Hidden Figures in Oxford Mathematics - the experience of three women PhDs in Oxford in the 1980s

Historically, mathematics has been a largely male-dominated field, with women in mathematical academia consistently being underrepresented. A report in 2013 by the London Mathematical Society [1] shows some progress has been made in increasing the participation of women in recent times, with the proportion of women pursuing an undergraduate degree in mathematics in the UK standing at around 42%.

However, when we look at the percentage undertaking a PhD this number drops to 19% and as we progress through the career stages of an academic eventually we reach the disturbing statistic that only 6% of maths professors in the UK are women.

This demonstrates what is sometimes referred to as a ‘leaky pipeline’ – one metaphor to describe the way in which women leave academia at a higher rate than men at every stage of a research career. The current female professors that make up that six percent have spent the last few decades working as mathematicians in a profession where they are largely outnumbered.

I wanted to speak to some women who chose to pursue a career in academia at a time when female mathematicians were few and far between, asking them to tell their stories, understand the challenges they have overcome and highlight the successes they have achieved. The common link between these women? They all started their journey into academia at Oxford in the 1980s, by undertaking a DPhil here at the Mathematical Institute.

The stories that follow come from interviews conducted with each woman: Sarah Rees, Frances Kirwan and Helen Byrne, (with full audio recordings of the interviews with Sarah and Helen available). These women have gone on to have varied and successful careers as academics, providing real insight and new perspectives into their respective fields of mathematics, as well as helping the next generations of women succeed in maths.  

Sarah Rees (pictured below at graduation)
Professor Sarah Rees grew up in Exeter, daughter to two mathematicians. She studied maths at Girton College, Cambridge and completed her DPhil at Oxford from 1980 to 1983 on ‘Diagram Geometry’. After positions across the world, including Brussels, Ohio and Warwick, Rees made her way to Newcastle University, where she is now Professor of Pure Mathematics (the first woman to be appointed to a permanent position in Newcastle’s Faculty of Science).

Frances Kirwan (pictured below)
Professor Frances Kirwan grew up here in Oxford, born only a few hundred yards from where the Mathematical Institute now stands. She studied maths at Clare College, Cambridge, before moving to Oxford to undertake a DPhil from 1981 to 1984 on ‘The Cohomology of Quotients in Symplectic and Algebraic Geometry’. After a short time at Harvard, Kirwan returned to Oxford as a Fellow, and is now the Savilian Professor of Geometry, the first woman to be appointed to this position since its creation in 1619.

Helen Byrne (pictured above zooming with Maddy Underwood)
Professor Helen Byrne grew up in Manchester. She studied maths at Newnham College, Cambridge, after which she completed a master’s at Wadham College, Oxford in Mathematical Modelling and Numerical Analysis, followed by a DPhil in 1988-1991 at Oxford on ‘Modelling Combustion Zones in Porous Media’. She worked in the cyclotron unit at Hammersmith Hospital as a postdoctoral fellow, and after positions in Bath, Manchester and Nottingham, Byrne is now Professor of Mathematical Biology here in Oxford. She was the recipient of the 2019 Society for Mathematical Biology Leah Edelstein-Keshet Prize.

“You kind of survive by not thinking terribly much about your gender”
All the women interviewed shared the experience of going from an education surrounded by women to suddenly studying maths in an incredibly male-dominated environment. Byrne went to an all-girls school, which for her she thought was probably beneficial, “in terms of not being scared or intimidated about studying maths”.

Being in a female environment can be advantageous in many ways, as girls are less likely to come across negative stereotypes and so therefore may have less anxiety about whether they are “good enough” to do maths. However, this often just delays the issue until women go to university and still does not address the systematic changes required to make women feel more included in maths.

Rees, despite going to the all-women Girton College for her undergraduate degree, still felt the impact of choosing to pursue a majority male subject such as maths at Cambridge (Rees estimated her year was around 8% women). She spoke of how “they made a difference between us [and the men]” - whenever the mathematicians were given in a list, the women were named differently to the men (they were always referred to as Miss, whilst the men were simply listed as their name).

