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Fairly Dividing Rent

How should you fairly divide rent among three roommates, given their different preferences, so that everyone is happy? Turns out that it’s a mathematically solvable problem, as Olin assistant professor Kelsey Houston-Edwards helped explain on the PBS Infinite Series YouTube show.

While in school at Cornell University earning her PhD in mathematics, Houston-Edwards researched, wrote and hosted “PBS Infinite Series” for PBS Digital Studios, knocking out 44 videos in just one year. She had spent the summer of as an AAAS Mass Media Fellow with NOVA Next, a digital publication of NOVA, and found that she was interested in blending media and math.

So when she saw a casting call from the team behind “PBS Space Time” to make a companion math show, she auditioned. Part of the appeal was making math concepts understandable to a wider audience. For example, she tackled topics ranging from the mathematics of quantum computers to the optimal way to pack hyperspheres. “We all know how three-dimensional oranges are stacked in grocery stores, but what do you think the best way to stack hundred-dimensional oranges is?”

Houston-Edwards also had another motive. “The more selfish reason I did it is that I really like talking to different kinds of people about math,” she says. “I like talking to mathematicians and also people with different math backgrounds. I reflect on the subject differently depending on who I’m talking to and it expands my own perspective.”

She got the idea for the rent division video from a friend who suggested that she check out a paper by math professor Francis Su, building on a mathematical proposition discovered in 1928 by the German mathematician Emanuel Sperner. She liked the idea and jumped on it.

But the timing was unfortunate. By an unlikely coincidence, the online channel Mathologer happened to release a similar video shortly before hers was released. In order to give the audience something different, Houston-Edwards decided to add an appendix to the video. Along with her friend who had originally suggested the idea and another collaborator, she shifted into research mode and set out to see if it is possible to use the proposition to fairly divide rooms and rent among roommates—but this time, one of them would keep their preferences secret.

The short answer is yes, and they published a paper on their findings. “I like that our starting point was a YouTube video, and that it inspired us to push the problem further and create new research,” Houston-Edwards says. She also liked the idea of taking the video a step further and created another one about the project for the National Science Foundation (NSF) We Are Mathematics Video Competition, which aims to bring math to life in a way that can help break down barriers for those who may not understand what it means to do advanced math.

This notion has played out throughout her Olin course, Video Communication, in which students create short educational videos for broad audiences. “Olin students have disparate interests and this course asked them to synthesize them through video for an audience that doesn’t have the exact same background as them,” she says.

Teaching the video class at Olin inspired Houston-Edwards to enter in the contest, which she won. “I realized that even though I wrote and hosted all these shows, I hadn’t much experience with production and animation and I wanted to talk to my students about those things,” she says. “I wanted to be able to add more to the class as a teacher and join in the process of learning about video with them.”