For mathematicians, getting to the “aha” moment can be a frustrating exercise. But in a field where it’s common to be wrong, Elizabeth Meckes has found passion. And those times when everything does align, she said, are “beautiful.”

“Those moments of clarity—those moments of ‘I suddenly see the light and I understand something I didn’t before’—are transcendent, but man, are they rare,” said Meckes, an associate professor in the Department of Mathematics, Applied Mathematics, and Statistics.

While she may never learn to love the time she spends struggling to solve a problem, Meckes said she’s become accustomed to it. And one of the ways she eases the burden is through teaching and helping her students understand complex concepts.

“You can explain things that you do understand very well to other people and then help them see the light,” she said. “And that’s a great feeling.”

Now, she’s taking her role of enlightening others in mathematics a step further. She and her husband, Mark, also an associate professor in the Department of Mathematics, Applied Mathematics, and Statistics, have a forthcoming textbook titled Linear Algebra. Set to come out this summer, the book will be used in the university’s MATH 307 class, which is required of all math majors.

Meckes and her husband wrote the it with the aim of having it take a student-focused approach, as they’ve found many advanced mathematics textbooks read more like plans for instructors, rather than a tool for students.

“That’s very unfortunate because we do want the students to read the book and to learn how to learn something from a math book—and that’s a skill,” she said.

In terms of helping students at Case Western Reserve University learn, Meckes also has a unique perspective, as she was once in the students’ shoes as an undergraduate and master’s student.

She earned her bachelor’s degree from the university in 2001 and her master’s in 2002. She went on to earn her PhD from Stanford University in 2006.

For Meckes, the choice to study mathematics was a natural one, as it was a subject she always enjoyed. But it was only when she got into upper-level undergraduate math classes that she realized just how perfect of a fit it was.

“You can tell when something’s clicking and when something’s the right subject for you,” Meckes said. “It doesn’t mean that it’s easy. It just means that it makes sense to you in a way that other things don’t always. There’s some kind of intuition that’s built in that helps you feel like you’re getting things better.”

That was math for Meckes. Since her time in school, her main areas of research have been probability theory and high-dimensional geometry, which explores what happens when geometry changes and the space goes toward infinity.

“That’s a strange kind of question, but it’s the kind of question that math is for,” she said. “You can start with this very concrete thing—like understanding shapes on a piece of paper—and you can take your intuition there and abstract it and build theories that make sense and actually teach you important things.”

And whereas many mathematicians focus on interesting examples of a problem, as a probablist, Meckes seeks to understand “what happens typically.”

“That’s how I understand the world and how I understand mathematics,” she said. “I’m interested in looking at things from that viewpoint.”

Take the time to get to know Meckes better in this week’s five questions.

1. What’s your favorite place to grab a bite to eat in Cleveland?

I like to go have lunch in the art museum, not so much because I like the food, but because I like to sit in the atrium.

2. Where would you like to travel that you’ve never been to?

This is something that people may not know, but mathematicians travel a lot. This past summer, I went to Barcelona and Marrakesh [in Morocco]; I’ve been to Singapore. You go to interesting places.

3. What is your biggest goal for 2018?

Certainly, work-wise, my biggest goal is to finish my other book. I’m working on a research monograph.

4. If you had to pick another field to work in or study, what would it be?

I’ve gotten more interested in physics lately. I used to think I wanted to do physics, but as an undergrad, I felt like it was just not right for me. Now that I am a mathematician and I would be coming at it from a very different perspective, there are times that I’m interested in getting back into physics. That’s the easy answer—something realistic in a way.

But I’ve always been really interested in linguistics, so that’s the kind of more pie-in-the-sky answer.

5. What’s your favorite thing about Case Western Reserve?

The thing that I think is exceptional about the university is the fact that we really try to do well by our students. We try to give them the best that we can.

I think a lot about the fact that I’m a research mathematician—that’s a really important part of my professional identity, but I’m also a professor and I teach students. I think a lot about what my value added is—what am I giving students that they couldn’t get from just picking up a book? I’m not alone among the faculty in thinking about this; I think all of the faculty thinks carefully about what they can add.

We also have a lot of important support for the students. The Office of Undergraduate Studies, for example, is great. I’m very impressed generally with what a good job they do of supporting the undergrads.

It’s hard being college students. If we can be supportive and provide both a good education and also a good environment for students as they’re going through that intellectual and also emotional coming-of-age, that’s really important. I hope we do a pretty good job of that.