“The Precision of Mathematics” ft. the University of Notre Dame’s Mark Behrens I Saturdays at Seven – Season Two, Episode Twenty-Six

Click here to listen to the episode on Spotify

In the twenty-sixth episode of the second season of the “Saturdays at Seven” conversation series, Todd Ream talks with Mark Behrens, the John and Margaret McAndrews Professor of Mathematics at the University of Notre Dame. Behrens begins by unpacking the unique ways mathematics provides logical and replicable results. He also notes mathematics can prove mysterious when connections between results one did not expect, or at least initially did not expect, emerge. Identifying those connections, however, yield some of the greatest forms of satisfaction mathematicians can experience. Behrens shifts to talking through the ways various mentors fostered his love for mathematics and eventually his expertise in topology. As one who served as the editor for various prominent mathematics journals, Behrens also offers insights concerning the rapid nature of new results emerging in subdisciplines such as topology. He also discusses how mathematics, once a discipline dominated by individual efforts, is now dominated by collaborative efforts. The conversation then closes with Behrens sharing his understanding of the virtues mathematicians are well served by cultivating, the vices mathematicians are also well-served by confronting, and the ways mathematicians can be of greater service to scholars in other disciplines.

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.

—

Our guest is Mark Behrens, the John and Margaret McAndrews Professor of Mathematics at the University of Notre Dame. Thank you for joining us.

Mark Behrens: Hi, thank you.

Todd Ream: I’d like to open our conversation by asking about a 1960 article by Eugene Wigner. For our audience members unfamiliar with Wigner, he served most of his career on the faculty at Princeton University, served briefly as the Director of Research and Development at what became the Oak Ridge National Laboratory, and won the Nobel Prize in Physics in 1963 for his contributions to the understanding of the atomic nucleus. 

In February 1960, he published the “Unreasonable Effectiveness of Mathematics and the Natural Sciences” in Communications and Pure and Applied Mathematics. When reading this article, I found Wigner resorting to curious and inviting forms of language. For example, in his first 2 points, Wigner claims, “the enormous usefulness of mathematics and the natural sciences is something bordering on the mysterious. And there’s no rational explanation for it.” 

In his second of two points, he then contends, “it’s just this uncanny usefulness of mathematical concepts that raises the questions of our physical theories.” To begin our conversation, I wanted to ask you how prone are mathematicians and physicists to using terms such as mysterious and uncanny in summations of their efforts? 

Mark Behrens: I think we use that terminology a lot but I think in a way that’s different from the way that, that, that Wigner is maybe talking about in his article. I mean, in the article, it seems to me like he’s asking, he’s suggesting that it’s, it’s mysterious or strange that we can describe the laws of nature with mathematics, like that mathematics is the right language or the right framework in which to describe these laws.

But I don’t think that, I mean, obviously everyone has a different relationship with their way of thinking about it. I don’t find that aspect mysterious at all because to me math is just logic, like and if you’re applying logic to understand behavior, predictable behavior of nature, that’s just what you’re doing. So naturally, it’s and you’re using quantitative techniques oftentimes, so naturally mathematics is going to be the way in which these things get expressed. That’s not mysterious to me. 

But we do use the term mysterious a lot because a lot of times what we do is we’re discovering different things that are true, like proving theorems, discovering different mathematical truisms. And all of these discoveries precede through logical deduction. So they themselves aren’t mysterious from the point of view that you’ve already shown them to be via mathematical logical deduction. 

What’s mysterious is when you find a connection between two things that you didn’t, you didn’t expect. And so that’s where we’ll often use the term mysterious, or maybe we’ll observe in a bunch of examples, a phenomenon that, that, that appears to always happen, or maybe in a, in many different contexts, but we can’t yet find a framework that explains that. And so then we’ll call it mysterious even though we know it to know it to happen. 

Todd Ream: Despite his command for math and physics, in what ways do you think Wigner resorts to making such observations, perhaps, due to his inability to draw upon other ways of knowing to draw from, perhaps, other academic disciplines that may be off able to offer him our resources?

Mark Behrens: It’s kind of weird. I mean, like, like, like it, in my mind, in my mind, math is sort of tautologically the right way to approach the questions of describing laws of nature. And so from that point of view, it’s like, okay, well, why would you take something that’s so perfectly adapted and swap it out with something that maybe isn’t.

Wigner seems to be suggesting in his article that be worrying that maybe there’s another way, another language or another framework to understand nature that we’ve never thought to use, you know. I don’t know, like, to me, it’s sort of tautological that math is the language because it’s just logic and deduction. 

