Let’s play a game, you and I:
We take turns writing a number from 1, 2, 3, 4, 5, 6, 7, 8 on the board.
Once 1000 numbers have been written on the board, the game ends.
You win if the sum of the numbers on the board is divisible by 9, otherwise I win.
If that challenge made your brain hurt just by reading it, then you probably wouldn’t get accepted into the mathroots program at Massachusetts Institute of Technology (MIT) like Patrick McHugh did.
As a junior, Patrick’s PSAT math score made him an instant target for MIT. He received an invitation to apply for the elite two-week summer program which only accepts 20 high schoolers from around the nation. He wasn’t accepted in 2020 as a junior but that didn’t stop him from applying in 2021 and his persistence paid off. Patrick was chosen as 1 of the 20 for the 2021 session of mathroots.
In a pre-COVID world, the program participants spent their two weeks on the MIT campus, all expenses paid. Unfortunately for Patrick, this year’s attendees had to attend the program virtually. While disappointing, it didn’t stop Patrick from thoroughly enjoying the two-week adventure. “We were all from different backgrounds and locations but we shared a common love of math and the energy it gives us,” said Patrick. “We had to work collaboratively and it was so fun to be around other people who think like me. We really bonded.”
So how did a kid from PA measure up to the best-of-the-best from around the country? On the first day, the Program Director presented a sample problem simply to demonstrate what kind of challenges they would be given, never expecting a student to actually attempt it. But Patrick put on his overachiever’s hat and decided to take on this challenge on his own time:
What is the limit as n goes to infinity of the ratio of the volume of the n-dimensional sphere centred at the origin tangent to the 2^n unit n-dimensional spheres centred at {-1,1}^n to the volume of the n-dimensional cube with vertices at {-2,2}^n. (Note the cube fully contains the 2^n unit hyperspheres).
By the end of the day, Patrick sent the instructor his solution and the teacher replied, “That was extremely fast.” While that was quite an initial ego boost for Patrick, after a few days into the program Patrick admitted, “I discovered I wasn’t as good at math as I thought I was. We all kept getting our egos destroyed. By the end though, camp had taught us how to structure our minds to think logically and creatively and to problem solve instead of just using our ability to memorize formulas.”
The photos to the right represent a sample of those problem solving challenges. But the students didn’t live in a world of numbers and equations for two solid weeks. MIT also understands the importance of mandatory fun. Logical thinking and problem solving skills were also challenged through games like mafia, Escape Room, trivia and an unique PowerPoint game where the person presenting had to speak about the random slides that appeared without knowing what topic the slides were actually teaching.
Pennsylvania also had representation on the mathroots teaching team. John Urschel, a former Penn State and Baltimore Ravens football player, was one of Patrick’s instructors. During Urschel’s time with the Ravens, he was taking courses at MIT and admitted he had always had a “lifelong tug of war between football and mathematics.” Urschel left the Ravens to pursue his doctorate at MIT where he is currently a fifth-year PhD student with plans to graduate this summer.
In addition to networking with MIT staff, the participants were given virtual tours of Princeton and Harvard by mathroots alumni. “They gave us advice on college admissions and interview tips,” said Patrick. “Like be yourself, which we always hear, but be real and not just say what you think they want to hear.”
So how has Patrick’s mathroots experience influenced his future plans? “Well, I’d really like to attend MIT and major in math,” he said with a grin. “We each received a personalized letter of recommendation to submit with our college applications so…we’ll see!”
Who knows? Maybe Middletown will be wishing Patrick McHugh good luck as he heads off to Massachusetts!