Part 2 (of a 2-part interview conversation). Click here for Part 1.
Continued conversation with Dr. Mike Janssen (MJ) and student researchers Jocelyn Zonnefeld (JZ) and Anika Homan (AH).
MJ: Mathematics has a (well-deserved) reputation for being pretty abstract, and mathematical questions can be investigated without a lot of obvious connections to the physical Creation. So why should Christians—or anyone, for that matter—bother with mathematical research at all?
JZ: The main reason that I became a mathematics major and desired to participate in research was its beauty. When researching, we can glimpse the power of our Creator through the mathematical patterns and designs throughout His handiwork. I have found that discovering a pattern in one area of research often connects to a pattern in another, speaking to the cohesive order ingrained in Creation. As any other scientist would argue, we are also glorifying God by using the gifts He has given us to explore creation. Even when we are seemingly lost in the chaos of abstract mathematics, our pursuit honors God and teaches us about Him.
The complexity of the mathematics that we are researching demonstrates God’s love for us when He designed a cosmos that we can explore. For every question we answer in any given area, there are five more raised, granting us a continual pursuit of knowledge and allowing us to explore even if only for the sake of exploring.
A final reason for mathematical research that may sound absurd to some readers is because it is fun! I have found genuine joy while delving into the depths of abstract mathematics. Throughout my research, I have begun to view proofs as a puzzle. In order to prove my theorem, I need to fully complete the puzzle. I am working to bring together pieces from different areas of mathematics, shuffling them around until they create a cohesive product. The joy of working on a puzzle is the same joy of writing a proof, and viewing the outcome brings the same satisfaction.
AH: Jocelyn did a great job of demonstrating our motivation for mathematical research. Not only do we view mathematics as a source of joy, beauty, and fascination, but we also recognize it as a way to directly serve God. We believe that mathematics is no less a part of God’s creation or a reflection of his character just because it can’t be examined under a microscope. Instead, we can’t help but see God’s wisdom and power revealed through mathematics.
The complexity, depth, and mystery of mathematics leads us to trust in God’s sovereignty over His Creation.
Though we believe that mathematics is in itself a valuable mode of exploration, we also celebrate its connection to other areas of study. Mathematics is integral to all parts of the world around us and is a powerful tool necessary for the development of Creation. Therefore, though the mathematical research we did may seem entirely abstract, we do not discount its capacity for future application to physical phenomena.
MJ: What advice would you give to future mathematical researchers?
AH: Some advice I would give to future mathematical researchers would be to be persistent yet adaptable. It’s important to approach your research with stubborn determination, because you will face obstacles. You will spend countless hours, days, maybe even weeks working on a problem.
In some cases, all your time and effort will be rewarded with a breakthrough, other times, you will not discover a solution. Since it’s often impossible to predict the results of your investigation, you must be willing to work through adversity, but also be open to changing directions when a problem is beyond your capabilities.
Be curious with multiple questions, and when you exhaust one idea, you have other directions to explore.
Finally, take good notes. Having a clear and thorough record of your thoughts and findings will help keep you from feeling overwhelmed. Not only is it something you can use to look back on your progress, but it will also help guide you forward on what new paths to take.
JZ: Before looking at any research questions or diving into a proof, my first suggestion is to develop a deep understanding of the subject area. I was regularly surprised by the insight that my understanding of the content area granted me. Though it is tempting to learn only as much as necessary to understand the problem, I would highly suggest going beyond the bare minimum. Many of my findings were the result of the knowledge that I felt was unrelated at the time. Second, utilize community. I would also suggest talking to somebody about your research when you get stuck. Whether they are a fellow mathematician or not, I greatly benefited from attempting to explain my thought processes to another person. I had multiple moments over the course of my research where I was discussing my work with somebody and had a sudden insight because of my effort to explain the problem. Third, in addition to discussing your work, I also benefited from writing down my ideas as Anika mentioned. No matter how revolutionary my idea felt at the moment, I was surprised by how quickly I could forget it. Finally, I encourage researchers to let themselves make mistakes. Some of my deepest insights came as a result of a previous error.
MJ: Thanks, Jocelyn and Anika, for your thoughtful reflections on our work this summer!
And thank you for reading our discussion! It surprises people sometimes to hear that there are unanswered mathematical questions—hasn’t that been done already?—but there are. Some of the unanswered questions (such as Goldbach’s Conjecture) are hundreds of years old, while many more are being published every day.
Mathematics is every bit the mysterious, wondrous study of Creation as any other, with new and surprising connections constantly made.
While I certainly feel called to teach, it was my own fascination with the mathematical aspects of Creation that drew me to advanced study in mathematics, and getting to share that with students each summer is a special joy.
Anika and Jocelyn’s work explored a new algebraic structure, the finite tropical semiring (first discovered and explored in 2020). In short, the finite tropical semiring is a structure in which addition is redefined as an optimization operation; that is, instead of 2+3=5, 2+3=2, since the smaller of 2 and 3 is 2 (or, if you are looking to maximize, 2+3=3). There are all sorts of applications of these types of structures in areas such as computer science or operations research, but our focus was on the structures themselves and how we can visualize them in the hopes of gaining further insight into the structures themselves. As this article is posted on In All Things, we are preparing our work for submission to a peer-reviewed undergraduate mathematics research journal so that others around the world can build on the ideas we discovered.