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In the twenty-fifth episode of the second season of the “Saturdays at Seven” conversation series, Todd Ream talks with Kim Jongerius, Professor of Mathematics and Chair of the Department of Mathematics at Northwestern College. Jongerius begins by exploring the role mystery plays in the pursuit of mathematical forms of truth. Shying away from mystery, especially when conjoined with an inability to appreciate what other disciplines offer, can greatly limit what mathematicians discover. In contrast, embracing mystery and what other disciplines can offer can open previously unimaginable possibilities. Jongerius offers details concerning her formation as a mathematician, the encouragement she received from teachers, and how she came to think of the study of mathematics as comparable to learning another language. As someone who greatly enjoys writing and studied English as well as mathematics as an undergraduate, Jongerius argues the distinctions between mathematical and linguistic abilities are more the creation of social comfort than reality. Jongerius discusses her service as president of the Association of Christians in the Mathematical Sciences (ACMS), lessons she learned about the role mathematics should play in general education, and ways to encourage and support the next generation of mathematicians. When closing the conversation, Jongerius explains how mathematicians can be of greater service to scholars in other disciplines as a well as the Church.
Todd Ream: Welcome to Saturdays at Seven, Christian Scholar’s Review’s conversation series with thought leaders about the academic vocation and the relationship that vocation shares with the Church. My name is Todd Ream. I have the privilege of serving as the publisher for Christian Scholar’s Review and as the host for Saturdays at Seven. I also have the privilege of serving on the faculty and the administration at Indiana Wesleyan University.
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Our guest is Kim Jongerius, Professor of Mathematics and Chair of the Mathematics Department at Northwestern College. Thank you for joining us.
Kim Jongerius: You’re welcome. Thanks for inviting me.
Todd Ream: As with the other guests who contributed to this series concerning mathematics as a vocation, I’d like to open our conversation by asking about a 1960 article frequently cited by Eugene Wigner. For individuals who are unfamiliar with him still, he served most of his career on the faculty at Princeton University, served briefly as the Director of Research and Development of what became the Oak Ridge National Laboratory and won the Nobel Prize for Physics in 1963 for contributions to the understanding of the atomic nucleus. In February 1960, he published “The Unreasonable Effectiveness of Mathematics in the Natural Sciences” in the periodical Communications in Pure and Applied Mathematics.
When reading this article, I found Wigner resorting to some curious and rather inviting forms of language. For example, in his first of two points, he claims that the enormous usefulness of mathematics and the natural sciences is something bordering on the mysterious and there is no rational explanation for it. In his second of two points, Wigner then contends, it is just this uncanny usefulness of mathematical concepts that raises the question of our physical theories.
To begin, how prone are mathematicians and physicists to using terms such as mysterious and uncanny estimations of their efforts?
Kim Jongerius: Well, I can’t claim to speak for or even to have read all mathematicians, and I’ve only read a little of one or two physicists. But my sense is that these kinds of statements would be much more common for non-Christian mathematicians and physicists than for Christians in these fields.
When you believe that God created the world and that human beings were created in His image, it’s not at all surprising that the mathematics we think we’re inventing, is actually part of His intricate creation and applies to other phenomena in that creation. And when you believe that all creation is interconnected under the sovereignty of God, it’s not shocking to see mathematics that was developed in one context, pop up in a significant way in another context.
Todd Ream: In what ways do you think then his efforts would have been enhanced if he would have been able to draw from other academic disciplines, for example, fields such as philosophy and/or theology?
Kim Jongerius: I think they would have been enhanced, but I don’t know that he would have, he may or may not have been aware of those theories in those disciplines, but I don’t know that would have helped his thinking because he would still not have found them to be reasonable explanations. Like a philosophical approach might have led him to see that mass effectiveness is a sign that mathematical objects exist independent of human conception. I’m not sure he would have thought that was rational thinking.
Christian theology definitely presents a way to approach his dilemma, but knowledge of theology isn’t really helpful if you don’t accept the underlying premises. So at best, I think he could say that for the Christian, this remarkable application issue wouldn’t be called a miracle as much as a perhaps unexpected, but nevertheless reasonable result.