But I think that what other disciplines can offer, say a physicist or a mathematician, are different perspectives that might cause them to define or think of new things that they didn’t think of. Like a mathematician they could only study the concepts that they first come up with. Like, we have to first define an object, and then we can study it, right? But we might have not thought to make a definition. We might not have thought to study. And so that’s where other disciplines come in. 

I mean, as a mathematician, it’s very common for concepts to come up in physics that we never thought about. And then, it’s like, oh, let’s make a mathematical framework and study that mathematical framework. We do that all the time. 

You know, I think philosophy, I think religion, I think all the theology, I think all different disciplines have different things they might come across that you might have not realized is a thing and then it might inspire you to create something that you’ve never created before as a result.

Todd Ream: In what ways, if any, is mathematics perhaps an expression as an expression of the academic vocation defined by persistence in the pursuit of truth through that which is otherwise mysterious, uncanny, or at least for a season, scholars think may not offer any particular rational explanation. Is mathematics defined by that working through those details to perhaps come out the other side?

Mark Behrens: I think in some sense, yeah, I mean, in the sense of mathematics is meant to like— say, there’s a phenomenon that’s mysterious, right? And then the goal of a mathematician would be to explain that phenomenon through a mathematical framework, through a series of deductions and therefore, make it not mysterious, right? You know to say okay, it happens because of this. That’s how I feel like what our job is.

Todd Ream: Thank you. I want to ask you a couple of questions now about your own journey with mathematics. And it started with mathematics and physics, actually, as an undergraduate. You were a double major at the University of Alabama, earned a master’s in mathematics, again, from Alabama, but then a doctorate in mathematics from the University of Chicago. At what point did you sense that mathematics would prove central to your sense of vocation?

Mark Behrens: I sort of chose physics kind of randomly. I was originally wanting to be a musician and then, then feeling like I wouldn’t make it. Then read a book about physics and it sounded interesting and so I went into that. But in the process of doing physics, you have to learn a lot of mathematics. And I quickly realized the precision of mathematics, the sort of absolute knowing of certain things and the defining objects very carefully so that you know what you’re talking about was very appealing to me.

But it also was there’s no way I would have gone down this path without many mentors that just spent hours and hours of their time helping me out so they helped what like, I got interested in this, but it was through their encouragement and through all their work that made it actually successful for me.

Todd Ream: Are there any individuals and/or experiences with those individuals that you would note that proved more formative than perhaps others in terms of your vocation?

Mark Behrens: I mean, even shoot, like my linear algebra teacher, Martin Dixon, he gave me my first kind of formal mathematics course with proofs and math mathematical rigor. And I had no idea what was going on at first and by the end of the, by the end of the class, I was loving it. You know and at the end of the class, he asked me, have you ever thought about becoming a math major? And I had not, right? But never would have thought that had he not said that, right? You know, so I think sometimes just for somebody to write to alert people that that’s a possibility. You know, that’s something. 

And then Alan Hopenwasser was another professor there who took me under his wing and did some mathematical readings with me. I worked for years with another mathematician, Bruce Trace, and then another professor there, Norhiko Minami, got me into my current subject that I do. You know, all these people, meeting with me every week, sometimes for hours. I mean, that’s a lot of time. And that’s I think that’s extremely valuable.

Todd Ream: Thank you. You began your career by serving as a postdoc and then tenure track faculty member in mathematics at MIT. And along the way, you served as a visiting professor at Harvard University and then more recently at Northwestern University. How did those experiences or commitments shape your sort of research efforts and your focus?

Mark Behrens: When I came to MIT, there, there was a lot beginning to happen and a lot unfolded while I was there in terms of a lot of research directions in my subject that have I mean, a lot of activities been going on in terms of solving big problems in my subject in the past several years. And a lot of that seemed to start while I was there. 

You know, other people were there doing this stuff. And so it was like, it was kind of like coming to like ground zero at this very exciting time and seeing all these new ideas gestate and come forth, so that was a huge influence for me. 

And you know, in general just being around other people doing amazing new ideas, they help you come up with new ideas. And you know, it’s inspiring.

Todd Ream: How did those experiences also shape your commitments, say, to teaching and then to service, both beyond and on your campus?

Mark Behrens: I mean, in terms of teaching, I mean, at MIT, I didn’t really have to think too much about teaching because MIT, MIT students are kind of intense and crazy in a certain way so they’re the only students I’ve ever met who might complain the homework was too easy or there wasn’t enough homework you know. I never really worried about what I kind of threw at them.

