David Jordan
ChenChen Zha and Franz Miltz worked together to produce this article as part of our series of Academic Interviews; featuring David Jordan!
Becoming a Mathematician
How does one decide to become a mathematician? Some may be able to clearly see their path ahead of them, but many others need to take a detour or two before they arrive at their destination. Take Dr David Jordan, for example. Since he had found his physics classes in high school to be fun and interesting, it was a natural decision to pursue a degree in the subject after graduating. However, having spent some time at university, he found himself enjoying the mathematical elements of his degree much more than actual physics. It then didn’t take him very long to change his course. Today he researches topological field theory at the School of Mathematics. Interestingly, he is still working very closely with physicists, helping them capture anomalies in quantum mechanical systems mathematically.
The Mathematics Community
Now, what does it mean to “do research”, practically speaking? Well, a lot of time is spent on looking for new papers online. Also, since he is working with colleagues all over the world, there is always something going on. To coordinate and communicate the progress that is being made, meetings need to be held. Before the pandemic, collaborators would visit each other for several weeks to work as efficiently as possible. When working together that closely, friendships would inevitably develop. Nowadays this is obviously not possible, so everything has to be done online. While this change in style might have taken away some of the closeness, it certainly hasn’t made mathematics any less of a social subject to be involved in.
This sense of community also has very positive effects on the competition within the field. While it is always possible to get “scooped”, as Dr Jordan calls it, i.e. have someone else publish something that you are currently working on, it becomes very unlikely when you are in contact quite literally everyone who is interested in the same topics as you. If someone happens to be trying to answer the same question, you can just approach them and ask “Do you want to work together on this?” In fact, essentially all of Dr Jordan’s papers have multiple co-authors and none of them are ever considered to be more prominent than others.
The problems Dr Jordan approaches and the way he does so may also have helped him avoid getting scooped. Of course, if you try and answer very popular questions within the scientific community, chances are that someone else is already trying to do the same. Conversely, if you avoid such mainstream problems you drastically increase your chances of your work being the first to be completed. Alternatively, if you are working on something popular, using an uncommon set of tools may help ensure that your work will still be valuable, even if you are not the first to answer the question.
Teaching
At the moment, Dr Jordan is not involved in a lot of teaching. However, he has taught a lot in the past. His favourite course so far has been Proofs and Problem Solving (PPS) - teaching pure mathematics to first year students, focussing on mathematical literacy and thinking instead of diving deep into one specific area. It’s a somewhat playful course that allows the lecturers to take some time and look at concepts from a few different angles before moving on.
Working with new students is especially enjoyable because they bring a lot of enthusiasm and motivation. However, it is no secret that mathematics, and PPS in particular, can make students feel like they have hit a wall. Up to that point, maths has been easy for most of those who chose to study it. This is not supposed to be the case at university. If Dr Jordan could say one thing to every new undergraduate it would be this: Mathematics is hard. It’s hard for the best mathematicians out there and it’s meant to be that way. If you put in the work, university will teach you to climb the wall that you will inevitably encounter.
That raises the question: why is mathematics so different between highschool and university? Should schools not teach more things that are relevant later on? This is a very difficult question to answer, especially if you’re an academic and not a teacher. Just because something is relevant for a mathematician, doesn’t mean that it is relevant for the general public. Instead of proofs and rigorous arguments, most people require numerical literacy and the ability to do calculations. Of course, there is always room for improvement. Dr Jordan suggests including a few more interesting, less methodical proofs. How this should be implemented is not for him to say, though.
News in press
David recently became a Principal Investigator on the international Simons Collaboration on Global Categorical Symmetries. He will be working with mathematicians and physicists around the world to understand symmetries of quantum field theory from both mathematical and physical perspectives. Read more here: https://www.simonsfoundation.org/2021/06/24/foundation-announces-the-simons-collaboration-on-global-categorical-symmetries/