Mathematics

Jun

2021

A Feminist Rant

Or a Plea for Change

by Joana Sarah Grah

Do you still come across the common stereotypes against mathematicians in general and women mathematicians specifically? Maths is boring, maths is for loners, maths is unsexy (and done by unsexy people – I just stumbled upon this again recently when reading a quote-retweet by Hannah Fry replying to someone who claimed there are no “hot” people that are good at maths – just for the record, I know quite a few), maths is dry and above all – maths is for men!

I don’t know about you but I’m so tired of it. When did we exactly start to think that being good at a subject at school is something to be made fun of or to be ashamed of? I have heard this so many times: “Oh, I’ve always hated maths.”, “Only geeks and losers like maths.”, “I always sucked at maths.”. But in a – you know – kind of proud way? What’s wrong? Do you like not being able to calculate the appropriate tip when you’re eating out? Do you enjoy not understanding probabilities, hence not being able to evaluate risks for instance? Did you never see the exponential growth of infections during the pandemic – which has always been exponential in the first place – coming? It’s always easier to deny things we don’t understand but are afraid of. In the current situation this is particularly dangerous and even probably harmful for others. Nothing to be proud of if you ask me.

A solid foundational education in mathematics is essential, no doubt. But maths is so much more than being good at calculating stuff. In fact, I couldn’t name any area of application where maths doesn’t play a role. Natural sciences like physics, chemistry and biology, earth sciences, astronomy, medicine, economics, arts restoration – those are just some examples that come immediately to mind. The variety of mathematical fields and the respective methods is similarly vast – there’s so much to explore and really something to be passionate about for everyone. In addition, maths is absolutely no discipline where teamwork isn’t encouraged. In fact, you discuss and brainstorm with colleagues day-to-day (although there are exceptions of course). Interdisciplinarity is key to most problems and projects arising in applied maths.

Now let’s get to the point that bothers me the most and that is the reason we set up this webpage. Unfortunately, it’s still a common misperception that maths is not for women. Pretty pathetic given that we’re living in 2021 you ask? Yes, absolutely, but it turns out we’re still living in a patriarchy. That is why we need to be feminists.

At the beginning of your studies, you probably won’t realise the disproportion between women and men in maths. You’ll notice that you have very few or even no women professors. Most of the academic staff is likely to be men. The gap becomes more obvious the further you get. Finding women working in the same field at conferences is probably much more difficult than finding men. Seeing women on discussion panels and giving talks will be the exception rather than the norm. It is getting a bit better though and many people are aware of the problem and encourage diversity. Yet the majority of women seem to decide at some point of their academic career that they don’t want to pursue it further. Why is that? Anti-feminists, mostly men, often claim that it’s their personal choice to leave because they prefer a part-time job, a job in a less competitive environment, a job that fits their “abilities” and “interests” more, because they want to have a family and won’t be able to have children and an academic career. Nothing wrong about any of this but the crucial point is having the choice. It is indeed possible to both have a family and a professorship. And it is indeed possible to be a professor while still prioritising your leisure time, your mental health, your family, your friends. Not all women are given those opportunities. Most women don’t have the choice. It is a structural problem, an institutional problem, a societal problem. Maybe you missed the important discussions because you left an informal meeting after a conference day, as you were the only woman and felt uncomfortable, or because you didn’t have childcare for the whole night. Maybe you risk a huge fight with your family, or even ending the contact altogether, or you lose a relationship, because you’re spending too much time writing grants (instead of attending family events, going on your long-planned vacation or caring for your kids – or having kids). Maybe all the people in power making decisions are men and they like to surround themselves with like-minded men.

We need to make women in maths visible for the next generation who are desperately searching for role models because they don’t see them. We need to amplify the voices of women in maths because oftentimes the voices of men in maths are much louder. We need to showcase the variety and – more often than not – non-linearity of career paths including failures, doubts, setbacks, maybe starting all over again, maybe changing fields completely, maybe having children. We need to raise awareness for the lack of resources in schools and universities to highlight women in mathematics, for the fact that mental health is actually physical health and just as important as making sure you stay up-to-date with the literature and back up your work regularly. We need to normalise not working crazy hours on a regular basis, having a family, not having a family, admitting that you don’t know something, asking “stupid” questions (I know it’s stale but there really are no stupid questions, most of the time those are the important questions to ask) and having interests that have nothing to do with maths.

Why do I write this now rather than at the time when we launched our page at the beginning of the year? Because I was afraid I would sound too aggressive, I would probably exaggerate things and because I’m sharing very private opinions and experiences. On the other hand, it was about time. I reflected a lot about this recently and realised how much of it I suppressed or dismissed as innocuous. What really fuelled my anger was when I saw injustices happening to other women, to friends, to the next generation. Most of the time they seem subtle but they do impact your day-to-day work life significantly. I experienced women suffering from imposter syndrome that came across so strong and confident yet still being at the mercy of the broken system and socially acceptable misogyny. Besides the structural problem, there is the everyday sexism all of us are familiar with. Do you find it hard to literally be heard in a discussion? Do you have to raise your voice a bit extra? I certainly had to sometimes. Another classic is when a man paraphrases something you just said and gets all the praise for it. Is this something we just have to cope with? What about strangers at conferences asking you out for dinner during a poster presentation? Uncomfortable to say the least. Something we have to bear? I have once been told that I should apply for a professorship simply because I’m a woman and these days it’s super easy for women to get a position, basically everyone is accepted. I don’t think that’s acceptable and I wish I had been more assertive in this situation.