But in other contexts, I did worry like I thought, okay like this is I’m teaching a calculus class. These are freshmen. You know, a lot of them probably don’t want to take this class. You know, they probably dislike mathematics. How can I make this bitter pill easier to swallow, you know. 

But lately, I’ve been rethinking that, I’ve been thinking instead that actually, maybe, maybe diluting it is not the way to go. Like maybe instead, the way to go is to instead is try to convey why to go full in and then explain why this is interesting, like you’re coming to a university to all your different classes, you’re experiencing ideas and things that you never experienced before. Why shouldn’t your math class be any different? It should be just as transformative as your first philosophy class. And so I’m trying to be more authentic in my undergraduate teaching. 

You know, in terms of service, I think a lot about all of those mentors that helped me over the years and I see if I can perhaps imitate or give back or, or do what they did for other people that want to follow this path.

Todd Ream: In 2014, yet, then you accepted an appointment at the University of Notre Dame. What led you to accept that appointment and in what ways maybe have these sensibilities in terms of research, teaching and service changed over the course of the 11 years you’ve been in South Bend?

Mark Behrens: I mean, I guess for Notre, Notre Dame I was, I was on the job market and I had different possibilities. And at the time Notre Dame had introduced an initiative to greatly enhance their topology program. And it just seemed like a great opportunity to get in right at the time when they were going to do this rebuild and then augment this group. And so that was very appealing to me. 

You know, another, another thing I was just beginning to re-engage with my Catholic faith. My child had been born in 2012. So my first child came into my life as a stepson, and he already kind of grew up in the Church, as it were. And so I never was really sort of concerned about him knowing anything about what faith is. I actually don’t care what my kids do in terms of faith, but I want them to have an idea of what faith is, you like, as opposed to not having any idea. And so I wanted to have some context for my daughter.

But you know, because I went to the only framework that I personally knew, which was Catholicism. And so I enrolled in an RCIA there, and so in that re-engagement, then the idea of going to an institution that was linked with this was kind of appealing to me as well, you because I was really inspired by the conversations that I was having with the with the retired priest that was running that.

And then frankly my wife also in terms of the various options, she told me like, based on what Notre Dame was doing, she’s like, you have to go there because this is going to be the best place for your research and I always listen to my wife.

Todd Ream: That’s smart on multiple levels, I would say, at least from my personal experience. In what way since coming to Notre Dame have you been able to take advantage of the insights and wisdom that are housed within other disciplines or by faculty colleagues, not only just within mathematics, but also beyond mathematics?

Mark Behrens: I mean, in some sense, I feel like I could do more in that regard. There are, there are people that I know have connections with the physics department or have connections with the philosophy department. And I’m not one of those people and you know, sometimes it’s just lack of time you know, there’s only so many hours in the week when you have enough weekly meetings and then you have to find time for your research and your teaching and before you know it.

I do find that sometimes they’ll have events, like you know, lectures and things like that, that are really enriching and thought provoking. And so I feel like just being on a campus that brings in a lot of these activities can also fulfill that role.

Todd Ream: Thank you. I want to ask you now about your area of expertise. You mentioned topology and that’s part of what led you in terms of the University of Notre Dame’s investment in its topology area within mathematics. For individuals who are unfamiliar with topology, how would you define it?

Mark Behrens: So basically it’s a study of higher dimensional shapes. So you can ask what are all the different surfaces that you can create? Now for a topologist, we say two surfaces are the same if you can deform one into the other. So for us, like a cube and a sphere are the same object because if you think about that cube is being like made of rubber and inflate it with air, it will eventually kind of turn into a ball. So for us, those two are the same. 

But a donut is distinctly different because no matter how you twist that donut or deform it will never turn into a sphere because it will always have that hole in it, so those are like two dimensional shapes sitting in three dimensional space.But we’re interested in n dimensional shapes, perhaps sitting in m dimensional space, or maybe not sitting in any space at all, right? 

And it’s reasonable to ask, well, why should you care? I mean, we live in a three dimensional universe, four if you count time, but we don’t know what the shape of the universe is. How can we even answer that question if we don’t even know what four dimensional shapes are possible? 

Todd Ream: Thank you. Of all the sub-disciplines within mathematics then, what drew you to the study of topology?

Mark Behrens: I started off in analysis, which is like calculus, basically just a fancier version. But I, but I was really interested in the idea of doing integration on these shapes and so we would call them manifolds.