Todd Ream: Thank you. In what ways then, if any, is mathematics, whether practiced by believers or non-believers, as an expression of the academic vocation, defined by persistence in the pursuit of truth through that which otherwise may seem mysterious, uncanny, or at least for a season even, with which there’s no rational explanation?
Kim Jongerius: Well, on one hand, I think that kind of persistence has to be the basis of scholarship in every academic field, though the non-mysterious doesn’t really require investigation.
On the other hand, it’s been some time since mathematicians claimed that we have anything to say about absolute truth. What we claim is that given certain assumptions, everything we prove based on those assumptions and using rules of logic, that’s true. So it’s all contextual for us. Like you might remember learning that the measures of angles in a triangle add up to 180 degrees. So every kid learns that at some point in school. And you might think about that as, as a truth about the world we live in.
And the thing is, if we assume that whenever you have a line and a point not on that line, that there’s a unique line through the point parallel to the original line, then all, all triangle measures add up to angle measures out to 180 degrees, but it’s not true if we toss out that assumption. So on a plane on a flat surface, that’s true. But if we look at the surface of a sphere, it’s not true at all. On a sphere, there’s no such thing as parallel lines. Triangles don’t all have the same angle sum.
And we do live on a sphere, right? We don’t live on a flat plane technically, unless you know you’re a flat earther. But most of us live in reality and recognize that we live on a more or less spherical object and it’s hard to argue that this new situation isn’t just as real as the one that we learned about back in elementary school.
Todd Ream: Thank you. I want to transition now to asking you about some biographical details and how you came to appreciate mathematics.
You earned an undergraduate degree in mathematics and English from Northern Arizona University and a Master’s and Doctorate in Mathematics from Colorado State University. At what point did you begin to sense mathematics would prove central to your sense of vocation?
Kim Jongerius: Well, it’s interesting. Until I was like 17, I actually didn’t even like math very much. I loved the problem solving aspect of it. I’ve always really enjoyed figuring things out, but the problems were just so dumb. How old is Bobby of 3 years ago? His sister Sally was twice as old as he was, and now she’s 5 years older. I always thought, oh, just ask him. It’s a stupid problem.
And around that time ,my grandmother actually suggested that I study math in college, and I said, I don’t like math. And she said, but you’re good at it. I’m thinking, well, I’m good at a number of things, but that’s just because we have to study them. Then I went to this sort of summer camp for engineering at the University of Arizona, and I learned that math is actually useful. Uh, who would have thought?
And the next summer, I worked at an outdoor camp, and I found that I loved teaching outdoor skills like using tools, building safe and effective fires, lashing together sticks for tables and shelters, trying specially knots, all that kind of stuff. Again, kind of problem solving. I thought it was super awesome. That made me decide to be a teacher.
And then my freshman year in college, I just found that I procrastinated all my other homework by doing my math homework so that suggested to me that maybe math is something I should pursue and that teaching math would be kind of a cool thing. And after that, it was really just individual professors along the way who encouraged me to not stop with the degree I was pursuing at the moment but to continue on in the process.
And graduate school definitely got harder, but it was still fun, particularly working with other graduate students to figure out concepts that just weren’t making sense to you. I came to think of math as a language and myself as someone who enjoys playing with language and teaching others to do the same.
Todd Ream: Would you mind saying a little bit more about the encouragement that you received from faculty members in mathematics, you know, as an undergraduate and or as a graduate student that proved to be helpful to you?
Kim Jongerius: Yeah, yeah, so my undergraduate advisor called me in at one point during my senior year and said, hey, what are you planning to do when you graduate? And I said, well, I’m gonna go teach high school math. And he said, oh, no, no, no, you should definitely go on to grad school. You should stay here and get a master’s degree.
And then a few weeks after that, I started to think about that. And then one of my other professors, I had him for both of the kinds of key courses that I use even to determine whether or not I should recommend that a student go on to graduate school. Like how well are they understanding abstract algebra and real analysis? And one day in class, he said: you, stay after class, I want to talk to you. And I’m thinking, like, I didn’t do anything, you know, I don’t cheat. I’m like, everything’s fine.
