Take 10 with... Mark Wilson

Dr Mark Wilson from the School of Computer Science gives us 10 minutes of his time to discuss how he finds better ways to count sets of objects by automating these computations.

1.  Describe your research topic to us in 10 words or less.

Computational discrete mathematics and applications, particularly to social science.

2.  Now describe it in everyday terms!

Finding better ways to (approximately) count enormous sets of objects, which helps in understanding the probability of an object having a given property. Most of my work goes toward automating (via specialised computer software) these kinds of computations.​ I have recently worked on applications to voting systems and social networks.

3.  What are some of the day-to-day research activities you carry out?

Proving theorems (occasionally), doing extensive computations by hand or with computer algebra software, working with PhD students.

4.  What do you enjoy most about your research?

The freedom to explore deep and beautiful topics that people have worked on for decades or centuries, and which have (eventual) useful practical applications. Also the ability to meet people from all over the world with similar interests.

5.  Tell us something that has surprised or amused you in the course of your research.

I am still amazed at just how powerful techniques from continuous mathematics have proven to be in studying discrete questions - at first it looks like magic.

6.  How have you approached any challenges you’ve faced in your research?

Mathematical research is like navigating a strange country in the dark. It is all challenge, all the time. You have to be very persistent, and have a lot of patience. I recently had an idea that enabled me to solve a problem that I first thought about in 2013 and seemed quite easy!

7.  What questions have emerged as a result?

I was using a standard technique and it almost worked. So I kept recalculating, doubting my work so far, etc. After leaving it for more than a year I looked at it afresh and tried a slightly different, but still fairly standard, technique. This time everything worked just as I had expected it would the first time. I can now move on to extensions of this problem and I intend to publish within the next year. Moral: don't give up, but sometimes you need to sleep on it (longer than you expected).

8.  What kind of impact do you hope your research will have?

I hope to automate whole areas of mathematical computation, so some of my colleagues stop wasting time on solving certain types of problems by hand, and instead use their talent for more important and creative problems.

9.  If you collaborate across the faculty or University, or even outside the University, who do you work with and how does it benefit your research?

I have a longtime collaborator at University of Pennsylvania without whom I would have done much less interesting work. We wrote a joint monograph that has been reasonably influential. I also have many other collaborators, and in particular I worked with my most recently graduated PhD student Dr Samin Aref on interesting questions involving networks.

10.  What one piece of advice would you give your younger, less experienced research self?

Be more confident when talking to big names at conferences. Of course you need to do background research, but most of these people are encouraging to their junior colleagues. In general, talk to more people about their work.