And so then that got me interested in it, got me into what we call differential geometry. And then I realized that the aspects of differential geometry I found the most interesting were those aspects where they didn’t change, if you change the shape and, you know, if you deform the shape, that is to say. And so this then becomes topological questions. And so I sort of realized this was what I found most interesting.

Todd Ream: In what ways, if any, might the study of topology lead to conclusions, or at least initial conclusions, that are mysterious, uncanny, or for which no rational explanation may yet exist?

Mark Behrens: Sometimes we might do what we would call computations, where we might see all the different examples of a different phenomenon happening and a different dimension or something like that. But then we don’t have an explanation for why you can do the computation in that sense, it’s not mysterious, you did the computation. It’s logic. 

I mean that’s the thing about mathematics. It doesn’t have contradictions. That’s what’s different about mathematics and just about any other thing. It doesn’t have contradictions by its nature. If there’s a contradiction, that means that you made a mistake, there was a human mistake somewhere, right? It’s there because you’ve got your deduction that says it’s there, but maybe you’re seeing a phenomenon that you can’t explain why that pattern is there, you know? And so then that’s the mystery and that’s what we encounter all the time.

It’s kind of like how a physicist does experiments, sees a phenomenon, and then has to, and then wants to come up with a theoretical framework to explain that phenomenon they witness in their experiments. It’s the same thing.

Todd Ream: Would you describe for us one of your recent research efforts, and what drew you to it, and how you came about to frame it?

Mark Behrens: I’ve got a paper I put out recently with a postdoc named Jack Carlisle where we study something called equivariant periodicity. So equivariant is basically the study of things with symmetry. And we’re thinking about very simple symmetries, like maybe things where, with a flip symmetry, like if you take them and flip them, they’re the same, or things that if you maybe rotate them by a quarter, you know, each time, then they’re symmetric. So something like that, right? 

And so equivariant topology is a study of shapes with symmetries. And so you could take any question that you would normally ask in topology and ask, okay, what if we add a certain symmetry to it, then how does that change this question? 

So the thing that I specialize in are what are called homotopy groups, specifically homotopy groups of spheres. So what these are is these are the different ways to wrap a high dimensional sphere around a low dimensional sphere, which might seem like a sort of weird thing, like why would you want to do that? But it turns out that every single one of these shapes that I describe, these higher dimensional shapes, is built by taking a higher dimensional ball, whose boundary is a sphere, and gluing that boundary along another shape and doing this iteratively.

And so basically you have to know how to wrap these higher dimensional spheres, which are boundaries of higher dimensional balls around other spheres in order to know what the structure of these geometric shapes are. So that’s why we do that.

Todd Ream: And I would assume that there may be considerable applications for such thinking in areas not only physics, but also engineering?

Mark Behrens: It’s kind of funny. I don’t really think too much about the applications to be honest with you, but that doesn’t mean they don’t happen. I think that they do, and I’m often surprised when they do, but I’m oftentimes oblivious to them and it doesn’t, in some ways, it doesn’t motivate me very much. I mean, that sounds weird. 

Like for me, I think that there’s questions that are natural, like that are natural and interesting to ask. And then you ask them and try to find the answer? You know, and then there sits a repository of answers to natural questions so when somebody in another subject asked this question, they were like, well, this sounds like something a mathematician would have thought of. And if we have the answer waiting for them, then we’ve done our job.

Todd Ream: So along those lines then, in say, in terms of the particular project that you and Jack recently pursued, what did the two of you find that was sort of intrinsically appealing or gratifying in the pursuit of that effort?

Mark Behrens: So one of the things that happens that, one of these sort of mysterious things that you might call it that happens in these in the regular homotopy groups of spheres, the non-equivariant, the ones without symmetry, is is that it turns out that there are certain, there’s certain patterns in the ways these things wrap, you know in these homotopy groups across many dimensions. And the dimensions are repeated with a fixed period. 

Okay. And so like maybe an eightfold periodic pattern emerges or, or a 192 periodic pattern amongst dimensions. Like it may be weird to think, we’re studying dimensions every 192, like what the heck, you know? So we’re studying hundreds of dimensions. That’s what we’re doing. Okay. So this is periodicity or chromatic behavior that I’m speaking of. So what we were looking for that equivariantly, and there were many other things that many people have done in this direction. And we were sort of building on that work. 