I don’t want to close on a negative note though. Thankfully, I had so many more positive encounters during the past years in academia than negative ones. Men and women who were genuinely interested in discussing research, appreciated my advise, gave me very valuable advice, motivated people – especially women – who were struggling and doubting themselves, facilitated socialising and networking at academic events, showed their own vulnerability and insecurities, shared their failures and how they overcame hurdles, educated themselves and were feminists. Let’s take them as an example.

Let’s try to be a bit more understanding, a bit more empathetic and a bit more supportive in this already stressful, fast-paced, competitive environment that academia mostly is. Let’s speak out clearly if we witness any kind of bullying, sexism and harassment. Of course things have to change on a much bigger scale and first and foremost systemically. But every one of us can make a difference – no matter how small – so let’s start today!

Jun

2021

Marianne Freiberger

Born in Münster, Germany • Birth year 1972 • Studied Pure Mathematics at Queen Mary, University of London • Highest Degree PhD in Mathematics from Queen Mary, University of London • Lives in London, UK • Occupation Editor of Plus magazine (http://plus.maths.org)

I first became interested in maths when I learnt about the epsilon/delta definition of a limit at school. The fact that something as intuitive as a limit could be expressed so precisely in symbols blew my mind. Despite that interest, I didn’t really plan on studying maths at university. The reason I did was that I had moved to the UK from Germany after school and, when I finally decided to do a degree, thought my English wasn’t up to studying a more wordy subject (which is ironic given that I am now a writer).

I enjoyed my BSc, but by the end of it still didn’t think that maths would be part of my future. I spent a year working in all sorts of jobs and travelling, until a book by Ian Stewart re-ignited my passion. I applied for a PhD place with Shaun Bullett at Queen Mary, University of London, where I spent the next few years studying and researching holomorphic dynamics (which involves things like Julia sets and the Mandelbrot set). Shaun was a great supervisor who safely got me through my PhD (can’t have been easy!) and enabled me to stay on for another three years as a postdoc.

Because I’d been interested in science communication for a while, I applied for a maternity cover job at Plus magazine

Finding the next postdoc proved tricky and my heart wasn’t really in it. I didn’t want my life to revolve around my job, which as a postdoc is something you usually have to accept, and wasn’t sure I was a good enough mathematician. (Whether the latter was true or just down to lacking confidence — a notoriously female affliction— I still don’t know.) But it all turned out for the best: because I’d been interested in science communication for a while, I applied for a maternity cover job at Plus magazine. That was in 2005 and I am still at Plus now, co-editing along with my good friend and colleague Rachel Thomas.

Plus is a free online magazine about all aspects of maths, aimed at a general audience. It’s part of the Millennium Mathematics Project based at the University of Cambridge. My job there involves writing articles, producing podcasts and videos, and editing other people’s submissions. We cover anything from abstract algebra to astronomy, and theoretical physics to the science of sport.

(…) Once you have an explanation of something in very simple terms, you’ve done some of the hardest part of the work that’s needed to explain it accessibly to others

Starting at Plus was quite a gear change initially. My command of English no longer felt like such an obstacle, but I had no journalistic or writing training. I did a couple of writing courses offered by Cambridge University, but all the really important stuff I learnt on the job from the two brilliant writers and editors then working on Plus, Rachel Thomas and Helen Joyce, and by example from my boss, the amazing John D. Barrow (who sadly died last year).

Ironically, my ignorance also helped me with my writing, I think. I knew almost nothing about most areas of maths, let alone other sciences. This meant doing lots of reading and then explaining things back to myself in baby language — and once you have an explanation of something in very simple terms, you’ve done some of the hardest part of the work that’s needed to explain it accessibly to others.

As a young researcher I’d internalised a fear of asking stupid questions, but as a maths communicator questions are your most important tool

While writing gave me lots of joy, other things were harder to learn. When I started at Plus, I think many mathematicians weren’t as familiar and comfortable with public engagement as they are now. I struggled sometimes to be taken seriously. As a young researcher I’d internalised a fear of asking stupid questions, but as a maths communicator questions are your most important tool. It took me a while to work that out and learn the courage to ask.

Today things are a lot easier in that respect (though I still sometimes spend ages trying to figure something out when I could just go and ask someone). The reason it’s easier is probably that attitudes towards science and maths communication have changed, and that I am older, a tiny bit wiser, and a little more confident.

At the moment we are collaborating with a group of diseases modellers (called JUNIPER) who have been advising the UK government, to bring important concepts and issues about COVID to a general audience

I love my job because it allows me to do what research didn’t: to learn a lot about all sorts of topics but without having to dig too deeply into the technical details. I get to meet amazing people and there are lots of opportunities to branch out and learn more. Rachel and I recently worked as science editors on a Discovery Channel series about the work of Stephen Hawking and privately co-wrote three popular maths books. At the moment we are collaborating with a group of diseases modellers (called JUNIPER) who have been advising the UK government, to bring important concepts and issues about COVID to a general audience. I feel very fortunate to have been given these opportunities.

To someone who’d like to go into science communication as a career, I’d say to get a good grounding in maths before (or while) you’re getting training in writing and communicating. Maths is everywhere in science, and if you can vaguely understand the maths in a piece of science, then you’re already a good way to understanding the rest.

May

2021

Candice Price

Born in Long Beach, CA, USA • Birth year 1980 • