Ben Goddard

Dr. Ben Goddard is a Reader here at the University of Edinburgh, working out of the School of Mathematics, whose research frequently involves collaborating with other sciences and providing mathematical insight and rigour to real-world problems.

At school, Ben enjoyed most subjects, but found himself gravitating towards mathematics, deciding to study it further at university without any explicit idea what to do after. It wasn’t until his final year as an undergrad that he considered doing a PhD. This came about after he worked on a project on mathematical quantum chemistry, which went on to be the subject area of his doctoral thesis. The attraction towards application, whether it be applicable mathematics or problems inspired by real-world phenomena, has been a driving force behind his work. “Ideally what you’d want is a very nice, mathematically elegant solution to your problem,” he reflects before granting, “then you hit the real world and it starts being hammered away and you start having to do numerics”.

Ben began his PhD at the University of Warwick, but ended up following his advisor to TU Munich for his last year of doctoral training. It was during these years in graduate school that he was introduced to a community that encouraged talking about one’s individual research to as many people as possible. “The more people you throw it out to, the better,” he comments. When talking about how discussing ideas with others who have different areas of research might generate useful suggestions, “you learn a lot of maths just from talking to other people as a PhD student.” It was during this time he learnt that he was drawn to problems with interesting applications; this led to him pursuing research as a career.

The application of mathematics to quantum chemistry remains one of Ben’s favourite topics. One of the more significant take-homes of doing his PhD was that everything that he did “could have been done, maybe a few hundred years ago,” not requiring anything modern, but just applying what we know to areas we had never been looked at before. One particular example of this is trying to solve the Schrödinger Equation for an atom to determine the arrangements and energy levels of electrons, which is a high dimensional PDE that can’t be solved numerically or analytically. However through fixing the number of electrons and increasing nuclear charge while studying the asymptotic limits of Schrödinger ground states, the system is converted from strongly interacting to weakly interacting, allowing it to be looked at more easily.

After defending his doctoral thesis, Ben held postdocs at Warwick, as well as the Chemical Engineering department at Imperial College London, before moving to take up a permanent lectureship in Edinburgh, where he lives with his wife, a statistician/data-scientist. They both share a mutual love of escape rooms, so much so that they’ve made and run their own during Scout festivals in Coventry as well as here in Edinburgh during the Festival of Creative Learning, incorporating maths-themed puzzles.

Currently, his research involves applying numerics, modelling, and analysis to various scientific disciplines; having collaborated with other academics from the Schools of Engineering, Biology, Chemistry, Physics, and Informatics. More recently Ben has worked with experimental biologists at the ‘Welcome Centre for Cell Biology’ and has developed a mathematical model describing how DNA is transcribed by RNA by polymerase, and implementing it numerically. Other recent projects he’s been involved in range from the statistical mechanics of opinion dynamics to fluid physics, which is reflective of his primary motivation of wanting to work on interesting problems from all sciences.

Speaking from his own experience, Ben acknowledges that “interdisciplinary research often sounds difficult” because it involves applying skillsets from two disciplines “and to some extent that’s true,” he admits, “but that’s why you have collaborators in the other discipline.” He goes on to say that “mathematicians tend to be very good at understanding complex ideas, explaining them in a relatively simple way, getting to the heart of the problem and asking why someone defines a problem the way they do.” He reiterates the usefulness and broad applicability of maths and leaves some advice to university students starting out: to not be discouraged by projects or pursuits that aren’t explicitly tailored for a maths skillset, because you might have a lot to offer a job or discipline. “If you find something interesting, then go for it because it might just work out.”