Great Professors: John Voight

Editor’s Note: We spoke with Associate Professor of Mathematic John Voight about his role, his time at Dartmouth, and his interest in cryptography.

The Dartmouth Review (TDR): Just to start off on a lighter note, what has been your favorite teaching moment in your time at Dartmouth?

John Voight (JV): You mean I have to pick just one? Mathematics has a reputation for being a difficult subject—and to some extent it’s true, usually we struggle at first to grasp the underlying concepts. But at some point, after contemplation and coffee, there is an “aha!” moment! In class, when this happens I can hear a little ‘clicking sound’ in my students’ heads when finally the ideas become clear. Those are my favorite moments: seeing my students empowered in their understanding of mathematics!

TDR: How did you come to teach at Dartmouth? What appealed to you about Dartmouth at the time and has it lived up to those expectations?

JV: I received my Ph.D. from UC Berkeley in 2005, and then spent a postdoctoral year at the University of Sydney and one at the University of Minnesota. After that, I taught for six years at the University of Vermont before moving down the road here to Dartmouth. I had visited Dartmouth before to give seminar talks, and I immediately recognized what a special place this is. On a superficial level, you can’t beat the splendor of Kemeny Hall, the handsomest math building around! But more deeply, I was drawn to Dartmouth because it presented me with an opportunity to work with talented undergraduate and graduate students while at the same time providing support for my research. The College is exceptional in the way it emphasizes these two activities as mutually reinforcing rather than as zero sum: we call ourselves teacher-scholars. The students here constantly blow me away, and I’m very glad I came.

TDR: When you were younger, did you ever envision yourself becoming a professor one day?

JV: I wasn’t sure what I wanted to do when I was young. My first passion was classical piano, and for a while I thought that would become a concert musician. But at some point—I recall being prompted by a certain frustration with a Bach three-part invention—I concluded that in the twenty-first century, we only need so many concert pianists. So my thinking shifted. I was also on the debate team in high school and college, and so like many of my friends I thought I would become a lawyer or work in government. But eventually, I heard my true calling. I realized that my curiosity never seemed to be satiated, and what I really wanted was to be uselessly over-educated! Hence a professor.

TDR: How does working at Dartmouth compare to working at UVM?

JV: Well, the institutions have quite different histories, and students go to UVM or to Dartmouth for completely different reasons. There are rather stark differences between working at a state institution and a private one—these start at the top and are felt all the way down. I went to Gonzaga University, a private, Jesuit, undergraduate school (go Zags!) and then went to Cal for my Ph.D., so now I’ve seen both sides, as student and professor. Somehow, I feel like Dartmouth captures the best of both worlds, if that makes sense. However, I miss living in Burlington, Vermont: it is a much more exciting town than Hanover, but then it’s hard to imagine a town that is less exciting than Hanover!

TDR: How do you believe the math department stands in relation to the other departments at Dartmouth? How has it progressed over time?

JV: The College president, Phil Hanlon, is a mathematician; and of course John Kemeny, a former president who was also a professor and chair of mathematics, transformed the College in profound ways. We count among our ranks a house professor (Craig Sutton) and the director of the East Wheelock cluster (Sergi Elizalde). So it seems that the math department is well-represented in campus, academic, and student life.

I became the vice chair of the department starting in Fall 2016—but I think I was nominated mainly for the “vice” part, less the “chair” part. Our department is growing in important ways as we reach out to majors and as we endeavor to raise the profile of our graduate program with a renewed focus on applied mathematics. What do we want for our students now? What kinds of jobs are they getting? What is compelling to them, what captures their imaginations? As we answer these questions, we’re designing and adapting our courses, hiring faculty, and so on. The future is bright!

TDR: Do you believe that Dartmouth provides its students, even those that do chose to major in STEM fields, with a strong background in the liberal arts?

JV: Well, at least the math major at Dartmouth is quite flexible, leaving plenty of room to take enriching courses in the liberal arts. I must assume the same is true for the other STEM disciplines. I think the term calendar at Dartmouth probably helps: you have concentrated courses which means you can take bites of many things. But I know it can be tricky with engineering: I started off as an electrical engineer at Gonzaga, and so my first two years I was taking overloads filled with the math, computer science, and humanities classes I wanted. But then I saw the light! And I changed my major to mathematics, which helped to relax my schedule.

TDR: Do you feel that there is a greater value in studying a particular subject over another?

JV: In my experience, the most interesting, most well-informed individuals—the ones that are making the greatest impact—they have a T-shaped, or pi-shaped, understanding. Let’s go with pi because, well, math. What I mean is that they have (horizontal) breadth over many different subjects combined with a deeper (vertical) understanding of two areas, hence the pi. For me, this justified my pursuit of the liberal arts—I care about government and economics and philosophy and biology and English literature and music—and then I went deep into math and computer science. Now, if I’m chatting with a colleague in an area like physics, I have some frame of reference, and perhaps I can connect our discussion to my finer mathematical senses. It’s probably a tall order to ask someone to be an expert in two things and at the same time to strive for breadth in many areas at once, but Dartmouth is the kind of place where you can actually do that! And my colleagues certainly fit the bill.

And outside Dartmouth, even if you’re not an academic like me but say you go to work for a consulting firm, it is still important that you understand the social and environmental implications of your engineering designs. Or if you’re a chemist in a lab working in medicine, it’s important you’re aware of the political ramifications as the health care landscape changes. Maybe you’re not personally involved in those decisions, but that awareness allows you to accomplish a whole lot more. So is it weird to answer that question with “both is better”?

TDR: You said both, but if you could go back would you focus on one of the humanities in addition to math?

JV: If I could, I would probably have been a graduate student forever. I’d love to go back and get a Ph.D. in the humanities if I could afford it! Being a student is awesome. In my junior year as an undergraduate, I dove deeply into the study of Japanese culture, economics, and government. In college debate, we would do the equivalent of a master’s thesis level amount of research every semester, and the topic that year was foreign policy in Southeast Asia. But I realized at some point I had to stop because of the other things in my schedule, so I would love to go back. Scholarship in the area of international relations is just as important now—the latest headlines being about the movement of carriers in the Pacific.

That all being said, computational mathematics has plenty to keep me busy now and, well, it’s the best! Math has always presented the greatest challenges, and to me that is the hook. Mathematical thinking is both creative and rigorous; it is artistic and analytical. You have a well-defined problem that you need to solve with logical arguments, but you have to be creative to find a solution—that lights up all parts of my brain. And at least from my point of view, some of the most exciting work in pure mathematics is computational and algorithmic.

The other thing that will keep me in mathematics is the cognitive refuge it provides. We live in chaotic times, and I am often left reeling from national events and the way they are discussed. To have a place where the rules are clear, where we employ careful deductive reasoning to come to a shared agreement about the facts—I rely on that. Mathematics has a power to speak a universal truth. If we ever met space aliens, we could quickly agree on the notion of prime numbers. Of course, mathematical truth is limited; but because we’re standing on solid ground and take sure-footed steps, we can securely build things in mathematics that tower into the heights.

TDR: We were looking at some of your research and watched your TEDx talk at UVM about cryptography. You said that “a real transition in cryptography is underway.” How should we be thinking about information security issues, especially in light of recent hacks against Sony and other companies?

JV: It’s a very serious issue. Cryptography is the study of secure communication over nonsecure channels. Mathematicians in the 1970s crafted cryptosystems based on the difficulty of solving certain number-theoretic problems that were in turn used for secure communication on the internet. Algorithmically, that work continues. One of the major new issues has to do with quantum computing. Quantum computers are on the horizon—or so I am told—and if they become available, we will have to fundamentally change our cryptographic systems. So mathematicians, computer scientists, and cryptographers are thinking very hard about how to design systems that will resist quantum attacks.

But at the same time, you have users whose password is ABC123 and who click on the dancing moose that they get in their email. Granted, it’s hard not to click on the dancing moose… [Laughs] Usually, when you see a headline about a hack somewhere, it can be traced back to something like that. This problem will not be solved by better abstractly formulated algorithms! It lies somewhere between mathematics and engineering, really a problem in applied computer science and social psychology. How do we zap the emails with dancing mooses? (Or should that be meese?)

