This post is in response to a prompt for Ada Lovelace Day: writing about a woman in science, technology, engineering or maths whom I admire. I would like to write about Prof. Lillian Lee at Cornell University, whose class Advanced Language Technologies made me believe I could do math again.
As a child, I had this fascination / veneration of mathematics. My dad got his Master’s in math, and he would tutor me by giving me hard problems. Problems I could never be expected to solve. It was difficult, and frustrating, and the fact that we never talked about it contributed both to a worsening relationship with my father and to a feeling that I was hopeless at the subject. I did well at school, sure, but my parents were quick to point out that this was “weak American education,” that “higher maths” was this beautiful thing that was hopelessly outside of my reach. Their words rang true when I went to college and did disastrously in my Linear Algebra / Vector Calculus class. I remember getting like a 50% on the first assignment — my first failing grade in ages! — and asking the Professor for help, and seeing his contempt at my pathetic work. I stuck through the class, just barely, then did not return for the second semester, convinced math was beyond me.
And yet, math was useful and beautiful and I kept coming back to it. I learned that, with math, one could analyze and even predict the behavior of human societies. I learned about complex systems, and how the interaction of simple rules led to the irreducible beauty of natural phenomena from atomic lattices to natural habitats to riots. I wanted to study human behavior at the group scale, to understand a sort of physics of sociology. That’s what I told my mom I would be working on in graduate school (I wasn’t talking so much to my dad at the time). She said that nobody was interested in the subject; that I should study linguistics, as she had; and that at any rate, I did not have the math aptitude to study something like that. Her words hurt.
Still, I gave grad school a try. I only got into one graduate program out of the five I applied to, but it was probably my favorite of the five — a program in Information Science at Cornell University, young and small and full of academics asking precisely the kinds of questions I was interested in: what motivates group behavior? How do societies form and collapse? What are the socio-physical forces acting upon friend groups, communities and whole countries to enact global change? The program also had a rigorous course requirement — seven graduate courses, in sub-fields ranging from technology in its sociocultural context (with Prof. Phoebe Sengers, another woman in science who inspired me!) to advanced natural language technologies with Prof. Lee. I remember fellow grad students speaking of Prof. Lee’s class with fear — the math was too hard, her standards too exacting, the subject matter too abstract. It was with a lot of nervousness, remembering my mother’s words about my math-inadequacy, that I went to the first day of class.
I expected twenty students, and was surprised to see only six or seven, including a couple of my friends. Still, the atmosphere was tense — little eye contact, little conversation before class. I remember Prof. Lee going up to the board and starting the first lecture.
Prof. Lee started class off with a Nabokov quote. Then she talked about language, linguistics, and what computer science tries to do differently from computational linguistics, and how it’s better by being simpler. I kept waiting for my eyes to glaze over, for the math to overwhelm me. Instead, Prof. Lee patiently walked us through tf-idf — one of the core formulae in natural language processing, developed by a woman — Karen Spärck Jones. I followed the explanation. I understood.
Surely this was just the first day, I told myself. Surely, things were going to get far too complicated for us later. I went back for the second class.
Prof. Lee had us break up into study groups and tasked each group with compiling lecture notes *ahead of class*, so they could better understand the material. She warned us when a formula was going to be especially difficult (like topic modeling and Latent Dirichlet Allocation) and she encouraged us to work together if we did not understand a concept or a problem. She was not condescending. She talked fast and thought fast, and sure she was intimidating, but she was kind and patient with all her students — a fact I did not realize for a long time, so intimidated I was by the class subject matter, so sure I was that I was going to fail.
Prof. Lee was also tough. I remember her calling me and my friends on the carpet when one of us had plagiarized notes from a textbook. Again, though, she did not belittle us or humiliate us — she expected us to do better. We worked together with the student who plagiarized to help them understand why it was wrong to do so — in their culture, copying a textbook was the norm — and we did not repeat our mistake.
Still, when time came for the midterm, I felt pretty hopeless. The questions were hard and I did not have a good grasp of all of the material — I hadn’t studied hard enough. I got a grade in the 30%s, not failing because of the curve, but far from an A.
It was high time for me to give up, to either accept a low grade or just drop the class altogether and find another way to satisfy that course requirement. And yet, I didn’t. Strangely, I felt motivated to study harder. I paid close attention to the complex lectures on Latent Semantic Analysis and context-free grammar. I read over my notes and did test problem after test problem. I stayed late for study parties with fellow grad students and started attending my office — something I hadn’t done before.
The final exam was brutal. I literally walked uphill, in a snowstorm, to the exam hall, where I was presented with 5 advanced problems in Advanced Language Technologies. I solved one to reasonable satisfaction, and made notes on the rest. It was the best I could do, but I knew that I was dealing with hard material. I walked out of the class with an A-, again thanks to the generous curve, feeling disappointed in myself for not really earning the grade, but at least proud of having learned something.
The next semester, Prof. Lee invited me to her seminar.
I expected that she, like most other authority figures in my life, would look down on my pathetic math aptitude. Instead, she wanted me to read cutting-edge research in the field! I joined, hesitant, but ever more excited. We met, talked about papers, joked. Prof. Lee kept things going at a quick pace, not letting us slack off, but always inviting conversation in computer science, even when it veered off into tangents about algorithm performance and syntax structure. I read the papers, even the ones full of math formulae, and slowly, they began to make sense to me.
At around the same time, I found that I was no longer struggling in my other grad school classes, especially the mathematical ones — I understood the material, I was able to read cutting-edge research and critique it. It wasn’t all thanks to Prof. Lee’s classes, but a good chunk of my newfound comfort with abstract topics like term-document matrices and linear programming was due to her teaching and to my hard work in her classes — hard work I would have never dared to do without her encouragement.
My thesis was, in a large part, a mathematical proof. I became the math guy on several of my academic projects. Today, I have a job at the forefront of industrial social media analytics, heavy in mathematical analysis. I explain multidimensional matrices to our company’s lawyers as part of developing our patent portfolio. Just this summer, I supervised a student who did some excellent Latent Dirichlet Allocation work on our internal data set to demonstrate the flow of news topics between journalists and high-profile media figures on social media. At no point did I stop to think, maybe I can’t do it. Maybe I am not good enough at math. I have Prof. Lee to thank for that.
You are an inspiration, Professor, and I hope you continue to enjoy an awesome, successful academic career, and introduce many more students — eager or nervous — to the mathematical analysis of natural language.