The Prime Number Theorem

This is a short film about the proof of the Prime Number Theorem. (Yes, that’s right – the mathematical proof.) The project was inspired by the complex analysis lectures of Dr. John McCarthy at Washington University in St. Louis, and the many elements of the film have a motivation from the steps in the proof. Through the process of planning, filming, and editing, I found a new way to learn and share mathematics, and I share that story here.

During Complex Analysis II, my professor announced that we would be covering the proof of the Prime Number Theorem over the next three lectures. In an attempt to combat the fatigue that comes with long proofs, he personified the important functions and sketched a plot of a play that followed the arguments in the proof. He casually announced, “Bonus points to anyone who acts this out.”

Of course, I picked up the gauntlet and began planning a short film. Over several weeks, I wrote up ideas, made some adjustments to the storyline, and planned out a filming day. I had no previous experience with filming or editing, and I learned a lot along the way. A couple of friends helped me out with props and filming, and I then began the process of editing. I followed my notes from lecture and Gamelin’s Complex Analysis to structure the content of the film and add in some extra elements. I also built a custom film leader with a prime number countdown. Overall, the process of editing was an enjoyable way to learn the proof, and I finished the film near the end of the course.

With the excitement and support from my professor, we planned a screening for the math department at my university. The “world premiere” had a large attendance, complete with champagne and audience members requesting photos with the stars of the show. I’m super happy so many people were interested in seeing the results of the project. In response to several requests, I posted it publicly to YouTube where you can find a shareable link.

Thank you all for the encouragement in the making and screening of this project, and a special thank you to my friends featured in the film. I hope this film inspires more mathematical short films and encourages people to find creative ways to communicate mathematics.