But so I stayed after class and he said, what are you going to do after you graduate? And I said, well, I was thinking I would teach high school math. And he goes, oh God, don’t do that. I said well, but then I was, I was talking to, you know, my advisor and he said he was trying to convince me to stick around here and work on a master’s degree in math. And he said, oh God, don’t do that.
And I, I think it wasn’t that he was thinking NAU was not a good school, but that NAU didn’t have a PhD program. And he already had it in his mind that I would go on for a PhD. So he started talking to me about learning other languages and just you know, you’d have to know other languages in, in graduate school. He found out I spoke some German, so he pulls out a textbook in German and, tries to get me to read the math in German, which actually wasn’t that hard, but yeah, so it was cool. So he was very encouraging.
I got into grad school, similar stuff. My master’s thesis advisor suggested that I stick around. I went to talk to another professor and said, hey, you know, would you write me a letter of recommendation if I stick around? And he pulled out a sheet of paper, ripped it in half and wrote: let her in, give her money. And he said, take this to the office.
And then the really funny thing is that same guy who was so convincing when I was an undergrad, actually, he had a friend on the faculty at Colorado State, and he found out that I was planning to just get my Master’s and stop, so he called me in my grad school office and said, hey, I was talking to my friend Bob, and he said, you’re going to stop after master’s degree. And I said, well, I’m kind of thinking about going on. He’s like, yes, yes, yes. So anyway, just real strong encouragement from, from people who had been there, felt that I had what it took, and, and encouraged me to continue going.
Todd Ream: And so that rather direct or blunt approach even perhaps works then for young people?
Kim Jongerius: It worked for me, and I’ve used it successfully in a few students, I think, myself, so.
Todd Ream: Well, and if you hadn’t heeded their caution and you would have taught mathematics, you would have had someone like me in your class. And that just didn’t, yeah. That’s not the source of our conversation today here.
Kim Jongerius: I have people like you in my classes all the time. So that’s part of the joy is being able to break through the barriers and help people who don’t think they can do math learn that actually it’s just a language and they can learn it.
Todd Ream: I can’t help but ask to, you know, when I think about NAU, which is in Flagstaff and, and Colorado State, which is in Fort Collins, both of them are college towns, which obviously, you know, embraced your educational pursuits, but offered quite a bit when it comes to outdoor recreation too and wonder if, if that perhaps also might be part of it in terms of your college choices in graduate school?
Kim Jongerius: Oh yeah, absolutely. I spent a year at the University of Arizona, and I grew up in Phoenix. I was really sick of the dessert so I was like no, I’m not staying here. I loved to ski, and friends at NAU, so totally rational, you know, legitimate academic reasons. I transferred up to NAU.
And then when it came time for graduate school, once I decided to go on, I was like, hey, you know, if I had lived in Colorado, I could ski more. And I applied to Colorado State and CU Boulder, they both accepted me. Colorado State paid more and it costs less to live there in Fort Collins than in Boulder. So I was like, okay, this is my place. And yeah, that’s all probably to blame for the fact that I have two artificial knees today, but totally worth it at the time.
Todd Ream: Skiing in your younger years then.
So you echoed this, but broadly speaking, your area of expertise is abstract algebra. For individuals unfamiliar with abstract algebra, how would you define it?
Kim Jongerius: I define it in a few words, the study of algebraic structures. Of course, that doesn’t mean much to a non-math person, so I’m going to go into a little more with some examples there.
Like we learned, starting really early in elementary school about the natural numbers. One, two, three, four, the so-called counting numbers. And it’s not too far into elementary school before you learn that, hey, there’s such a thing as zero, also. And, in fact, there are negative numbers. So we call those the integers. Zero, plus and minus one, plus and minus two, right, and so on.
