Regeneron STS 2019 finalists learn how to use math for good from fellow STS alumna
How can math be used to make the world a better place?
During finals week of the Science Talent Search (STS) 2019 in DC, STS finalists had the opportunity to learn from fellow STS alumna, (STS 1993, ISEF 1993). Moon鈥檚 STS project during her senior year was on the geometry of numbers, titled 鈥淎pplications of Minkowski鈥檚 Theorem to Classical Number Theory.鈥� Today, 25 years later, she is an associate professor of mathematics, a senior fellow at the Tisch College of Civic Life and the founding director of the interdisciplinary program in , coincidentally also STS for short.
Moon鈥檚 current work is focused on applying mathematics to political redistricting, also known as gerrymandering. The subject, according to Moon, 鈥渙nly makes sense if you think about it in an interdisciplinary way.鈥� This involves considering the human interfaces of data and algorithms, work Moon was doing just hours before meeting the finalists for dinner. She and other experts had filed an to the Supreme Court regarding a case about political districts in North Carolina and Maryland.
鈥淏oth parties gerrymander as much as they can,鈥� Moon explained. To illustrate how math can evaluate fair representation, Moon showed the students various state maps where districting was done by hand. She directed their attention to the districts that resembled 鈥渢umors and fractals,鈥� pointing out that such gross shapes were signals of discriminatory intent. Even with new redistricting software, results can still be biased and substantively partisan.
Moon鈥檚 research addresses this issue by using math, specifically Markov chains, to determine whether a proposed districting plan is normal or an outlier based on a distribution of all possible plans. 鈥淚f you run this process long enough, you will end up with a representative set of the full space even though the full space is too big to explore,鈥� elaborated Moon. The end result shows how districting plans can be expected to behave and indicates when they have gone too far.
The students were very intrigued. When Moon opened the floor up for questions, they asked about how factors such as urban density and the central limit theorem could impact district maps.
As the night wrapped up, Moon implored the students to ask 鈥渨hat is the science telling you?鈥� in their own research pursuits. She imparted the importance of using empirical methods to answer questions that 鈥測our gut cannot answer.鈥� Furthermore, Moon encouraged the finalists to use their work as platforms to involve others. 鈥淔orget about tumors and fractals. It鈥檚 about having lots of conversations about how we want democracy to function and then design and analyze systems accordingly.鈥�
