On a math buffalo

For me, doing mathematics is like hunting. Mathematicians are predators and math problems are our prey, and to solve math problems is akin to hunting them down. Hard questions are our math elephants, while others are like fast rabbits that are hard to catch. A very talented mathematician is comparable to either a lion or a tiger, although every generation has at least a few Tyrannosaurus Rexes. They are the badass mathemagicians ruling this land. Still, most of us are wolves or foxes. We may hunt a sheep or a rabbit by ourselves, but sometimes we team up to pursue a buffalo or other bigger prey.  In math land, we must hunt or perish. 

Hunting is not effortless; a math buffalo does not go down smoothly, and they should not be approached lightly. They fight back, bite, kick, and run away. Even more worrisome, math problems play dead. They appear to be solved when in reality, they are not. Whenever a mathematician wants to claim a prey, other ones are invited to prod the hunt to find out if the solution is correct. To learn hunting techniques as well as teamwork, we spent our cub years practicing problems. We must also help training those taking their first steps in mathematics, so lion cubs can be identified and enrolled in their optimal path. During my graduate school years, the math department was the savanna where I wandered, and I met two baby cubs who forced me to think why and how I approach mathematics.  

On a Wednesday during that time, I received an email saying  “Dear Patricio, I came across the description of yourself on the math department website. You look like an interesting fellow. My very bright son Alex needs tutoring in Algebra. I am interviewing a few graduate students and tutors, so please email me.”

I thought about declining the interview because tutoring students might distract me from math. Money was not a problem as long as the university restaurant kept selling one-dollar burritos after 10 pm. However, the claim of a very bright kid sounded intriguing, so we scheduled a meeting.

I started tutoring Alex because he was undoubtedly much more gifted than me, and I could not turn my back to such talent. Soon enough, Alex’s mother asked me to teach some math to her four-year-old daughter Sara. My role with Sara was a bit confusing for me. She had incredible talents for singing and music, but I wondered, "What is the purpose of my teaching her elementary math instead of any other person?"  After all, everybody knows that 10+2 is 12! 

The lessons with Sara started after her piano classes and ended just before the family chef served dinner, to which I was usually invited. Alex and Sara’s parents, a medical doctor from Cornell and a physicist from MIT, were always so welcoming and amicable. From the legions of fancy tutors in the New York area, I still do not know why they picked me, a particularly scrubby graduate student, to teach their kids.

My home was few hours away from the university and in the middle of Queens, New York. Every so often, I went to visit my family, sleep curled on a sofa, and fight with my younger sister over frijoles, arroz y maduros at lunch. Around the time that I started to teach Sara, my mom’s neighbor Maria asked me for help with her ten-year-old son Anthony. She was anxious about Anthony’s education, but unable to help him because she did not speak much English. She worked cleaning an array of houses and offices in New York, and I do not recall ever seeing Anthony’s father. I started meeting with Anthony whenever I went home.

At dinner time, Maria would ask me, “Quieres lentejas?” 

She cooked while I was teaching Anthony at the kitchen table of their small apartment in Queens. Anthony’s brother slept in a subdivision made to the living room; his room was being sub-let because they needed help paying their own rent. 

Occasionally, Maria whispered, “Estoy preocupada mi hijo no se concentre en la escuela.” She was worried about Anthony having ADHD.

I was quiet for a second before I answered, “I am sure he is just being a kid.” Neither of us knew the symptoms of ADHD. Was it the same as being a particularly energetic child? 

Anthony and I studied everything from mathematics to science fair projects. What we did not study was English. He soon realized that his English was better than mine, and he promptly teased me about it. 

“How can they let you go to school if you speak like that?” he used to ask me. 

I smiled back. Kids can be too honest sometimes.

The days slowly went by. Sometimes, Sara and I had the class on her family’s private beach. My computer broke in the middle of my semester, and Sara’s mother gifted me a new one. “Consider it your Christmas gift,” she told me.  Anthony’s mother gifted me some shirts as well. "They are as good as new, and they will fit you well,” she said. 

By the end of Fall, Sara was struggling to add larger numbers, and Anthony was increasingly frustrated with his school work. I started wondering if I can teach them anything at all. Why did I, or anyone, enjoy mathematics? How did I manage to get so far into this field? 