Kirwan expressed a similar sentiment – she went to Clare College, which had been mixed-gender for about 5 years before she arrived, and she never particularly noticed her gender in college, but within the maths department she could feel that she was anomalous; one example she gave was that “whenever I got anything, any communication from the maths department, they always addressed it to ‘Mr F. Kirwan’, which really annoyed me”

These are small things, but as is well known, small acts like these can often have large impacts. The atmosphere was pervasive yet according to Rees wasn’t seen as unusual: “it was just how it was and so we didn’t think it was odd”. Now we can recognise the negative impact that these actions can have on the choices women make when pursuing a career in a subject that they have been consistently reminded was not built for them.

The way Byrne found to deal with being outnumbered in her undergraduate time and beyond is described in a very straightforward way: “you kind of survive by not thinking terribly much about your gender”. Women should not have to ignore their femininity to cater to a masculine environment – they should be able to exist as their full and true self without it impacting their confidence or success in maths.

“There weren’t people who felt responsible for me”
The interviews conducted with these women highlighted the need for young researchers, especially women, to have a strong community around them and to feel like they have a support network that they can go to when they need it, including both peers and mentors. Kirwan spoke very positively of her time at Oxford. This seemed to be influenced in part by her supervisor Michael Atiyah (1929 – 2019, Fields medallist, world-renowned geometer): “he was great, he was full of energy and full of ideas […] mathematics would come pouring out of him”.

Having a supervisor who can not only provide guidance with the academic side of your studies, but also provide moral and emotional support can be a great help in ensuring young academics progress well through their DPhils. This certainly seemed the case for Kirwan – she lit up when talking about her previous mentor: “one of the most inspiring figures in UK maths for many decades, and he was a great person to have as a supervisor”.

She also spoke of the camaraderie of sharing an office with other DPhil students. In my own experience doing my undergraduate degree, having peers around you that are going through similar experiences can really help to make you feel less alone, and sometimes it’s easier to talk about issues you face with other students rather than your supervisors. Byrne similarly spoke of the benefits of having others around you, even if they were working on different things: “it was good just being around other people who were also trying to work in the same way […] there’s a solidarity in that”.

In contrast, Rees said she felt as though she struggled during her time at Oxford because she didn’t really have anyone who looked out for her, which led to her “not feeling tremendously confident at all” during her time there. Rees believes that for a woman to thrive in this profession, they need to have a strong support network around them, something she didn’t feel she had as much when she started her journey into academia, saying that she “was always a bit on the outside” when pursuing her DPhil, and that she was never really ‘in the system’ at Oxford. She emphasised this when I asked her about what can be done to ensure female mathematicians succeed: “It’s all about providing an environment that they’re happy with isn’t it? I don’t think it’s about providing money or anything, it’s about making them feel comfortable, it’s about the culture.”

“They don’t understand it and you just can’t talk about it”
Part of women feeling as though they belong in maths includes having role models in positions they can aspire to and having support from female mentors who can provide advice on everything from how to cope with setbacks in research to more gender specific issues such as maternity leave. 

The conflict between academia and having children has been shown to be one of the big reasons for women leaving the profession, and although Rees did have her daughter whilst continuing to remain in mathematics, she thought that having more women around her and more female mentors during this time would have immensely helped her navigate the situation: “if you’re with other people who are dealing with the same situation then it helps. The men are not dealing with that situation, well they don’t have the time pressure, do they? And so, they don’t understand it and you just can’t talk about it”.

Rees couldn’t see many women ahead of her, which may have been discouraging as she first started out: “I think you gravitate a bit towards them […] I’ve got close to some other women, and I’ve worked with some other women but there weren’t the women ahead of me who would have mentored me, they just didn’t exist really.” 

Byrne felt as though she didn’t have any female role models; however, she felt that it wasn’t as much of an issue when she was an undergraduate. “I was dealing [with problems where] I didn’t think it really made a difference that I was female or had I been male; my problems were more technical […] questioning one’s ability”. Yet she said that “where I think it becomes quite useful to have a mentor is when you do things like have children […] having a mentor or seeing people who have done that and that you can discuss […] how they managed the things that you’re dealing with, that’s quite helpful”. Even just having these women visible can go a long way in assuring women that you can be a mother and a mathematician, and that you do not have to sacrifice one for the other.

