Earlier this year, Professor Paul Flavell, Head of Mathematics at the University of Birmingham, gave a public talk to celebrate becoming a Professor.   

The talk, entitled Numbers, was part of a series of Inaugural Lectures hosted by the College of Engineering and Physical Sciences to showcase its leading academics who are pushing the boundaries in their disciplines.

His achievements, which include proving and then significantly contributing to ‘very difficult’ theorems, are the fulfilment of a childhood ambition – nurtured by a number of primary and secondary school teachers, who recognised his potential and enthusiasm. To Paul’s delight, two of them were in the audience for his lecture.

‘An Inaugural Lecture is a once-in-a-lifetime event and I was determined it was going to be something special,’ says Paul, who is also Head of the School of Mathematics. ‘I wanted to convey something about me and I also saw it as an opportunity to give a wider group of people an insight into what mathematicians do. Everyone knows who the great composers and writers are, but do they know who the great mathematicians are? Probably not, and I wanted to correct that. For me, Carl Friedrich Gauss is the greatest mathematician.

‘One of the things people like me do is prove theorems, so I wanted to take the Fundamental Theorem of Algebra proved by Gauss in his PhD thesis and get the audience to understand it. It involves things called complex numbers, but before you get to the complex ones, you need to know about ordinary numbers – hence the title of the lecture. So I set about proving this result, using lots of equipment and visual displays.’

And did the audience, at the end, understand the theorem? ‘I think so, yes.’

Paul can trace his love of mathematics back to when he was eight or nine. ‘I was always interested in science and technology, particularly physics, inspired by Einstein and Star Trek. I started exploring the library and, of course, next to physics books you find maths books. So I became rather captivated. I think what captivated me was the difficulty of some things, and I developed the desire to get my head around big developments in physics, mathematics and technology, and in due course to make my own contribution.’

By the age of about 14, he was ‘absolutely set’ on wanting to study physics or maths at university and becoming a researcher. His ambitions were encouraged and supported by several ‘wonderful’ teachers, two of whom were at the lecture.

‘The examples set by these teachers have remained with me always and is something I think about when I’m doing my own teaching. In fact, I’m absolutely convinced that my interest in teaching – which I discovered when I came to Birmingham – is connected to those teachers I had at school. In particular, I am keen to try to explain things to people, to demystify mathematics, to get people interested in the subject. I really love my teaching, and although I am Head of School, I still teach all year round.’

After gaining an MA(Hons) in Mathematics from Cambridge, Paul moved to Oxford to do a DPhil before getting a lectureship at Birmingham in 1990. Here, he continued to ‘aggressively pursue’ his research interests in group theory. In very general terms, groups are used to measure the abstract notion of symmetry. As a consequence, they appear in very many areas of science as well as being ‘fascinating objects of study from the pure mathematical point of view’.

There are two themes to Paul's research: the further development of the abstract theory of finite groups, and participation in an ongoing international project to produce a new and simplified proof of the Classification Theorem for the Finite Simple Groups.

‘As a mathematician, what I really like doing is proving very difficult theorems,’ explains Paul. ‘One of the main reasons I chose my particular field of mathematics is because I was really inspired by some of the work that had been done in the subject area.’

A particular inspiration was the Feit-Thompson Theorem, which states that every finite group of odd order is solvable. It was proved by Walter Feit and John Griggs Thompson in the early 1960s. ‘I wanted to understand it, which was quite a lofty ambition: the proof is 255 pages long!’

Paul not only succeeded in understanding it, he has since significantly contributed to the subject area.

As well as making contributions to the world of pure mathematics, Paul has always been eager to contribute to the School in an administrative capacity. He has held several positions, including Head of Education, and five years ago was made Head of School. In 2016, he was appointed for a second four-year term.

Although Paul has fulfilled – and, indeed, surpassed – his childhood ambitions, there is still a lot left he wants to do.

‘I certainly have ambitions for the School, including expanding it and attracting high-quality appointments,’ he says. ‘We are becoming even better known internationally and we are making the School a more student-centric environment.