Interview with Derek Thompson, 2019 CSF Grant Recipient

ESN loves to provide opportunities for members, and there’s still time to apply for the 2020 Christian Scholars Foundation Grant, offering $20k this year. A key membership benefit of ESN, this junior faculty grant is offered to an ESN member every year by the Christian Scholars Foundation (CSF). CSF generously partners with ESN to support a junior faculty member with funds that can be used for research or other projects exploring Christian scholarship. Enjoy our interview with 2019 grant recipient Derek Thompson below, and stay tuned for an interview with Jennifer Hawk, 2018 CSF awardee.  Image Credit: 2019 CSF Grant Recipient Derek Thompson with Research Students, image and permission to use supplied by Derek Thompson, 11/26/2019.

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Biography for Derek Thompson

In high school, I decided to become a math teacher while covering a Pre-Calculus course for our instructor that was summoned by the National Guard after the war with Iraq began. In college, I learned the hard way that I didn’t want to teach secondary school, so I pursued graduate school in hopes of being professor. A year after finishing my PhD, I began at Taylor University in 2014.

Three things stuck out to me right away: this is a Christian college that was “loud and proud” and very social, the teaching standards are very high, and the mathematics majors were extremely talented. Pursuing undergraduate research is much easier when you have the kind of students that our department attracts. It’s also close to home for me and my wife, so it’s been a great place for us and our two children. Taylor was also highly supportive of our call to adopt a child and even has a small reimbursement program for adoptions. It’s been a great fit for us in every way imaginable.  

Interview with Derek Thompson

1. ESN: Would you tell us a little bit about your field and specific area(s) of study within that field?

My PhD is in mathematics; my area is called Operator Theory. The simplest way to explain it is this: in school you learn about numbers, and then you learn about functions that act on those numbers. So, something like x2 sends 2 to 3, 3 to 9, and so on. The operators that I study are functions that act on other functions.

2. ESN: Would you describe your Christian Scholars Foundation Grant project for our readers?

The project is actually a bit out of my normal area of expertise. It is a geometry project. The idea is this: a circle is the set of points the same distance from the center (we call the distance the radius). For an ellipse, you do the same thing but add the distances to two points (the foci) and require that sum be equal for every point. Why not use three points? We call this a 3-ellipse. It’s a concept that’s very easy to visualize: go here (https://www.desmos.com/calculator/sltud8pesu) and drag the red points around to see the red 3-ellipse take on different possible shapes. The goal of the project was to understand different facts about 3-ellipses, which have not been studied much.

3. ESN: How did you develop an interest in this particular project?  

In the study of vectors, there is an idea called the numerical range. Basically, for each unit vector, you measure the angle between where it was, and where an operator (a matrix in this case) moved it to. This creates a bunch of different points, and the shape created by those points is always convex (a “fat” shape that never turns inward). For a 2-by-2 matrix, the shape is always an ellipse. My PhD advisor had hypothesized that a 3-by-3 matrix would always have a 3-ellipse as its numerical range. I believe we’ve discovered that’s false, but there are still lots of questions to ask about 3-ellipses. I had only ever heard of the idea because of his hypothesis, though.

4. ESN: How does the Christian Scholars Grant support you in this work?  

Ever since I started doing undergraduate research, I’ve been pursuing ways to get students and myself funded for the work. Most students are not willing to pursue research simply as an extra thing on top of class, so summer REUs (research experiences for undergraduates) usually give a stipend (often funded through the National Science Foundation). This project is over the school year rather than the summer, but through the Christian Scholars Grant, I was able to get them funding for the work. Hopefully an NSF grant will be the next step in a year or two.  

I had applied to the grant several times prior with other projects, but none had been successful. I thought a big part of the problem was that my area of operator theory involves very few pictures, and mostly just piles and piles of equations, making it hard to explain the work to people who are not mathematicians. When the idea of this project came up, I knew it would be much more interesting because it’s so simple to show what a 3-ellipse is. Fortunately, that new strength worked out as I had hoped. I’m not much of a visual learner, but I have a new appreciation for the importance of pictures and graphs!

5. ESN: This is a big question, but I know our readers will be interested in at least the short version of your answer to it. How does your faith influence your scholarship and teaching, and vice versa?  