Kirwan felt that she could see women around her during her time at Oxford, saying that “it felt perfectly natural to have women around as faculty members, and doing research”. However, she recognised that she was lucky to experience that, and that at most UK maths departments of the time, this was a rare occurrence. She thought that the time that she was there also had an impact on her experience: “the timing was such that people were just beginning to realise it was a bit of a problem, that there weren’t enough women in maths”, and that she thought this played to her advantage rather than her disadvantage. Kirwan agreed that having these women being conspicuous in the department was helpful.

The impact of having more women visible in senior roles cannot be underestimated; it can give women the confidence to continue to succeed, knowing that there are people like them that have gone through it, survived and flourished, as well as providing a person who can uplift and inspire, who can advocate for the women around them and so much more.

However, we must note here that women in positions of being considered role models should not be expected to carry the load of advocacy or inspiration for all other female mathematicians around them – institutions need to be working to put measures in place so that it is not the responsibility of sole individuals. In addition to this, there was one very pertinent point Kirwan made when it came to talking about diversity in academia: “one of the issues that I think we really, as mathematicians, need to be thinking about very hard now is other sorts of diversity and not just gender diversity, particularly race and social background”. We must recognise that women are not the only minority in maths, and that more work needs to be done to improve the environment in maths for people from all backgrounds.

“I think you gravitate a bit towards them”
When I asked her about why she loves being a woman in maths, Rees made some interesting comments about the different ways in which she thinks men and women can approach maths, explaining that “some of the women I know have done some beautifully visual things. I think maybe it is something that women appreciate more, the visual side of it”. If students are only ever shown one way of doing maths, that might stereotypically be a ‘masculine’ way of approaching problems, it might dissuade them from thinking they are good at maths if their approach does not align perfectly with this. Rees alluded to this also: “maybe it was just because there was just so few of us and so naturally the culture wasn’t one that fitted us”.

Now Rees has found connections with other female mathematicians across the globe and is currently working in a fully female research collaboration which she finds “rather exciting because you know, it’s four women working together.” This makes a stark difference to her interactions with women early on in her career, as she explained. "I didn’t really learn to talk to women for an awfully long time because I never met any". Rees suggested a DPhil can be quite lonely at times, especially in maths where “you tend to need to be by yourself quite a lot in order to work things out and […] have the big ideas”. Add to this the social isolation of not seeing anyone around you that looks like or shares experiences with you, and you can see the issues that might arise.

Byrne expressed a similar sentiment about the joy of connecting with other women in maths, saying that she enjoys the relationships she has formed with other women, and that she has conversations now where "you can probably be a bit more of your whole self if you like, not just your mathematical self, and that’s really nice".

“Those are achievements that I enjoy”
When I asked her about her biggest success, as is unsurprising with such a large, open-ended question, Kirwan struggled to come up with any specific answer. However, when I asked about her love for mathematics, the adoration she has for her subject was clear. She shared a wonderful childhood story: “my first mathematical memory was my father explaining to me how you could prove Pythagoras’ theorem, that it always is true, and the idea that you could prove that it was always true meant a lot, made a big impression on me”. What I found touching was that the thing that first sparked her interest in maths is still the reason to this day she loves what she does: “the idea of being able to prove that you’re right and to understand why what someone else has done has got to be right […] in many areas there isn’t really a good notion of truth, but in maths [there is]”.   

Rees emphasised her need to “have a life beyond just being a mathematician". When she talked about her successes, barely any mention was made of her work beyond the book she has written. Instead, she spoke of the home she has made in Newcastle, the daughter she raised, and the half marathons she has run. “I don’t think when I retire from Newcastle I will get massive […] praise, and I don’t think they’ll have a big party to celebrate me as I leave but that’s fine". Rees said she wanted to live a “well rounded life” and was happy that she thought she had managed to find that balance.

