May, 2021

Math Central (MC):

Can you tell us your job title and who is your employer?

DANNY:

I am a professor in the Department of Mathematics and Statistics at Memorial University of Newfoundland

MC:

How would you describe your job?

DANNY:

As a Professor, my job is normally broken down into three categories: teaching, research, and service. I enjoy working in all three categories. I normally teach 3 courses per year, and the topics vary a great deal. I often teach sections of Calculus that might have as many as 300 people in them, to classes in my own subject area, discrete mathematics. (The smallest class I taught was a fourth year enumerative combinatorics course with only 1 student!) I like teaching, because I love the “lightbulb” moments, when you’re talking to students and you can suddenly see that they get it. Something has finally clicked, and what was impossible becomes transparent.

My own research, in graph theory, lets me chase my own lightbulb moments. Graph theory is the study of graph, which are a way to model the connections between things. A famous graph is the Bacon graph: imagine a collection of actors as dots, and there is a line between two dots if both actors have been in movie together. It’s widely believed that the actor Kevin Bacon is at most 6 movies away from any other actor. In graph theoretical terms, this would mean that the Bacon graph has diameter 6!

In my own research, I am interested in cops chasing robbers in graphs, as well as graphs that come from board games. The board game “Scotland Yard” is an excellent combination of both.

The service part of my job typically means serving on committees. Part of my service is also spent doing mathematical outreach. I help create and run math competitions for Junior High students. Our competitions are run in groups, and live, so that students can put their heads together and solve a problem. It’s the aspect of mathematics that I love best myself – getting together with collaborators and kicking around ideas about how to solve a problem. It’s an aspect of mathematics that students sometime miss – in research, we don’t know the answers, and even when we believe we have the right answer, we don’t always know how to prove it.

 

 

MC:

Tell us a little about your background and education.

DANNY:

I was born and raised just outside St. John’s, Newfoundland and Labrador. I went to Memorial University for my first degree in Pure Mathematics, and then went to Simon Fraser University for my Masters and PhD work, though I ended living in Regina for a few years, and working at the University of Regina.

I’ve come full circle – I ended up back at Memorial University, and have been working there for 15 years.

MC:

Why did you decide to make a career of mathematics?

DANNY:

I’ve always loved puzzles. I think that mathematics, at least the kind I do, is as close as I can get to solving puzzles for a living. I love finding the right trick, the right way of thinking, that lets me solve a problem. A good puzzle is often just a kicking off point for some great mathematics.

As a graph theorist, I’m interested in the connections between things, and what those connections mean. In a board game like Risk, that means that I’m interested in connections between countries, and how to figure out the right order to conquer them in.

But I also think about these problems in the things I do every day. A classic graph theory problem is finding the shortest distance between two points. (This is the heart of mapping apps like Googlemaps.) If I leave my office, and walk to the food court, what’s the best route to go? Walking from one class to another, should I take the physically shortest route, or a longer one, but with fewer people so that I can walk faster? A more complicated variant: if I’m at home and I have 5 errands to do around town, and then want to return home, how can I do it as quickly as possible? Finding an efficient answer to this question, in general, is worth at least $1,000,000, but you’d make a lot more money by not disclosing how to do it and just setting up a private consulting business. It turns out that an incredible number of “interesting” problems are equivalent to being able to solve this one efficiently!

MC:

What are your hobbies and other interests? What do you do when you are not doing mathematics?

DANNY:

I read a lot. Mostly fiction – sci fi, fantasy, mystery are all favourites. I love role-playing games and board games. I’ve been playing Dungeons and Dragons and similar games for 30 years, and I still try to get in some role-playing every week. Lots of television: my favourite shows right now are Star Trek: Discovery, Line of Duty, and the panel show, Taskmaster, which is the funniest thing I’ve ever seen.

From my T-shirt it's clear that I am also a Lego fan.