Interview with Dr. Jonathan Jedwab

Professor, Department of Mathematics

Combinatorics, Discrete Mathematics, Mathematics of Communications

Dr. Jonathan Jedwab loves the simplicity of combinatorics, in that the problems are very easy to state and typically, they have a low barrier to entry, i.e., you don't need to know a whole lot of advanced mathematics to get started. The problems may be deceptively simple, but reaching a solution can require some very complex mathematical tools – that's the attraction to the subject.  As a mathematician, what began for him as mathematical problem solving in digital technologies has evolved into a prolific research program that tackles problems across all facets of science, from determining the most stable way an RNA sequence can fold in three dimensions to communicating securely using the principles of quantum mechanics.

What life experiences led you to pursue a career in research?
I was born to do this job! My mom still tells the story of when I was a very young boy and I would beg her to give me sums, more sums, harder sums; I was fascinated by numbers and puzzles.  My work now is a natural extension of that, tackling hard problems and puzzles. I am fortunate that I found a way to get paid to do what I love.

How did you arrive at the interface between mathematics and digital technology?
After completing a Masters equivalent at Cambridge, I found a Ph.D. supervisor at the University of London. He had contacts in industry and suggested that I do my Ph.D. part-time while working in industry. As it turned out, I spent 14 years with Hewlett-Packard, which was an exciting place to be. I could combine theoretical investigation with applications, working with digital communications engineers to design systems that communicate through space or time, to build networks, and to design measuring devices. These projects all involved solving problems in combinatorics, namely arranging objects subject to multiple constraints. I got lots of practice solving them and also developed my own research interests around that work. However, I didn't have much autonomy, and I was always at risk of having to change projects.

I've been at SFU for 14 years now. I truly enjoy having the freedom to craft the job to my liking.

What part of your research gives you the most satisfaction?
I still regard my research as a collection of puzzles and solving any of them is satisfying. Sometimes when you solve more than one and see them side-by-side, a pattern emerges that tells you something about the bigger picture; when you establish that, it really is the most satisfying part of research.  I also love to present the work I have done in public and get new ideas from the reactions of others, as well as to help others develop their skills.

Do your students find their own problems or do you assign problems to work on?
Initially, I thought I needed to supervise people doing the problems I was interested in, but I've relaxed on that score over time. Students sometimes ask for problems I'm interested in, but others will tell me that none of those problems excites them. So I encourage them to find a problem that we can work on together productively and they can educate me as to why it is an interesting problem. This brings a much greater range to the group.

What problems are you and your research group working on?
I've been working in the area of combinatorial designs for quite some time, but my group works on all kinds of other interesting problems too.  For example, one student was interested in tackling a problem with biological relevance, so she identified an RNA design problem in combinatorial biology. Another student was interested in graph theory, and brought a research problem I’d never heard of to the group for discussion. Both students ended up with very nice solutions and a great thesis, and I learned a lot about subjects I never knew would fascinate me.

A recent project with a postdoc combined many different areas of mathematics in order to solve a problem in cryptography that several people had concluded was impossible. We used tools from finite geometry, combinatorial designs, and a special kind of symmetry structure to solve the problem.

Recently, we've also become interested in quantum information theory, involving very small scales where the conventional laws of physics tend to break down. My view is that many of these problems are naturally described by the combinatorial mathematics I study, whereas people in physics typically use very different approaches. This is an opportunity to apply what I know very well to a new area of application.

What is special about the learning environment in your group?
I try to create a learning environment in which people are not afraid to say silly things for fear of losing face. For some students, it is difficult to come forward when they know the answer because they're worried about the small possibility of being wrong, so I encourage them to be more creative and experimental. I support friendly competition, which is a highly productive team approach to problem-solving.

What other role at SFU or in your scientific community do you find rewarding?
Something that really excites me is coaching for the Putnam Mathematics Competition, which is the most prestigious and insanely difficult undergraduate competition in the world.  If you place in the top 500, your name gets published and it establishes you as a talent, enhancing your chances of admission to a good graduate school.

As the Putnam coach at SFU, I run a course and training sessions that prepare students for this competition. Students often tell me that solving just one of these problems in the actual competition was the highlight of their undergraduate studies. Over the years, I have had more than 30 students come out in the top 500.

How has the funding landscape for your research program changed since you joined SFU?
For me, the funding situation has improved a great deal. When I first came to SFU, referees of my Natural Sciences and Engineering Council of Canada (NSERC) Discovery Grant application had trouble evaluating the research I had done in industry developing technology and patents; I got a very minimal grant initially. My next round, three years later, was still under the old NSERC system, which gave modest increases relative to your previous funding level. Then the system changed – we are now evaluated on three things: excellence of the researcher, merit of the proposed research, and your contributions to training.  When that happened, I did a lot better and even got a Discovery Accelerator Supplement. My latest renewal far surpassed my expectations, so for me, the merit-based funding environment is great.

What contemporary scientific issue concerns you the most and needs more attention?
What keeps me awake at night is that because some technological advances are so rapid and powerful, particularly in genetics and artificial intelligence, we need to be mindful of pitfalls as well as opportunities.

When I started out, artificial intelligence was very ‘pie-in-the-sky’. However, over time we have developed machines that can beat humans at complex games like chess and Go, and at social activities like the quiz show Jeopardy; so what is the limit to artificial intelligence? It can now solve problems of such incredible complexity that we need to think carefully about the way things could develop.

Likewise, in genetics: the pace of invention in the field has become so fast; interventions that were once impossible are being realized. We need to think about the extent to which we are willing to apply these genetic advances. Just because we can do something doesn’t mean that we should.

What will be the next step in the evolution of your field?
The discipline of combinatorics is maturing to the point where connections are emerging with many other kinds of mathematics that require a very long time to understand. Now with mathematicians from other areas starting to apply their powerful, advanced techniques to combinatorics, a significant transformation is occurring. Some of these methods are being used to solve problems of combinatorics that are more than 100 years old. I don't think we've reached the peak yet in this field. I love the subject and I love watching the field transform.

______________________________________

Read more: Dr. Jedwab’s profile on the Department of Mathematics website, his personal website, and the Featured Researchers page

Interview by Jacqueline Watson with Theresa Kitos