When I asked Byrne about her biggest successes, she was keen to emphasise her personal triumphs, fellowships, grants, and other academic accomplishments: “there are all of these stepping-stones in your career that are really good”. Women often can undersell themselves and have less faith in their abilities, so it was refreshing to hear a woman advocate for herself and be rightly proud of the achievements she has had. She also spoke about her pride of the numerous students she has mentored: “seeing them develop and get to where they want to be, […] those are achievements that I enjoy”. Her care for her students, whether that be undergraduate, PhD students or Postdocs, really shines through. When talking about her opinions on research vs teaching, Byrne stated: "if you have students […] to me they’re my priority, which, I don’t know, maybe that is a female thing and other people would perhaps prioritise themselves above that".

Kirwan similarly spoke of her love of teaching – she had originally planned to become a teacher before she was persuaded to explore her maths ability first. She described her enjoyment in finding a balance of the two: “it’s very nice at the end of a week, even if your research hasn’t been going well, to have been able to feel like you’ve contributed in some other ways”. What I think is important to draw from this is not that woman should prioritise themselves over anyone else, but that they should have the choice. The choice to focus on their students, or to make their research a priority, the choice to not feel obligated to take on extra pastoral responsibilities if they don’t want them, and to only be on as many committees as they want – women should have a say in how their career is run, whatever that may look like.    

We cannot make huge generalisations based on the information presented here; only three interviews were conducted with women with very similar backgrounds, ethnicities, and nationalities. All went to Cambridge before coming to Oxford, successfully completed their DPhil and managed to find permanent positions, all whilst balancing maths with personal lives. For a real insight into difficulties faced by women we would need to speak to many more women, with larger diversity, as well as speaking to the ones who did not end up making the leap into academia (they would be much more difficult to locate; however, they would probably be able to reveal more reasons as to why the so-called ‘leaky pipeline’ still exists in maths).

We are learning more and more about this topic, due to research being conducted by many different groups, but there is always more to discover. However, what we can draw from this project is that despite having this small number of interviews, the experiences of these women are vastly different, due in part to the circumstances surrounding them during their academic career that have been discussed here.  One thing they do all share is the following opinion: even though we’ve come an incredibly long way in levelling the playing field for women, more work needs to be done. Increasing the numbers of women pursuing maths at all levels is important, but we also need to ensure that once these women enter the system they do not get forgotten about; that the support and opportunities that are created for them are maintained, so these women can continue to succeed.  

Whilst they have been small in number, the female mathematicians I’ve met have been anything but small in nature: from my maths teacher who spent her free time working with me to help me get into Oxford, who inspired me with her stories of being told “women don’t study maths” and doing it anyway, to my college tutor in first year who was the first woman doing maths as an academic that I’d ever met, who made the three girls in my year feel so welcomed and included.

From the beginning of this project, I knew I wanted to speak directly to women to understand their experiences, but what I didn’t realise was that I’d come away feeling so inspired. The opportunity to meet people who are leading experts in their field, highly respected in their subject, who have accomplished some incredibly impressive things in their career was an experience that left me in awe.  Whilst choosing to do maths nowadays means I’ve still experienced being outnumbered to an extent, I admire the women who made the choice at a time when they were not just a minority but almost an anomaly. I’ve not met many women in maths so the opportunity to speak with these women, realise I relate to many of their experiences, and just see them rightfully exist and make themselves heard was something that will stick with me. I am grateful to these women and to all others who faced so much adversity and made that leap so that young women like myself feel like being a woman and being a mathematician is something that can and should coexist".

Maddy Underwood

Maddy Underwood is an undergraduate at Worcester College. This article is the fruit of her Student Summer Research Project here in Oxford under the guidance of Mate Szabo. The Summer Research Projects aim to give our undergraduates a taste of the world of mathematical research.

Acknowledgments: the work is funded by UK Research and Innovation, through grant  EP/R03169X held by Professor Ursula Martin.

[1] LMS report on Advancing Women in Mathematics