You mentioned the Sony hack from my TEDx talk: that attack was because of a lack of randomness in the system. Basically, a function that was supposed to return a random integer always returned seven. Can you imagine? If it’s not random, you can quickly break the system. How did that happen? For these reasons, I believe that the future of information security and privacy, something essential to modern communication and commerce, requires the efforts of mathematicians for proofs, cryptographers for application and design, computer scientists to code, software engineers to study user interface—and some thinkers who grasp all of these aspects.

TDR: Some journalists have reported that the United States has hacked into the North Korean nuclear program and other parts of their government. Do you think that this is possible? What, if anything, should the US do to strengthen its own information security in terms of algorithms?

JV: There were similar reports a few years ago about the US hacking into the Iranian nuclear program. And recently, possible Russian hacking into DNC emails and weaponization of social media. I don’t have any particular insight or knowledge into North Korean particulars. But at some point, do we acknowledge that there is a cyber war going on? And that we as a society should decide our approach to war, just like we would if it were a conventional war? I’m a little anxious about the role of certain federal agencies and our ballooning governmental information security infrastructure—building a lot of big computers with big databases under the general premise that it will make us safer. I guess we don’t have a lived human history of cyber wars like we do of military wars; but then that history seems forgotten anyway. We need clear and careful conversation, but not everyone making these decisions understands technology. And many Americans seem to have a Hollywood style-understanding of what hackers are about. It all makes me nervous.

TDR: You’ve been drafting a textbook on quaternion algebras. What motivated you to take on such an endeavor and what challenges have you faced?

JV: Here it is! I printed the sucker out, can you believe it?

TDR: Wow. It’s very long. How long did all of this take?

JV: Weighing in at over eight-hundred pages, it has been about seven years in the making—not continuously, because I had to get tenure and sleep—occasionally. It’s a great question, why does anyone write a book? As a research activity, it is of a different nature than publishing journal articles, proving new theorems, and being on the frontier of your discipline. I had worked with quaternion algebras over a decade going back to my thesis, but I found there wasn’t one place that you go to and learn about the topic in a coherent and self-contained way. My book is aimed at graduate students, and it was motivated by my fervent goal to welcome as many of them as possible into the subject. I’ve tried to cobble it all together: in a motivated way, with clear notation and proofs, so that everyone can learn, apply, and generalize. I found that there were arguments “well known” to the experts but that weren’t written down anywhere—that can be a real block to scientific progress. I guess one of my real passions is effective mathematical communication. Given the reputation of mathematics as a subject that is difficult to grasp, I take it as my personal charge to provide a rebuttal—to make math accessible, intuitive, attainable, inviting. As for the subject of the book itself, I can say without equivocation that quaternion alegbras are pure mathemagic. They appear naturally in so many areas, being basically as ubiquitous as 2×2 matrices. So the topic is at the core of mathematics.

Writing was not easy for me, and I have many people to thank for their help, both financial, mathematical, and personal. The book started with some notes from a course I taught at McGill University in 2010; gradually, 150 pages of notes became a monster! I have been writing during the summer, on weekends, late nights, on holidays, at the cost of some amount of sanity, health, and personal hygiene. But after submitting the latest version, I heard last month that my publisher, Springer-Verlag, is enthusiastic about the text, subject to some final edits to complete this summer. So some time in 2018, it’ll be out there in the world! I should be excited, but mostly I’m anxious. First of all, I hope it’s correct! When it’s 800 pages, that’s hard to do; this summer, I will do my best to eradicate all typos. But second, I also want the book to be useful. I want people to be able to pick it up, to pick and choose what’s useful and interesting to them, and go on and use that for their mathematical research. It’s fitting that I would be writing a book like this while a faculty member at Dartmouth. On the one hand, like I said we’re serious about the teacher-scholar model, and this book represents my best effort in that regard: it has allowed me to combine my aspirations for teaching and scholarship as represented in the dissemination of fundamental mathematics. But also, the story of the quaternions is interwoven with the history of mathematics at Dartmouth. The only mathematical output by a Dartmouth professor in the 19th century was by Arthur Sherburne Hardy, the author of an 1881 text on quaternions entitled “Elements of quaternions”. It had a reputation for being uninspiring text in an abstruse field. I can only hope that my book will receive better reviews!