Integers have an operation on them. Well, several, but the one we’re going to focus on for the moment is called addition, right? If you take any two integers, you can add them together, you get a third integer, always, no matter what two integers you take. And that operation has an identity element. Um, it’s zero for the integers. If you add zero to anything else, you don’t change that other thing, five plus zero, seven plus zero, still five and seven.
And the operation has inverses. Given an integer n, there’s another integer, minus n, that you can add to it to get back to the identity, back to zero. And that operation is associative. If you’re going to add 2, 3, and 5, it doesn’t matter if you add 2 and 3 and then add 5 into that, or if you add the 3 and 5 and then add 2 into that, you’re going to get the same result.
Okay, now, forget the integers. And see what you can understand about a generic set with an operation that has those properties. You can prove that, well, I can prove, and I think you could prove if you’re in such a class, that such a set has exactly one identity element that every element has exactly one inverse. There’s not like two minus twos out there, right? Then, there are cancellation properties, like if two plus n is the same as two plus k, then k and n have to be the same number. You started doing a little abstract algebra now. Yeah, so that’s kind of my, my general definition.
Todd Ream: Thank you. Of all the sub-disciplines within mathematics that you could have chosen, what drew you to abstract algebra, then?
Kim Jongerius: I think probably just that I had more fun writing the proofs. So a proof is always a puzzle, and different types of puzzles require different approaches. Abstract algebra approaches just kind of clicked for me.
Todd Ream: In what ways, if any, might the study of abstract algebra, then, lead to conclusions, at least for a season, that are mysterious, uncanny, or for which, no rational explanation at least yet exists?
Kim Jongerius: Well, I think if you were to ask an undergrad who’s taking abstract algebra, what’s mysterious and uncanny about it, they’d probably tell you everything, but but that just, to me, that just adds to the fact, and I think for a number of them as well, that there’s significant joy when a bunch of seemingly unrelated ideas come together into a coherent explanation of something that just seems unbelievable. And this is just the way math is.
As a mathematician, I might think something is likely to be true or likely to be untrue. But intuition only gets you so far, and it’s often just flat out wrong. To us, a conclusion isn’t something we think might be true. A conclusion is something that’s been proven using rules of logic, using appropriate axioms, using related results that were proven earlier. It’s not something we believe because we’ve seen lots of examples where it’s true.
The mystery is the journey to a valid proof. With that said, some proofs are more insightful than others, so it’s possible to know something’s true to be able to prove it, yet still be kind of surprised that it actually is true.
Todd Ream: Would you please describe one of your recent research efforts and what drew you to it? And how did you frame it? And what did you find in particular satisfying or gratifying about that pursuit?
Kim Jongerius: I’ve really been spending more time at this point in my career on editing and reviewing the work of others, rather than doing my own mathematical work. But I’ve found it to be really rewarding with similar questions, like how are these ideas fitting together? Is this a clear and valid way to explain what’s going on? Would others learn from this?
What’s missing for me, though, in that work is the creativity of doing math. As my dissertation advisor, Frank DeMeyer, used to say, a mathematician is closer to a creative writer than to a literature scholar. We write the stories, the proofs, rather than analyzing what someone else has written. So I guess that professionally I’m more on the lit scholar side of things now.
These days I get my creative outlet by writing songs about math and or teaching. So I’m not a musician at all, but I’m pretty good at rewriting given song lyrics to match a different situation. One of them was actually published in the Journal of Humanistic Mathematics. It’s to the tune of “Memories” from Cats, and it’s incredibly cleverly titled “Mathematics.” And another one will be coming out, I think, anytime now in a journal called Mathematics Teacher: Teaching and Learning Pre K through 12. It’s kind of the back page, you know, join Mathematics section, and it’s basically my favorite thing from the Sound of Music, but with all those things being a variety of mathematical concepts.
Todd Ream: So are you drawn first and foremost then to tunes from musicals when you think of this?
Kim Jongerius: Yeah, usually but not always. So one of my recent efforts was an end of the semester song to Leonard Cohen’s Hallelujah. It’s a tune that I’ve loved for, you know, years and years. And just suddenly one day the right words came to me to put the right theme anyway, to put to this tune. So it just kind of depends.
