Arend Bayer

Jue Gong and Lucas Fothergill worked together to produce this article as part of our series of Academic Interviews; featuring Arend Bayer!

In a way, the process of writing this article sums up the nature of working during a global pandemic. A piece on Arend Bayer – a Professor of Algebraic Geometry at Edinburgh – is being written by a student who has never met him in person. The two interviews on which the article is based, conducted by two students who themselves have never met, took place over zoom.

Like with many other things this past year, one can’t help but be impressed by the adaptability of all those involved, but is also left with a longing for the simpler days of face-to-face human contact. It is the personal connection that Arend values in his career. “The way our brains work… they always work in part by treating mathematics as a social activity”. This is just one example of how Arend’s perception of a University mathematics department might differ from that of an outsider.

The story of how Arend came to be a University Professor seems familiar. An able mathematician from a young age, he went on to study at Heidelberg and Bonn – two of the most prestigious Universities in Germany – with a year at Cambridge along the way. After being given a taste of academia during a thesis-focussed undergraduate degree, he felt further study was the natural next step, with the research for his PHD following on from his earlier work. He has been in the department at Edinburgh since 2012.

Arend stresses the fact that “there are many different ways to be good at research mathematics”. According to Arend, not subscribing to the competitive (or, as Eugenia Cheng might describe it, ingressive) culture in lower level mathematics is not necessarily an indicator of success as an academic. When asked about his experience of the International Mathematics Olympiad for example, in which he twice achieved gold, he says that “you should never think that just because you didn’t take part in Maths Olympiads that that’s a reason not to do research mathematics”.

Indeed, the picture he paints of his life as an academic is a far cry from the one presented in textbooks and the media, where a series of Eureka moments are punctuated by periods of solitary study. As he points out, the nature of research mathematics implies that you spend most of your time stuck on problems, and, for Arend, the best way to spend this time is being stuck with someone else. Earlier in his career, he made the decision to write the majority of his papers jointly “because [he] found it much more stimulating” to have someone to interact with, someone to “bounce ideas off”.

Too singular or narrow a set of interests is to be avoided in Arend’s opinion. Whilst he doesn’t question the importance of knowing where your passion lies, he acknowledges that the many conceptual shifts he has made throughout his career would have been more difficult if he hadn’t maintained a broad range of interests. Different branches of mathematics often share non-obvious symmetries, and, like in other subjects, a breakthrough can often come when contemplating an unrelated problem.

One way in which Arend is unsurprising is his evident passion for Algebraic Geometry. As the name suggests, this branch of mathematics is centred on the use of algebraic structures, such as polynomials, to describe geometric objects.  To understand his work in detail would, of course, require a level of technical knowledge exceeding that of an undergraduate. The heart of the subject can be summed up by simple, powerful questions. Arend tells us that distinguishing one geometric shape from another – which, in a rudimentary form, is perhaps the first geometric problem confronted by children – remains one of the most difficult things to do.

For Arend though, his love for his subject goes hand-in-hand with the atmosphere in which he works. “The way I live research mathematics, day-to-day … it’s a collaborative environment”, he says, and it seems he has found such an environment at Edinburgh. Those in and around his research area create a “very productive, nice group”, which he hopes to help keep thriving and developing for a long time.