doing well, but the math just felt like a means to an end.

Then I signed up for calculus, and my life changed. The professor was known around campus for being the most difficult math teacher. So I wasn't sure what to expect. I'd never taken calculus before, and I'd heard it was hard.

It turns out this professor taught calculus with proofs. I'd only seen proofs in my high school geometry class, and I remember them being an exercise in pedantry. But these proofs were different. They felt like stories.

The characters were the definitions of things like limits and derivatives. The stories became theorems, and we referred to them when telling other stories about continuous functions and convergent sequences. It was like we were building up an entire mythology of mathematical ideas from scratch.

I started to write miniature essays on my math tests. I spent as much time practicing taking derivatives as I did crafting written explanations for solutions.

I stopped reading science books and started reading math books. I found a used copy of a book called Mathematics for the Nonmathematician by Morris Kline. It told the story of mathematics in a way that was both engaging and thought-provoking. I'd never thought about math having a rich heritage, and I was intrigued with how integral mathematics was to the human experience.

Pretty soon, I had forgotten about physics and chemistry and knew exactly what I wanted to study: Math.

The First Trial

Around this time, my first daughter was born. Raquel and I started to get serious about establishing her permanently in the United States. See, Raquel didn't have any papers.

Thinking it would be easy for a US citizen to get permanent residency for his wife, we started meeting with immigration attorneys. We were wrong. Raquel had orders for deportation for failure to report to court after entering the US.

Not only would she have to leave the United States voluntarily, but she would also have to remain outside of the US for ten years before she'd be eligible to apply for a spouse visa. Because she was married to a US citizen, she could qualify for a pardon after five years, at which point she could then apply for permanent residency. All of this, of course, as long as the immigration laws didn't change.

We were devastated. But we had to do it.

Raquel moved back to her home country of El Salvador in 2008 with our one-year-old daughter. I took a semester off of school to move with them but eventually returned to the US to continue studying.

For the next five years, I spent about nine months living and studying in the US each year and three months visiting my wife and daughter in El Salvador. Three months a year with my daughter for five years. That's all I got.

The Incubation

After a few years of community college, I transferred to the University of Houston – Downtown (UHD) and entered the mathematics program. I decided to minor in computer science since I had some programming experience from earlier life interests.

My time at UHD was one of relentless focus. The only upside to being involuntarily separated from your family is that you end up with a lot of free time. I dedicated myself to studying mathematics, and I devoured the curriculum with the appetite of an American pygmy shrew.

I took several mentored studies, which put me one-on-one with professors exploring topics in more depth than a traditional course allows. My favorite was a study in linear algebra, and I credit that course for introducing me to "higher-level mathematics."

I'd always viewed linear algebra as the study of matrices. It's an easy mistake to make, given the typical linear algebra curriculum. But a matrix is just a concrete representation of an abstract mathematical idea. The mechanics of matrices, while important for computation, are just a means to an end. And in all reality, they distract from the beauty of linear algebra.

The mentored study used Sheldon Axler's classic textbook Linear Algebra Done Right — which remains one of my favorite mathematics books to this day — and his manifesto Down With Determinants!, as well as Paul Halmos's Finite Dimensional Vector Spaces.

Reading Axler and Halmos I fielt, for the first time, a textbook speak to me as a future mathematician. Those books are deep. They're technical, for sure, but they also spoke to me on a human level. Axler and Halmos are expert teachers. Their expository style is refreshing, and it planted in me a seed that would grow into a love of writing mathematics.

The UHD mathematics department is small, but it had a massive impact on me. I had the opportunity to take a graph theory course taught using the Moore method. Each week we were given a packet with some definitions of key terms and concepts and a list of twenty or so mathematical statements about graphs. Our task was to determine the truth of as many of the statements as we could. The following week, we took turns presenting our ideas to the class.

Finally, I got to experience what math research felt like first-hand. And I was addicted.

After my graph theory class, I'd pretty much made up my mind that I wanted to be a graph theorist. I approached Dr. Ermalinda DeLaViña, one of the graph theorists at UHD, about working with her for my senior thesis. I also started regularly hanging out in Dr. Ryan Pepper's office, the professor who taught my graph theory course.

My last year at UHD was one full of research. I spent countless hours with Dr. DeLaViña working on conjectures generated by her computer program graffiti.pc. Under her tutelage, I learned the value of using computers to aid mathematical research. I also learned how controversial that topic could be. I wrote and published my first paper with Dr. Pepper.

In the Spring of 2013, I graduated from UHD with a Bachelor of Science in Applied Mathematics and set out to complete a Ph.D. at Texas A&M University.

The Second Trial

While I was moving to Bryan, Texas, and preparing to start graduate school, the immigration situation with my wife started moving, too. The five years were up, and Raquel was now eligible to apply for a pardon for the remaining five years of her exile from the US.

At the same time that I was taking graduate-level courses in things like abstract algebra, combinatorics, and differential geometry, I was putting together a statement. I had to prove, with evidence, that I would suffer tangible harm should the government decide to deny Raquel her pardon.

I wrote a comprehensive statement in an effort to give the government zero reasons to deny our family the chance to live together in the US. I think it was around forty pages, including all of the appendices with supporting evidence.

I bound everything together and mailed it to some address in Virginia. Or was it Washington? It doesn't matter. All that matters is that I poured my heart and soul into that statement. And nearly six months later, I received a reply stating that the government had only received a single bank statement from me showing that I sent Raquel some money back in 2008. I had a few weeks to submit the rest of my statement, or we would lose our place in line and potentially the chance for a pardon.

I scrambled to re-assemble and re-submit my statement, absolutely bewildered — although, in hindsight, it's not at all surprising — that the government had managed to lose a forty-page bound document.

Then, the unthinkable happened.

One evening, while visiting my parents in Houston, I got a call from Raquel's cousin. She was in the hospital, and it was serious.

While withdrawing money from an ATM, she was assaulted by someone at knifepoint. They took the $20 or whatever she had and then slit her throat. She was found sometime later by the police.

My entire world caved in.

Suddenly, all that mattered was getting to my wife and getting her and my daughter out of El Salvador.

The Escape

I filed for a leave of absence at Texas A&M. They agreed to hold my spot in the Ph.D. program for one year. Then I moved to El Salvador and started working on an exit plan.

We couldn't come to the US. Even if we did apply for asylum, the process was so backlogged that it wouldn't provide any immediate relief for our family. And we needed to act fast, especially since my wife had recently given birth to our second daughter.

As citizens of El Salvador, Raquel and our daughter could move freely between the five Central American nations. We decided to move the family to Guatemala.

I needed a job. I reached out to a friend from my days as a live sound engineer. He had opened his own event production company, and I was desperate. It would be tough to work for an event production company in Houston while living in Guatemala, though. But he knew someone that needed a programmer.

I traveled to Houston and met with the owner of an audio/visual installation company. The industry was shifting. The systems they installed were controlled by central servers that processed all the audio and video throughout the facility. He needed someone who could program the servers and build user interfaces for customers to interact with the system from a phone or tablet.

I'd done lots of scientific computing in college, both for mathematics research and while working in a computational chemistry lab (read: a closet with a computer) for a research grant I'd been awarded as an undergraduate.

I had no experience with the kind of programming he needed. But I was desperate, and so was he. Plus, I could work remotely from Guatemala, email files to the company, and support the installation crew via video chat.

The Return

We lived in Guatemala for nine months, and our family situation stabilized. I loved getting to spend every day with my wife and daughters. And finally, after a total of seven and a half years of dealing with immigration hurdles, Raquel was issued a pardon.

She applied for permanent residency, and a few months later, we were on our way back to the US.

For almost an entire year, I had done practically no mathematics. There were too many urgent priorities that demanded my attention. But I was anxious to get back to Texas A&M.

There was a problem, though. We were broke. We'd spent all of our money getting the family to safety and paying immigration and legal fees. My parents had helped us cover expenses beyond what we could afford, but even then, we had very little left when we came to the US.

Every Ph.D. student at Texas A&M is supported. Your tuition is paid for, and you're given a monthly stipend for living expenses. And that stipend is enough for a single person living in a tiny apartment or splitting rent with roommates. But my wife and I had to support a family of four.

I had to make a choice.

And I decided that, for the benefit of my children, I needed to leave graduate school and focus on a tech career.

I stand by that decision. But I'd be lying if I told you it didn't leave me feeling hollow.

The Recovery

I've had the privilege of finding moderate success in tech. I never worked at a big tech company, and honestly, I never wanted to. But I found a niche that has afforded me a comfortable lifestyle.

After working for about five years as a programmer, I landed a job at Real Python writing about the Python programming language. The job put me back into the education space, and I've loved it. I get to write and create video courses, and I help other content creators as a technical reviewer.

I even got to write a book, something I'd always wanted to do and something I hope to do again. But the hole that formed in my soul when I left Texas A&M has never been filled.

I don't know if I'll ever go back to graduate school. My oldest daughter is a teenager, and the youngest is halfway between a toddler and a pre-teen. Both are busy with activities: swim team, soccer, gymnastics, violin lessons. Our life is busy, and it's hard enough to find time to write a blog post, let alone finish an advanced degree.

So, I'm still recovering. I might always be recovering.

I might not get the chance to finish my Ph.D., but I've realized that I don't need a doctorate to make an impact in mathematics. All I need is my passion, a drive to continue learning, and a desire to share what I learn with others.

Let's learn some mathematics together. Whaddya say?

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