On the other hand, once I guess during Covid, when when the makers of Hamilton filmed it and put it on *Disney+ for free for everybody. Well, for everybody who subscribed to *Disney+. Watching that, I watched the king come out and start singing, you know, you’ll be back. And I thought, oh, that’s totally a professor, particularly a math professor of saying, like, yeah, you’ll look back and you’ll see how much I helped you. You know, you might hate my class now. You might hate me, but someday this’ll mean something.
Todd Ream: Thank you. I want to ask you about a couple of other related themes in terms of your career. And I’m going to go back to your undergraduate career in particular, and your study of English and mathematics. But we often hear people identify themselves in terms of how the SAT may categorize them or even silo them. I’m a math person. I’m a verbal person.
But one thread in your scholarly work, and it comes out and what we’re talking about here in terms of some of these examples, but also in your teaching seems to complicate or even defy that logic. In your estimation, then, can you say more about what mathematical abilities have to do with linguistic abilities?
Kim Jongerius: Yeah basically math is a language. It’s got its own symbols and its own grammar and it’s got definitions. For most people, I think learning math is like learning a foreign language. Sometimes the nuances of the grammar can make you afraid to use it, but you don’t have to be completely fluent to do a lot of things with it, and to have a lot of fun with it, just like you can with any language.
I think the main difference is that in English, if you misspell a word or you use a non-standard word order, people can usually still tell what you meant. Misspell a number, a formula, or some other mathematical construct and it’s like all over, right? Though, even then, as C.S. Lewis once said in an analogy to comparing religions, in arithmetic there’s only one right answer. But some of the wrong answers are closer to being right than the others.
Actually, I think he’s a great example of someone who defied conventional wisdom on this. Although his early years wouldn’t really lead you to believe that he was notoriously bad at math. He was, in fact, admitted to Oxford provisionally because of his low math scores, and he was supposed to be studying math to get his scores up so he could be fully accepted, which he was not doing. He continued to study more languages because he saw himself as a language guy.
Ironically, he probably would have been kicked out of college, but World War I intervened. He went off to war, and when he came back, they let the returning vets in with no entrance exam so we might not have the C.S. Lewis we know and love if, if World War I hadn’t, hadn’t been in the way.
When you read his work, you’ll find lots of insightful mathematical analogies, and even in his conversations with people and in his writings, writing of letters and other stuff. He has this great analogy to the Trinity. There’s this famous mathematical book called Flatland about a two dimensional world and what it would be like for a three dimensional creature to interact with it.
And he says, you know, if you try to explain to someone who lives in this two dimensional world, what a cube is like, they’re going to picture either, you might tell them six squares. They’re going to see six squares sitting side by side and lose the unity of it, or they’ll see six squares sort of superimposed and lose the individuality of it. And he says our struggles with the Trinity are much the same. So a lot of, a lot of insight there.
Charles Dodgson, you might have heard of him. He was a math teacher and author of a number of math books, perhaps better known as Lewis Carroll, his pen name, under which he wrote Alice in Wonderland and other things. And honestly, I would say maybe, of course, I would say this, but that either/or thing, it’s just not true. Like I’ve seen a lot of ACT and SAT scores over the years, and plenty of students with high math scores also have high English scores.
Todd Ream: Why is it, if I may ask, do you think that, you know, at times we would socialize and even reduce ourselves to referring, I’m not a math person? Or, yeah, why does that seem to occur more in this space than perhaps in others in life?
Kim Jongerius: I don’t know. I mean, that’s sort of a continuing mystery for those of us on the math side of things, like it seems acceptable sometimes, like an issue of pride with people, like, oh, I’m no good at math. The first thing they’ll say when they meet you is, oh, I was never any good at math. And you’re like, well, okay. I have friends who started kind of turning that around on people. Like if their dental hygienist says it, they’ll go, yeah, I never really liked looking at people’s teeth or something like that. And if you’re lucky, you get someone who goes, oh, yeah, I see what you’re doing there. But that could backfire, of course.
