In conversation with Alison Etheridge

17 March 2025

During a red weather warning in January, we hunkered down, made a cup of tea, and had a chat with the soon-to-be Dame Alison Etheridge. We talked all things statistical modelling, her recent damehood, and the divides between different mathematical factions. Having dabbled in statistics at university, I was vaguely aware that we often make assumptions about our data before we apply a statistical model. But it wasn’t until talking to Alison that I realised how problematic this can be and how important Alison’s work on this is.

The beauty of cyclic quadrilaterals

Alison grew up in Wolverhampton and never imagined she would become a mathematician. At school, her favourite subject was chemistry, but she does remember being taught about inscribed quadrilaterals (you may know them as cyclic quadrilaterals). “I just sat there, thinking they are really beautiful,” she recalls—not that she would tell her fellow classmates this! Her chemistry teacher pushed her towards a maths degree, saying “you can do anything with mathematics”—as our A day in the life feature demonstrates. Thanks to huge support from the maths department, she was able to leave school a year early and take a gap year before starting a maths degree at Oxford.

Alison fondly remembers inscribing quadrilaterals from her school days

Even at Oxford, Alison still did not think that she was going to be a mathematician. She thought she could be a physicist, while her mum wanted her to go into the humanities. But it was through a tutor at Oxford that she really fell in love with mathematics, because she was challenged. “It is only when you are challenged by mathematics that you really begin to enjoy it,” she explains. As she neared graduation, she began thinking about what she wanted to do with her maths degree: She decided that she could either be a mathematician or an accountant. At the time, she felt that “there didn’t seem to be many choices. Of course, there were—I just wasn’t aware of them”. In the end, she chose to go further in academia and become a mathematician.

Pure maths v applied maths?

Alison has worked all over the world and in many different areas of mathematics. In the early 1990s, she lectured pure mathematics at the University of Edinburgh and spent time in probability and statistics departments at UC Berkeley and Queen Mary & Westfield College in London. In 1997 Alison returned to, and settled at, the mathematics department at Oxford. Historically, though, she has a family link to Cambridge—she found out when she was 21 that one of her ancestors designed the famous mathematical bridge!

This range of mathematical interests can also be seen in her research. Despite having a background in functional analysis (which is considered by many as a pure mathematical subject), Alison has done a lot of research into mathematical modelling of biological ideas, looking at genetics and evolution (a very applied topic). Her work output shows her belief that mathematics should not be divided into categories such as pure and applied, but should be thought of as one large group of mathematical sciences.

The mathematical bridge in Cambridge was designed by one of Alison’s ancestors.

She realised that she likes her mathematics to be motivated by a real world biological question because it gives her intuition about the problem. “I find the questions intriguing, but they’re also very mathematically challenging,” she explains. “They often spin out things which are probably of more mathematical interest than they are of biological interest in the sense that they generate new techniques and they are hardcore analysis: infinite dimensional, stochastic processes, measure value processes.”

Despite this wide-ranging research, Alison’s absolute favourite mathematical topic is complex function theory: she just thinks the proofs are really quite beautiful. Complex function theory is the study of functions of complex variables and has uses in topics across the mathematical spectrum from number theory to engineering. It is also within this field that the Riemann hypothesis arises.

She partly blames the mathematical culture at Cambridge and Oxford for this big divide between different topics in mathematics: Oxford used to have different buildings for the applied and pure mathematicians, and Cambridge still does. Alison thinks this is a shame because people missed out on those little informal moments. “Mathematicians don’t meet at coffee or have those conversations at the water cooler” to learn about others people’s research. This means they don’t learn to respect the work and ideas that go into other types of mathematics and see the intricacies that are involved in different subfields.

At any given time, Alison is involved in at least five or six different projects, working with lots of different people. And at the moment many of these projects are developing models which can try to give us some idea of the way that spatial structure interacts with genetic structure. In particular, one project is looking at common mathematical models used in plant genetics. These models make assumptions such as “over very long time periods, genetic variations in a certain type of plant will just wash out and so we can treat it as homogeneous”. As such, you assume that there is no need to take account of the spatial variation experienced by this plant when applying the model to your data. Alison and a colleague wanted to ask if this assumption is valid, and they found that it is not quite so simple. This then made them look at other mathematical models and ask questions about what assumptions were made and how this will change the output from the mathematical model.

There are half a billion gnomes in the UK Biobank alo… wait, sorry, genomes? I suppose that does make more sense.

Alison is also interested in human genetics. We have so much data, with “something like half a billion genomes sitting in the UK Biobank alone.” This work is looking at the infinitesimal mathematical model developed by Ronald Fisher in the early 1900s. Alison and her colleagues want to know if older models (such as the infinitesimal model) are still relevant when we apply them to the huge amounts of data we have in the modern world. What do we need to do to make sure these mathematical models can still give us useful information? It is important for the mathematical model to give us correct information because they are being used for projects such as helping to identify the personal risks of certain diseases. For Alison, this research demonstrates the great thing about mathematics: “the ability to abstract things and think very clearly about them, and then come out with kind of a clean argument as to what the answer is”.

P(damehood) = 1^[1]

Alison will also be awarded a damehood for her services to the mathematical sciences. This is a well deserved honour, as alongside her many years of teaching and research she is also president of the Academy for the Mathematical Sciences.

The Academy for the Mathematical Sciences brings together the five existing UK mathematical societies, like a mathematical society megazord.

The impetus for founding the academy came following an independent review in 2018 that suggested the UK mathematical sciences community needed a single authoritative voice. Since then, a lot of hard work has been put in to design and create an academy that will benefit the whole of the UK. The organisation wants to incorporate mathematics within academia, education, business, industry and government across the country. The goal is to increase the number of mathematical scientists, improve diversity within mathematics, and help support the government to create better public policy. It was planned for the academy to fully launch later this year but recent government budget changes mean it is currently looking for other sources of funding. So watch this space!

Despite this challenge, Alison is very excited by what the academy has been able to achieve so far. “The past two-year setup phase of the academy has given us a tantalising glimpse of what can be achieved when mathematical scientists from different parts of our community work together.” The academy’s outlook aligns closely with Alison’s ethos that mathematics is one huge subject. As for the damehood, Alison is actually a little embarrassed—but she is looking forward to a fun day out in Windsor with her family.

Alison tells me that in the autumn, before hearing of the award, she was feeling quite down about her work. With so much time spent in meetings and less on research, she felt that all the time and effort she had put into the mathematical community wasn’t worth anything. But since the announcement of her damehood, lots of people have reached out and sent messages of support and admiration, reminding her why she wanted to work in mathematics to begin with. I really appreciate her sharing this story: it’s reassuring to see that even the most accomplished mathematicians experience ups and downs in their careers.

Looking to the future, Alison sees herself doing mathematics for many years to come, well into retirement. Although, she hopes to wake up a little later and enjoy more of her other hobbies such as walking in the Scottish hills, good food, theatre and time with her family.

So as you go about your week, take a leaf out of Alison’s book: find something that challenges you, and let yourself fall in love with mathematics.

[1] Chalkdust cannot reproduce the mathematics that led to this result. We take no responsibility for the implications shown above and will not be responding to any further queries.