Christy Hovanetz, Ph.D., is a Senior Policy Fellow for ExcelinEd focusing on school accountability and math policies.
On Dec. 2, 1997, the feel-good drama Good Will Hunting premiered at the Fox Bruin Theater in the Westwood neighborhood, near the University of California in Los Angeles.
Will Hunting—played by actor Matt Damon—is a young janitor working at the Massachusetts Institute for Technology (MIT). While mopping the hallway floor, Will encounters a chalkboard with an advanced Fourier system, which he anonymously solves. He returns the next week to find a more difficult problem, which he begins solving, to the chagrin of Professor Gerald Lambeau who posts the problems for his class. Eventually Will is “discovered” and brought under the wing of the Fields Medal-winning professor.
The story is cleverly written and retains a theme steeped in math throughout, but how difficult are the problems in reality?
Spoiler alert: They are tough, but solvable.
Prof. Lambeau posts a Fourier systems graph theory problem first:
Will constructs the adjacency matrices and generates the function walks for the problem. The Fourier transform for graph signals is used to study the spectrum and properties of graph adjacency matrices and is a powerful tool for representing and analyzing periodic signals.
The Fourier series is used in acoustics, engineering, optical engineering, image processing, quantum mechanics and several variations of signal processing.
While there is significant math involved, real-world applications of the Fourier series include digital signal filtering, noise removal (for example, Microsoft Teams filtering out barking dogs), identifying the resonant frequency of a structure (for example, helping with structural engineering in seismic-rich environments), compression of audio signals and speech recognition.
The second problem—“Draw all the homeomorphically irreducible trees with n=10”—is one Prof. Lambeau states took him and a team two years to solve (but probably shouldn’t have). Tree structures are used to determine an optimal strategy while considering multiple factors. Real-life applications include game development, databases and machine learning.
Although Damon’s character has a photographic memory, the problems posted on the chalkboard didn’t require that level of wicked smartness and actually are taught in college-level linear algebra classes.
Good Will Hunting reminds us not to underestimate any kid.
Challenging students with high expectations ensures they are ready to succeed in advanced math courses. Policymakers can help more kids access higher-level math courses by implementing ExcelinEd’s automatic enrollment model policy.
How do you like them apples?
The Good Will Hunting story loosely resembles George Bernard Dantzig, a student at the University of California in Berkley who arrives late to math class one day to see two problems on the board he assumed were homework. He turns in the assignment late, apologizing to his professor Jerzy Neyman for the lateness and quipping the problems seemed harder than usual, which is why it took him longer to complete.
The problems Dantzig solved were two famously unsolved statistical problems, not homework. While he didn’t get homework credit, he was able to use them for his thesis.
As we head into the new year, we wanted to let you know this will be our last edition of #MathMonday. We’ll be focusing in 2025 on building our email lists across all of our policy areas so we can make sure you’re getting news and updates that are tailored to your interests. Thank you for reading!