Yeah, so I’m not sure why, like, it’s not acceptable to admit that you’re not, you can’t read. People are ashamed of that. But somehow it’s this pride thing, like, oh, I can’t do math. And, and and of course, I think everybody can learn to do math. Now, maybe not the level that I do it, but it’s a language. If you can learn to speak a language, you can learn to speak math.
Todd Ream: Thank you. You served as president of the Association of Christians in the Mathematical Sciences from 2011 to 2013. In what ways, if any, did your service in that role, perhaps along with your ongoing involvement in the association, impact your views concerning the formation of the next generation of mathematicians?
Kim Jongerius: The ACMS and my own experience definitely convinced me that there’s a need for mentors in the mathematical community, ideally, academic advisors and then senior math faculty, once you have a job in academia, fill that role. But honestly, not all of us are equally equipped for advising and mentoring. And some grad students just don’t mesh with the professor whose research most attracts them.
Project NeXT is an organization started by mathematicians Jim Leitzel and Chris Stevens back when I was just beginning my career, and they took on this challenge of mentoring new mathematicians. It’s a really wonderful program that I learned a lot from. Not from my mentor, though, and I don’t think I’ve been all that helpful to the couple of people over the years that I’ve been a mentor for in that program, because I don’t think mentoring works when it’s assigned. It’s better to find ways to connect young scholars with lots of people with more experience in the field. Eventually, they’ll find someone they mesh with.
Aside from the difficulty of finding professional mentors, I’d say that Christian graduate students can feel particularly isolated. In grad school, the focus is almost exclusively on your research or on work you’re doing to support the research of your advisor. Maybe you’re at a school, like I was lucky enough to be at Colorado State, where teaching is considered valuable. And if you’re lucky, you get some mentoring into that role, not everybody does. But the faith side, there’s like zero encouragement to think about your faith life.
At one ACMS conference I was at mathematician, computer scientist, Satyan Devadoss was one of the main speakers. And he commented that the ACMS is a place where you can be your whole self. You don’t have to leave your faith life at the door when you go to a professional talk and you don’t have to leave your math life behind when you step into worship.
So yeah, starting a bit when I was on the board, but increasing over the years, the organization has continued to reach out to graduate students and to people early in their academic careers in math and in computer science. They provide panel discussions on topics of particular interest to grad students and faculty just starting out. They provide some financial help in attending the conferences. Information about area activities for families who come along, things like that.
At these big joint mathematics meetings that happen once a year, like thousands of mathematicians from around the country. The ACMS hosts an integrative talk one evening and then follows that by sending small groups out to restaurants around the city. All of this can help facilitate professional formation of the next generation of math and CS professors at schools like you and I serve.
Todd Ream: Thank you. In what ways then, if any, did your service in that role perhaps as well as ongoing involvement, inform your views on the role that mathematics plays in general education or on some campuses is called the core curriculum?
Kim Jongerius: I’d say the biggest influence on my thinking about the value of math has come from Francis Su’s book, Mathematics for Human Flourishing. I got to know Francis as we served together on the ACMS board for eight years. So in that sense, my membership in the ACMS played a really significant role. I think if I hadn’t known Francis, I probably wouldn’t have attended the really wonderful talk where he later expanded into this book.
On the other hand, just on my own, I’d always recognize the importance of both analytical and critical thinking, not to mention a certain foundational understanding of numbers, size, probability, other mathematical concepts. But Francis helped me realize that studying mathematics satisfies important human desires: play, beauty, freedom, justice, among others. And it leads to the development of related virtues. I use this book as one of the texts in my senior SEM course, and every time I read it, I’m just amazed again at his insights and his ability to explain them well.
If developing virtues isn’t enough reason to include significant math, there’s also the fact that mathematical theory, at least at the undergrad level, is pretty impervious to opinions. Like, you know, students say, I don’t like this. Well, you know, I don’t really care. This is the math. It just is. Sorry about that. So it’s a good place to learn to focus on logic and problem solving because what the professor thinks about how you’re talking about isn’t as important as what you’re actually writing on the paper and, and and explaining.