And so one of the things that I studied in my thesis, was this, this thing called the Mulholland variant, which was a transformation that took one kind of periodicity to another periodicity in the homotopy groups of spheres and this construction itself, people have observed that it can be made from one of these equivariant or symmetry kinds of perspectives.

And what we discovered was that the equivariant periodicity explained the connections between the periodicities in the input and the output of this invariant. So to me, that was like great. That was really interesting.

Todd Ream: Thank you. You’ve served as the editor for several journals and presently serve as the editor for Geometry and Topology. As an editor and a prominent scholar in your field, what advances in topology have you witnessed over the course of your career?

Mark Behrens: I mean, a heck of a lot. I mean, our, our whole, our it’s, it seems as if it seems as if things are just always happening and, and changing. You know, our whole sort of language that we’ve been using to express our results was revolutionized by this mathematician, Jacob Lurie, who really turned the subject towards thinking about these things called infinity categories as a different kind of operating system to work in. And that seems to really be taking hold and doing, doing amazing things. 

There was these equivariant techniques that I was speaking of really came back into the forefront after many years of sort of not being widely considered when Hill, Hopkins, and Ravenel solved this long standing problem, like this 50 year old problem called the Kervaire invariant problem, which was about certain, what dimensions certain manifolds could have certain properties, and they did it using these equivariate techniques. So that was interesting. 

And very recently there was another longstanding problem about this periodicity phenomenon that I speak of called the telescope conjecture, which is really a question about whether there can exist certain periodic families that are almost undetectable, a kind of a dark matter in our periodic homotopy groups. It was something we never actually witnessed in our computations, but knew theoretically could be there. They proved that, in fact, it’s there and most of the groups out there are predominated by this dark matter. So like, that’s a fascinating discovery. And now, we have to go out and see if we can actually detect it and see it in our computations.

Todd Ream: So there’s no shortage of activity going on and no shortage of possible topics moving forward then?

Mark Behrens: Oh, no, no, it just multiplies and multiplies. It’s almost hard to keep up with.

Todd Ream: Yeah, that’s great. 

As we turn toward the end of our conversation, I want to ask you, as a mathematician and topologist, qualities and or characteristics define your understanding of the academic vocation. And in what ways have those qualities perhaps maybe even changed over the course of your career from when you started at MIT to where you are today?

Mark Behrens: I mean, definitely when I first started out, I was just trying to get a career going, right? So I was just like, okay how can I get my foot in the door? How can I make this a successful career? You know, how can I get a job? You know, how can I make sure how can I get tenure? You know, these are pretty practical questions, you know. And this was sort of the things that were driving me in addition to just my interest in the subject, right. 

Now, I feel like I think a little more with a lot more perspective both realizing the privilege and the gratitude that I have for being able to do this as a career, this thing that I love and interact with other people that do it. That’s just great. 

But also thinking about how I can help other people that are trying to follow this path. You know, how can I use my perspective? How can I use my learned experiences to help them on this very difficult and challenging path?

Todd Ream: What virtues then, whether they be intellectual virtues, moral virtues or theological virtues, do you believe are most important to cultivate as a mathematician and perhaps also as a topologist in terms of one’s ability to, to succeed and flourish in those fields?

Mark Behrens: I think the virtue of openness, of like open knowledge of open, like, I think there’s a lot of tendency to want to carefully guard the things that you learn or discover like that you might be worried, okay, other people are going to are going to, if they, if they have this, then they might sort of jump ahead of me or something. To think more about your position in the race, as it were, rather than our collective knowledge as humankind of mathematics and sort of what we know and what we can know. 

When we work together, when we share our ideas openly, then we’re going to, we’re going to move much faster to answer these questions. We can make discoveries much more quickly by working together and, and, and just forgetting about the idea of personal glory or personal gain. If we just put up, pull on, put all our cards on the table and tell everybody, everything we know, that’s a virtue that can help the subject.

Todd Ream: Ask a related question here, in other fields within the natural sciences, but also in the social sciences and to some extent even in the humanities now, we’re seeing more and more people working in teams and working together on problems. Is that beginning to, you talked about your work, say with Jack Carlisle, who’s a graduate student with-

Mark Behrens: He’s a postdoc, yeah. 

Todd Ream: Postdoc. Is that becoming more and more common?

Mark Behrens: Oh, yeah, yeah. No, that’s another way in which the subject has changed a lot since. When I was just graduating, it seemed to be very common. I mean, collaborations always happened through history, but it’s very common to just write papers just by yourself or work on projects just by yourself.

