Classroom puzzles to cosmic insights: Students and professor demystify mathematical theorem

John Musgrove, ‘20, and Tyler Schimleck, ‘21, heard about the theorem in De Leenheer’s Vector Calculus 2 course and approached him after class. He enthusiastically brought them on board what turned into a five-year project.

“For me, it was my first time jumping into real mathematical literature. Reading papers by other mathematicians working on the same problem and diving into their research was super exciting for me,” Musgrove said.

Having access to undergraduate research helped both of them successfully pursue a postgraduate degree.

Musgrove graduated from Columbia University with his MS in Operations Research and Schimleck is currently a graduate student at UC Santa Barbara in the Department of Mathematics. Schimleck is interested in differential geometry and mathematical physics.

“It can be so scary at first if you try to read mathematical literature. There is a huge gap between a lot of high-level research and what you learn in undergrad,” Schimleck said. “Doing undergraduate research was a massive confidence boost that helps me say, ‘No, it’s okay, I can do this. I may not understand it at first but eventually, I’ll figure it out and it’ll be okay.’”

Working with a faculty member can be equally terrifying but Musgrove and Schimleck said De Lehneer helped every step of the way.

“One of my favorite things about working with Patrick, would be sitting there in the room and we’re staring at equations on the blackboard in silence for a few minutes and then we will have an “Aha” moment and Patrick will actually say “Aha” and go run to the blackboard with the solution,” Musgrove said. “It's labor. Math doesn’t look appetizing but once you are in it, the energy and emotions sustain the whole thing.”

He said that in a typical undergraduate classroom, students don’t get to experience facing a wall because everything is set up with an answer already.

“That’s the difference with doing research, there is nobody who will tell you the answer. You just have to keep looking at it and thinking about it. There are no shortcuts,” he said.

De Leenheer said it feels like serendipity that a question he had as a young adult, he was able to answer years later.

“I got to know two guys here in class and they showed excitement and they had the dedication, they never quit. Even today I am still thinking about it and it baffles me when I talk to people about this result. All together it was very rewarding,” he said.