That said, a disciplined and determined student can learn math on their own if they need it later on. And some might argue for that going, well, it’s going to mean more to them when they actually see they need it. But it’s not as simple as just reading about it. Like to understand the concepts in the math books, you really have to work things out as you read, you have to check the details of the examples to make sure you understand them. You have to work problems from start to finish on your own. Make sure you see how the definitions and theorems are fitting together and being applied.
Most people find it a lot easier to learn in a community in the classroom than to try to do that on their own. It doesn’t mean that students that I would say have a deficient math background can’t make it through graduate programs that require analytical and computational skills, but they will have to work harder than colleagues who were better prepared. And a lot of people just avoid such programs because it means a lot of extra work.
I get, though, there are limits to this kind of thinking. Like, we can’t make every student minor in every discipline in case someday they might want to pursue something that uses that. But given how many disciplines require mathematical thinking, math does not seem like a good idea to skimp on that.
Todd Ream: In addition to limiting a young person’s ability to thrive in graduate school, what other hindrances might we be allowing young people to walk into by reducing or even in some cases eliminating mathematics from general education? What sort of problems are we inviting or limitations even if they’re not studying formally mathematics?
Kim Jongerius: I really think just, just an understanding that they can figure things out. Figuring things out in math was always part of my studying, and I wouldn’t say I had always the best math teachers. I had some really good math teachers, some maybe not so good, but there were always problems I had to work through on my own and think about. I didn’t find that at that level in other disciplines, so just be able to persist through to a solution in the face of stuff you’re not understanding.
I think not enough young people, well, people in general have that, right? We tend to just look at something and go, oh, that’s too hard. And we give up and we don’t, we don’t keep thinking about it and see if maybe there’s some background information we know that could help us understand that problem better, or maybe just an idea that we can then look up more information about that might help us understand it better. I think we’re too quick to give up. And I think that mathematics can teach us the value of persisting in, in our work.
Todd Ream: Yeah, of which there’s been an increasing amount of conversation about in terms of young people and their ability to persist and how do we cultivate or develop that?
So our time, unfortunately, begins to become short. I want to shift now to asking you about your understanding of the academic vocation and your role as a mathematician in helping you understand that.
What qualities and or characteristics define your understanding of the Christian academic vocation? Especially, from the perspective of serving as a mathematician?
Kim Jongerius: Well, I’ve mentioned some of these already. I think curiosity, perseverance, the desire to find and communicate valid explanations and connections. Those to me have always been the hallmarks of the academic vocation. I’d say the only thing that’s really changed over the years is my increasing awareness that students don’t all have access to the same resources.
Even things as simple as getting good sleep and getting three good meals a day. Both of those have well documented effects on learning and ill effects if you aren’t getting those. I wonder sometimes how many potential scholars we’ve never had the opportunity to learn from because of factors that really have nothing to do with their ability.
Todd Ream: Thank you. In addition to certain virtues that mathematics requires, and needs to be, and mathematicians need to cultivate, are there any vices that you would identify may prove important for us to be vigilant in observing, and perhaps even confronting?
Kim Jongerius: Yeah, this one is true of academics in general, but maybe particularly for mathematicians the vice of arrogance. It’s really, really common, as we’ve already discussed, for people to say to mathematicians something along the lines of, I was never any good at math. You must be really smart. And I mean, who doesn’t like to think they’re really smart? But it’s like there’s no awareness that hard work is involved, you know?
I’ve even been told by a few people with PhDs in other fields. Like I could never have gotten a PhD in math. I mean that stuff can go to your head and maybe it’s a little worse for me perhaps than for some because I love reading and writing too and I’m pretty good at writing. I wouldn’t say I’m better at reading than anybody else, but I’m a decent writer. And I’m pretty sure I could have pursued any graduate degree that I might have wanted to.
So instead of focusing on that idea, I frequently remind myself and others that it’s about hard work, not about some innate gift. Many so-called non-math people, I really believe, if they had wanted it badly enough, and had been willing to work hard enough, could have gotten a PhD in math.
