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Problem Solving in the Lab and the Classroom

Photo by Justin Lewis

Dr. Mark Hughes is a problem solver—that’s why he’s always been so interested in math.

However, now that Hughes is teaching here at BYU he has a new type of problem to solve: balancing research with teaching.

“I think you will find mathematicians who are interested in a lot of fields, but the common thread between them is that they like to solve problems,” Hughes said. “They like to take what at the outset might be a complicated and a deep problem and dissect it piece by piece, seeing if they can figure out how to put it together.”


Hughes received his bachelors in applied mathematics from the University of Calgary in 2006, his masters in pure mathematics from the University of Waterloo in 2008, and his PhD in mathematics from Stony Brook University in 2014. Hughes started working at BYU as a visiting assistant professor last semester after graduating with his PhD.

Despite his undergrad in applied mathematics, Hughes didn’t always want to go into math. When he was in high school, he thought a career in mathematics was out of the question.

“In high school I was presented with the options of, ‘If you like math, you can be an engineer, or if you are good in the sciences, you can become a doctor,’” Hughes said. “I didn’t really know what other options were available if you were interested in studying math.”

When he got into college, Hughes decided he would pursue a degree in physics.

“Originally I was interested in physics. I wanted to pursue that, but I knew that to do any high-level physics you needed to know a lot of math,” Hughes said. “I decided to study applied mathematics for my undergrad degree, but I found that the courses I enjoyed most were not so much the applied math courses but more the pure math courses. I started taking more and more of those, and then when I applied for a masters program I decided that I wanted just to try and focus on pure mathematics instead of the applied route.”

Now that he is here at BYU, Hughes is excited to teach, interact, and mentor the students in his classes.

“I have always enjoyed teaching,” Hughes said. “I enjoy working with the students. When you have a student who is interested in understanding the concepts, when you can actually see when it clicks with them, and you see that they get it and actually understand it, then that’s a satisfying feeling. You get to pass on that enthusiasm for math that is not as common as maybe it ought to be.”

In addition to teaching, Hughes focuses his research on studying 4-manifolds, or four-dimensional shapes.

“I’m interested in how two-dimensional surfaces can be knotted or tangled and be arranged in four-dimensional space,” Hughes said. “I use two-dimensional surfaces in four-dimensional spaces to uncover things about their geometry.”

Throughout his schooling, teaching, and researching, Hughes has learned to apply his love of problem solving to his career.

“I think you need a good balance between (researching and teaching),” Hughes said. “I did research at a place in Germany, and . . .  sometimes I’d hit a brick wall. I’d find that I wasn’t making much progress. When I am working with students it can stimulate activity in my research. I think there has to be a mix of both. I learned to strike a balance, and it can be very rewarding.”