Mathematics was largely a solitary game, and that’s just transformed in the past few decades, like the last couple decades. It’s just now it’s like a team sport, you know. It almost seems as if it’s very rare for problems to be solved by one individual, rather, it’s usually a team of people. And usually you’ve got a problem, you put together a team solve the problem. Improvements in communication just like, look at us talking by video from two different places. I mean, the fact that we can do that revolutionizes these possibilities.

Todd Ream: In your estimation, have tenure and promotion processes then kept up with those changes to honor and recognize the validity of contributions that are done in collaborative contexts, say solitary or individual contexts?

Mark Behrens: I mean, in my subject, the answer is definitely yes. I mean, like we’ll say, okay people it’s a collaborative game now everybody recognizes that. Nobody’s going to see that most of your papers are collaborations are they that that shouldn’t count. All your papers are collaborations.

Todd Ream: For asking the flip side of the question in relation to virtues, then are there any particular vices that you believe it’s important for mathematicians to be vigilant against that can creep in and cloud perspective or pose challenges to a proper understanding of the vocation?

Mark Behrens: I think the thing I mentioned about you know, about people, maybe getting too worried about the person or as opposed to the math. I think that’s a vice. I think that’s, I think that’s a danger. I think competition can be healthy in the sense like sometimes it can help you bring your A game to feel a little competition, but it can also be destructive. It has to be very careful to keep it healthy and not allow you to do anything that would, you know, jeopardize the integrity of what you’re doing. 

I mean, it’s really a sacred honor to be able to study this sort of fundamental problems of thought and that’s what we’re here to do. So I think it’s important to keep that in mind.

Todd Ream: As we get ready to close our conversation, I want to ask you if there are about mathematics and its impact in other areas, fields beyond mathematics, and what that could look like, what contributions do you believe mathematics is uniquely positioned to make to colleagues who are called to serve in other disciplines?

Mark Behrens: I mean, we have a way of thinking. I mean, as I mentioned we have this, we have this luxury that our objects are so well defined that, that contradictions aren’t then a matter of debate. They mean, okay, somebody made a mistake, right? You know, almost no other subject has that. 

But it causes us to think in a certain way that I think is different from certain subjects. It’s kind of like extreme logic of some kind and I think that that kind of mathematical thinking or that sort of the sort of idea of trying to make your ideas very precise I think that that kind of thinking translates into other disciplines. It’s inappropriate to expect that there is that level of precision possible. It still gives you the idea that you could think in these terms is a different way of thinking.

And so I think that, I mean, mathematicians it’s very common for mathematicians to go off into other disciplines, right? And I think that they bring with them a different way of thinking that, that, that other people enjoy and find interesting, or people that even study math as part of end up doing something different or just to get exposed to mathematical thinking and do something different. I think that that kind of mathematical thinking can give them a different way of approaching their problems. You know, so I think we have a lot to offer in that respect.

Todd Ream: In what ways can colleagues in these other disciplines become more aware of the contributions that mathematicians can make, become more receptive and even make more use of those contributions?

Mark Behrens: I mean, maybe it goes on both ends, right? Like maybe we as mathematicians need to be able to engage better with other, with people in other disciplines and be able to convey our ideas in ways that are understandable and can be received. Then, of course, other disciplines then probably should realize that mathematics can be a very valuable tool. 

You know, I think economics and in pretty much any science and biology in many different areas the idea that mathematics can help your subject has taken hold that we have something to offer that when you apply it to your problems could give you surprising results.

Todd Ream: To close then I want to ask these kinds of contributions that we’re talking about in what ways do you think they can be of benefit to the Church? And can the Church become more aware of them and make more use of them moving forward as it thinks about its engagement with the world? 

Mark Behrens: I guess there’s several layers to this, right? I mean, like, like one is, I’ve talked about the mathematical way of thinking, and then there’s like what mathematics actually can do for a subject, right? 

From my, from my personal point of view what I’m not saying is take every word in the Bible and make logical deductions from that. I think that is very damaging, right? I think that things need to be put into context and layers of meaning need to be applied as people do, so well. I think that maybe our perspectives on problems, maybe that kind of perspective can be ported beneficially to other areas, including the Church.

Todd Ream: Those habits of mind so to say.

Mark Behrens: Exactly. Exactly. Yes.

Todd Ream: Thank you. 

Our guest has been Mark Behrens, the John and Margaret McAndrews Professor of Mathematics at the University of Notre Dame. Thank you for taking the time to share your insights and wisdom with us.

Mark Behrens: Well, thank you. I appreciate it.

—

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.