Todd Ream: Thank you. For our last set of questions now, I want to ask about mathematics and the contributions that it can make to other disciplines. In particular, how do we help colleagues and other disciplines become more aware of the contributions that mathematics can make and become more receptive to those contributions?
Kim Jongerius: I think maybe I’m being a little unfair to other disciplines here, and particularly in the humanities, so you can correct me if I’m wrong. But one example is I remember attending a faculty research in progress group in my early career, and my humanities colleagues would literally read their papers to me, and I found it really frustrating.
Like, I can read, and I can do it faster in my head than someone else can read it for me. Uh, just just hand me the paper, you know? If you’re not going to summarize it for me just give it to me and I’ll read the thing. I think I’ve seen someone read a paper exactly once at a math conference, and I’m pretty sure that everyone in the audience was mentally pulling their hair out. Like we want to know the results. We want to know the key details of the proofs, but we do not want them read to us. We’ll read the paper later ourselves to get those details.
So I’m going to this group. I’m the newbie in the group. I’m like, 29 years old. You know, everybody else has been doing this for decades, whatever it seemed like. And after a few weeks in the research group, I asked my colleagues, why are you reading all your papers? Like in math, this is actually frowned on. You would, you would never read your papers, so on.
And one of them said that at their conferences, you submit your paper prior to the conference and someone else prepares a response to your paper. And if you don’t read your whole paper, then when the audience hears the response, they might not understand how the response is even connected to your paper. Which, okay, I can sort of understand, except this still remains a completely foreign idea to me.
I mean, after our math talk, someone might offer us a somewhat similar verbal response would be in the form of a question from the audience usually. Something like, hey, have you thought about the connection between your ideas and this other concept already, this is a more cooperative approach, right? The speaker could say, yeah, I did think about that, but I decided to pursue this other angle instead. Or maybe they say no, but that’s really interesting. Hey, you know, my email is up on the slide. Why don’t you contact me later? And let’s talk about this a little bit.
Part of the distinction is definitely because of the difference between proof and other disciplines. Sorry, if I can’t help myself, and proof in mathematics. If I applied the theorems correctly, you know, if I use logic correctly, if I have my axioms clear, then my proof is going to stand the test of time. But I think there’s more, so I’m watching someone else. I might think there’s a more clear way to go about the proof, but if the proof is valid, I’m not going to tell them they’re wrong because, because they’re not wrong. You know, it’s a valid proof.
But I do think that these kinds of research and progress groups with members from a variety of different disciplines can really offer a fantastic way for different disciplines to learn from each other. And in that kind of setting, mathematicians might show by example how sticking to the key ideas of an argument can make for a far more compelling presentation and one that would stay with the listeners longer so they engage those ideas longer.
Todd Ream: Thank you. Our last question is then, the Church as a public that mathematicians can serve, what contributions do you believe mathematicians are uniquely positioned to be able to make to the Church? And in what ways can the Church become more receptive to those contributions?
Kim Jongerius: I guess I’d still say persistence, cooperation, organization, and clear communication, including wanting to really understand what somebody else is saying, not just assuming you know what they’re all about. I think those are important things mathematicians can contribute. Generally, I’ve found that even people who are not particularly logic-focused themselves can appreciate the skills offered by those who are.
To get people in church to recognize that, you can’t tell them it’s there. I think you have to be willing to participate in significant ways. You have to attend and perhaps lead Sunday school sessions. You have to be willing to serve in church leadership positions. You have to offer your organizational skills to service opportunities that your church provides. When, when people see that you’re willing to help out, I think they’re more likely to pay attention to what you bring to the table.
Todd Ream: Thank you very much. Our guest has been Kim Jongerius, Professor of Mathematics and Chair of the Mathematics Department at Northwestern College. Thank you for taking the time to share your insights and wisdom with us.
Kim Jongerius: You’re welcome. It was fun.
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Todd Ream: Thank you for joining us for Saturdays at Seven, Christian Scholar’s Review’s conversation series with thought leaders about the academic vocation and the relationship that vocation shares with the Church. We invite you to join us again next week for Saturdays at Seven.