I have been incredibly blessed to work at a department where faith-learning integration is something taken very seriously. There is an excellent book called Mathematics through the Eyes of Faith, and a former Taylor professor, Matt DeLong, wrote the chapter on Beauty. Likewise, professor emeritus Dave Neuhouser wrote a book called Open to Reason before he passed away a few years ago. He had retired before I got here, but he was a very large influence on the department and that is still felt. We have a math course called Ways of Knowing designed for Honors students where students read several books that bridge philosophy and mathematics, and do math problems aimed at the idea of how humans truly know and understand the world around them.  

The cool thing about mathematical scholarship is that you are literally trying to prove facts about the universe, however obscure. Mathematical theorems are a great way for us to understand the idea of absolute truth. Was the Pythagorean Theorem true before Pythagoras discovered it? Yes! So I view my scholarship as an act of worship, because I’m actively pursuing facts that God has laid out since the beginning for us to discover.

While we all take care to insert Christian ideas into our classroom and ways that mathematical ideas tie to them, there is a holistic aspect to faith-learning integration that students often don’t recognize. Another retired Taylor math professor, Ken Constantine, once told me he disliked the phrase “faith-learning integration” because, he asked, “When are they ever separate?” When we pursue whole-person education, when we let students cry in our office for an hour, when we pray with them and over them, when we mentor students in undergraduate research, when we attend their weddings or their baptisms, we are integrating faith and learning, perhaps in the most important way.  

6. ESN: As someone who studied literature in grad school and once taught an honors writing class on fantastic literature, I have to ask you this, even though it’s slightly off topic. Your profile page at Taylor University says you enjoy medieval fantasy literature. Which authors or works do you especially enjoy? Does your enjoyment of fantasy literature connect at all with your interest in mathematics? Or do you see them as completely separate interests?

I’ve always been a geek; in elementary school I had discovered Magic: the Gathering shortly after it came out, I somehow found my parents’ VHS tapes of the original Star Wars trilogy and watched them on my own, and my first fantasy books were the Dragonlance novels by Margaret Weis and Tracy Hickman. Lately, I’ve been really enjoying Brandon Sanderson’s novels; I’m caught up on the Stormlight Archive series and am currently reading the first Mistborn novel. Harry Potter is also another (unsurprising) favorite.

I definitely view them as connected interests. Even in liberal arts colleges we have a bad habit of making a false dichotomy between STEM fields and Humanities. But really, mathematics involves using reason and logic to parse meaning out of sentences and phrases, while English and Literature focus more on the qualitative side, but in a way both are about using words to construct meaning about our world. And both are for the glory of God at the end of the day.

I’ve always enjoyed writing, and shortly after I began at Taylor I began writing for Geeks Under Grace (http://geeksundergrace.com). I started by doing Tabletop game reviews like I had done for a few years prior, but since then I have reviewed video games, music and anime, and done a few articles tying video games to Christianity. We do content guides and other “typical Christian site things,” but what makes our site unique is the focus on using stories from pop culture to spread the Gospel. For example, this piece ties a scene in Legend of Zelda: Breath of the Wild to our adoption story: http://www.geeksundergrace.com/gaming/zeldas-prayer/. I also did a six-part Devotional series on Breath of the Wild (http://www.geeksundergrace.com/tag/zeldadevotional/). Another big thing we do is that we have Bible Studies that you read after seeing a geek movie in the theater. Having a geeky creative outlet that is also a ministry has been a real blessing to me in the past five years.

7. What else would you like to say to other emerging scholars who are followers of Christ?

1. Find an hour a week, if not an hour a day, to do something at work that refreshes you but is still important for building your relationships at the university. Go out to lunch with a colleague. Have coffee with students. Read another colleague’s published work that you might enjoy. Don’t get burnt out.  
2. Don’t get discouraged when you fail to get grants or other opportunities. Apply again. And again. And again.  
3. At small colleges, it’s likely you don’t have a colleague that you can do research with. None of my mathematics colleagues do the same scholarship as me, and I don’t understand any of theirs. Your students are your best possible co-authors. Don’t dismiss them.
4. Pray about your scholarship. God knows the answers to the questions you are researching. He’s the number-one scholar you should be contacting for help.