# A Conversation with Lola Thompson

Q. What year did you begin teaching at Oberlin?

Fall 2013

Q. What inspired you to pursue a career in mathematics?

I loved math as a child. I would beg my parents to send me to math camp every summer. However, by the time that I was in high school, I found math to be painfully boring. I actually attended a performing arts magnet high school where I majored in vocal performance (opera). My high school was short on classroom space, so the rooms in the main building were reserved for black box theaters, dance studios, and art studios. My math courses were relegated to the "math trailer.” Needless to say, math was not a priority at my high school and my background in the subject was fairly weak when I left for college.

When I arrived at the University of Chicago for college, I thought that I would just take the calculus sequence and then be finished with math forever. However, each semester I would find an excuse to sign up for one more math class... I think I was in denial about falling in love with math. I finally declared a math major halfway through my third year of college. Even at that point, I didn’t see myself having a future as a mathematician. I think that part of the issue was that I had never seen a female mathematician (none of my math professors at UChicago were women). A major turning point came when my department sent me to the Nebraska Conference for Undergraduate Women In Mathematics (NCUWM). While at NCUWM, I received a huge amount of encouragement. The idea of going to graduate school and becoming a mathematics professor had never occurred to me. It was also extremely helpful for me to see examples of female mathematicians. For the first time, I could imagine myself as a mathematician!

Q. What are some intriguing or exciting developments in mathematics that people outside the field probably don’t know about?

There is a famous conjecture in mathematics called the Twin Primes Conjecture, which says that there are infinitely many pairs of prime numbers that differ by 2. There are lots of small examples of pairs of primes that differ by 2: (3, 5), (5, 7), (11, 13), (17, 19), etc. However, these pairs become much scarcer as the primes get larger. That’s why it’s not clear that there should be infinitely many of them.

The Twin Primes Conjecture has been open for at least 150 years. Until recently, no one could even show that there are infinitely many pairs of primes that differ by any finite number. In 2013, Yitang Zhang stunned the mathematics community by proving that there are infinitely many pairs of primes that differ by at most 70 million. This means that some number between 2 and 70 million must appear as a difference of two prime numbers infinitely often. In the same year, James Maynard and Terence Tao independently proved a stronger result that uses a drastically different approach. Further improvements were crowdsourced, which means that a large group of mathematicians worked together to chip away at tiny parts of the problem, which was coordinated via Tao’s extremely popular math blog. We now know that there are infinitely many pairs of primes that differ by at most 246. (The question of whether there are infinitely many pairs of primes that differ by 2 is still open.)

Q. What are your current research interests?

Much of my work over the last four years has involved applying Maynard and Tao’s approach (see my response to the previous question) to solve other problems about prime numbers. Here is one such application. Let s(n) be the sum of the digits of an integer n. For example, s(523) = 5 + 2 + 3 = 10 and s(541) = 5 + 4 + 1 = 10. There are a few things to notice in these examples. First off, the inputs 523 and 541 are both prime numbers. Moreover, they’re consecutive primes, which means that there aren’t any other primes between 523 and 541. Finally, the two digit sums in this example are equal, i.e., s(523) = 10 = s(541). In 1961, the Polish mathematician Sierpinski (after whom the Sierpinski triangle is named) looked at examples like these and posed the question: Are there arbitrarily long sequences of consecutive primes p for which the digit sum s(p) is constant? This question was considered by a number of mathematicians over the years, including the legendary Hungarian mathematician Paul Erdos. It remained unresolved until 2015, when I answered the question along with my co-author, Paul Pollack. We showed that, yes, there are arbitrarily long sequences of consecutive primes that have a constant digit sum. One of the key ideas in our proof came from Maynard and Tao’s approach.

More recently, I have been working on some geometric applications of the Maynard-Tao approach. I have also been branching out into problems in algorithmic number theory, which involves coming up with efficient algorithms for computing various sums that are of interest to number theorists.

Q. How did you get involved with the Oberlin College Aerialists? Did you have a background in tumbling or circus?

I studied aerial silks while working as a postdoctoral researcher at the University of Georgia, and was thrilled to discover that Oberlin has an aerial circus group. I actually contacted the Oberlin College Aerialists a couple of months before I showed up on campus, just to make sure that they would welcome a non-student participant. I feel so lucky to be part of the Oberlin College Aerialists. When I train with them, the roles of “teacher” and “student” are normally reversed—I learn so much from the Oberlin student aerialists! We have an incredible training facility at Hales Gym. I also train with professional aerialists in Cleveland on a regular basis, and they are very jealous that I work three blocks away from Hales. When you spend all day sitting in your office thinking about difficult abstract problems, it’s wonderful to take a break and do something intensely physical, like aerial acrobatics.

Q. What classes do you especially enjoy teaching?

I’m very lucky in that the classes that I teach at Oberlin are the ones that played a special role in my own mathematical training: Calculus was the first course that exposed me to the beauty of theoretical mathematics, including proofs; Discrete Mathematics is the course that made me fall in love with math and convinced me to declare a math major; Abstract Algebra (Group Theory, Rings and Fields) were the courses that gave me the confidence to apply to graduate programs in mathematics; Number Theory is the course that inspired me to become a number theorist.

Number Theory will always hold a special place in my heart because it’s the course where I get to expose students to my own research area. I also love teaching this class because I take a very unusual approach: I don’t give any lectures and I explicitly ban my students from reading textbooks on the subject. Instead, the students work in groups on carefully scaffolded worksheets that lead them to discover the major ideas from the last 2000 years of number theory.

Q. What is one word students would use to describe you?

Enthusiastic!

Q. What advice would you give to someone considering a major in mathematics?

Hollywood often portrays mathematicians as geniuses who isolate themselves from the rest of the world in order to dedicate their lives to solving a famously difficult problem. Most mathematicians, even the very top researchers in their fields, aren’t anything like the Hollywood portrayal. Most of us will readily admit that hard work, perseverance, and a bit of luck, are the most important factors in mathematical success (much more important than supernatural “genius” abilities). Moreover, these days the vast majority of math research is collaborative, which means that we talk to each other a lot.

I bring this up because I have interacted with a number of Oberlin students who worry that they aren’t cut out for a math major (or for a career as a mathematician) because they have to spend a lot of hours digesting the course material and working on their problem sets. They worry that they’re not smart enough to study math because they don’t instantly “get” everything. Some students feel discouraged because one of their classmates seems to be able to answer all of the questions before they’re even able to process what the questions are asking. Guess what? The person who seems to know all of the answers has probably seen the material before.

I’ve also taught some Oberlin students who feel that they have to work on their problem sets alone because they perceive working with others as a sign of weakness. This couldn’t be farther from the truth! One of the most valuable skills that I learned in college was how to work on math with others, which has served me well in my career.

In short, don’t let stereotypes about mathematicians keep you from pursuing a math major. There is room in mathematics for everyone!