Stuyvesant’s Math Modeling Team Wins International Competition

Recently, Stuyvesant students competed in the International Mathematical Modeling Challenge (IMMC). One team consisting of juniors Ryan Park, Ethan Sharma, Ethan Sie, and Jackie Zeng developed a model that won the competition’s Regional Outstanding distinction—one of two teams in the nation to do so. 

In the competition, students worked to study problems and understand them effectively using math. “Mathematical modeling is the process of using math to analyze real-world problems—like how to deploy drones to detect wildfires or how to effectively manage a city's water supply—and using that analysis to propose solutions,” faculty advisor and math teacher Patrick Honner said in an email interview. “Through collaboration, computation, and creativity, the team builds their own unique mathematical model of the situation and then uses that model to explore potential solutions to the problem.”

The IMMC is an invitational competition, available to those who compete in the international High School Mathematical Contest in Modeling (HiMCM) contest and place in the top 20 percent. “Out of the teams that competed at HiMCM at Stuyvesant, ours was one of the two to advance to IMMC…we competed [in the IMMC] in the same group,” Sharma said. 

In the competition, students were asked to judge a person’s reliability as a pet owner. “Based on factors like household income, living space, free time, or anything else they felt was relevant, teams had to assess a person’s ‘pet readiness’ so that pet shelters could use to determine if a potential pet adopter was likely to keep and care for their pet long term,” Honner said.

Honner worked to prepare the team before the competitions started. “Mr. Honner held a few really helpful meetings where we got our first introduction both to mathematical modeling and to working together as a team to solve these types of problems. All of us also have Mr. Honner for our math classes, and our background in mathematical thinking definitely contributed to our solutions,” Park said. “Working with my team to break down these real-world issues was a really unique experience, and I’m glad I got to explore math through this lens.”

The IMCC is held in five-day windows from February to April, and Stuyvesant’s team completed it over Midwinter Break. “We pretty much spent all of [our] break doing it, with the exception of an occasional outing or going to sleep. It was a lot of hard work and pretty much 24/7 attention to it over that time period—from me, at least,” Sharma said.

The team used a Hyper-Rectangular Space Partitioning with Linear Inequalities Technique (HR-SPLIT) model to solve the given problem. “This method uses a system of linear inequalities to partition space into regions representing different levels of readiness. Each factor was assigned a value based on user inputs, and these values were combined using the geometric mean to produce a Household Readiness Index (HRI). We extended the model to dogs, parakeets, goldfish, and red-tail boas, adjusting factors like required space, care time, and life expectancy. We evaluated six households for multiple species, highlighting the model’s flexibility in assessing readiness for various pets,” Zeng said.

More than one mathematical model was needed to fully tackle a problem as complicated as pet ownership. “We also developed a model to project pet ownership and retention rates over five, 10, and 15 years using stochastic differential equations. This model accounted for the inherent unpredictability of future events. By integrating lifetime density functions and data on current pet ownership trends, we projected future pet demographics in the U.S., U.K., and Japan for cats, dogs, parakeets, goldfish, and red-tail boas,” Zeng said.

Although team members had distinct roles in creating the model, they worked closely in collaboration with each other. “During the HiMCM, Ethan Sie and I were responsible for programming models, and Ethan Sharma and Ryan were responsible for most of the writing and analysis and that made our paper feel somewhat disconnected. So, for the IMMC, we wanted to work together across the different sections really efficiently. I had to utilize data to perform statistical analysis on our HR-SPLIT model, designed largely in part by Ethan Sharma. Ethan Sie obtained data that was really difficult to find on such niche topics which allowed me to perform the analysis. Ryan would then edit what I wrote and cut down or expand on any details,” Zeng said.

On the very last day before their work was due, the team faced grave technical difficulties. “Abruptly around 3:00 a.m., Overleaf, the program we used to code our paper using LaTeX [a software system for documents], began crashing, and we were worried that we wouldn’t be able to finish on time by 8:00 a.m. as we couldn’t download our paper and still [had] a considerable amount of work to finish. We pushed through and luckily, around an hour before the paper was due, Overleaf stopped crashing, and we were able to submit everything on time,” Sie said.

Mathematical modeling is a difficult task, since there is never a single correct answer to a problem. “There is no one right way to judge whether a person will be a responsible pet owner. There is no single correct answer to a question like ‘How should the United States best manage its water supply?’ Modelers have to be confident enough to make judgments about what’s important but humble enough to remain skeptical about the conclusions they draw from those judgments,” Honner said.

The IMCC is one of many math modeling competitions that the math modeling team at Stuyvesant participates in. “We had over 50 students involved in mathematical modeling at Stuyvesant this year, and had great results in competitions like the HiMCM, IMMC, the M³ Challenge, and the Wharton Data Science Challenge,” Honner said. “We’re looking forward to new projects and even more success next year!”