My early education was a mixed bag, and I never finished middle school due to economic turmoil at home.  My father is an artist, and selling paintings was hard. He mentioned the possibility of enrolling me in a trade school to learn baking.  “It is a good job, and you will never go unemployed because everyone eats bread,” he told me. However, baking was never a good match; cooking has always been hard for me.

“How did I learn to count?” I asked my mother.

“I taught you and your older brother when you were little,” she explained to me. 

The key detail was that when I was three years old, I sat with my older brother Nelson next to the lavoir where my mother hand-washed our clothes. We worked on adding numbers, and every time one of us solved a problem correctly, my mother gave the winner kisses and hugs. 

My brother and I went to study physics and mathematics, respectively. J.L Borges praised "love which lets us see others, As God sees them." I solve math problems because I learned to see them as the divinity sees me through the gaze of my older brother and mother.  If family love was the source of success, then Sara and Anthony were as lucky as me.

I do not recall all the topics that I worked on with Anthony or Sara. Here, I must say that graduate school was hard for me. I spent nights working on math problems while watching friends more clever than me failing at the hunting trials and being forced to leave. I felt like a soldier in a war zone, and the odds were no bueno. During those days, I used to think about my brother Nelson and my friend Julie. We all took a calculus class together, and on the final day of the course, I found out that my grade was an uneventful A-.  Meanwhile, Julie was running around, smiling and happy. “I got a C+,” she told me with bright eyes. Everyone else went to hug her. She failed that class before, and a C+ was required for her to stay in the University. “I will earn a Ph.D. in Physics,” Julie told everyone who wanted to listen while perusing her astronomy books.  She went to earn that degree.  My brother was also in a celebratory mood. Nelson required a 70 out of 100 on his last exam to get a C+, and he got 71.  “Precisely, the grade that I needed, and I do not work more than I have to!” he asserted exuberantly. Everyone was laughing. Nelson has always had a knack for celebrating and he felt like a daredevil.   

Truth be told, Nelson and Julie studied many afternoons and solved an uncountable number of exercises. My brother stayed up many nights while I was sleeping on a sofa next to him. I don't even recall having a notebook for that class. He had pages and pages of solved problems before the exam. 

Many years later, I found myself in graduate school with a grade of 30 out of 100 on a math exam. I had studied many nights, solved all the exercises, and reviewed all the homework.  

“How did you do on the exam?” I asked my office mate.

“I got 95 out 100. The exam wasn’t hard,” he answered.  

Without my knowing, Nelson and Julie had taught me something significant all those years ago. If I was going to become a hunter's apprentice, then I should learn to be beaten by math problems, to stand up, and to charge again. This insight hit me one afternoon when Sara was struggling to add 13+9. I am a hunter, and I must teach her to approach a math problem like a predator approaches a kill—without fear, hesitation, or defeatism. I  had chased a math deer for months only to see it escape. I had felt the satisfaction of capturing a problem after a long pursuit, and I had felt the sadness of the one that got away. I could teach Sara and Anthony the lesson that I draw from Nelson and Julie; to stop being students and to instead become hunters. Hunters respect the prey, but they do not fear it. They are prepared to chase the problem during many moons and to learn from their kill. 

A lot of people do not approach math in this way because they are afraid mathematics will fight back.  They are right. Math kicks and bites. We all feel frustrated with it. The biggest Tyrannosaurus Rex in my field said once “I felt clumsy, even oafish, wandering painfully up an arduous track, like a dumb ox faced with an amorphous mountain of things I had to learn (so I was assured) things I felt incapable of understanding the essentials or following through to the end.” (see [1]) However, we should learn to persevere despite that.  Nelson and Julie showed me that, so I could teach it to Anthony and Sara

After a while, I stopped tutoring Sara, as our schedules conflicted and her parents start debating which foreign language she should learn instead. Anthony began an after-school program and soccer practice during the weekends. I did not take more students and instead focused on my mathematical research. Years later I learned that both Anthony and Sara are pursuing careers in arts and acting.  However, I hope to have had a contribution to their education. I hope that they learned to acknowledge the difficulty of a math problem without being afraid. To deal with frustration. To pursue with perseverance. To be a tiger never afraid of the deer.

REFERENCE

[1] Alexander Grothendieck, Récoltes et semailles: Réflexions et témoignages sur un passé de mathématicien. 2.2 L'importance d'être seul. 1986.