This mathematician solved a 100-year-old math problem — in high school

By Franklyn Wang, senior at Thomas Jefferson High School for Science & Technology and Regeneron Science Talent Search 2018 finalist

Franklyn Wang presenting his work at the PRIMES-USA conference, using a Frisbee to explain the symmetries in rational functions.

I never thought that that someone like me — a relatively inexperienced high schooler — could make progress on a nearly 100-year old math problem.

Many have tried. Countless mathematicians, including the winners of three Wolf Prizes, two National Medals of Science, and one Fields Medalist, had worked on this problem, making significant progress but were unable to bring it to a conclusion. Through my research, I was able to solve the problem and bring insight into rational functions.

I’ve always been interested in math. In 5th grade, I was introduced to the world of math contests. These problems were unlike anything I had seen before. Instead of repeating a straightforward algorithm over and over again, like long division, I had to develop new ideas to solve each question, whether it was drawing a line not present in the diagram or performing a tricky reduction. While it was challenging, it was also invigorating. For the first time in my 10-year life, there was something which genuinely interested me.

When I applied to MIT’s PRIMES-USA program, a math research program for high school juniors, I saw another opportunity to further my problem-solving skills. Until this point, I devoted my efforts to solving problems whose solutions were known. After all, in a contest environment that is all I had time to do. But with research, you set your sights on a problem whose solution is not known, and hope to find a solution. This really captured the ultimate goal of problem solving: to advance human understanding.

With this in mind, I got down to work with my mentor, Dr. Michael Zieve, on this scary problem:

Describe all monodromy groups and ramification types of non-random indecomposable rational functions.

Beginning this project was difficult. I had no clue what a monodromy group was, and only barely knew what an indecomposable rational function was. Yet while the months passed one by one, I found that with every passing day, I began to understand what was going on. (Monodromy groups and ramification types are key properties of rational functions, and thus knowing all possibilities for them is helpful for the study of rational functions.)

As I closed in on my problem, I suddenly had an insight while reading The Great Gatsby one day in English class. Through a tricky algebraic manipulation, I could finally get a handle on the ramification types, which were composed of multisets of numbers. After writing more than one computer program focused on ramification types, I drilled the final nail into the coffin of this problem..

Before I began mathematical research, terms like cosets, Galois Groups and Irreducible representations all sounded like a foreign language to me when I was younger, but now feel as simple and natural as addition (okay, well maybe not quite as simple). Through this research, I realized that things are never so complicated as they seem.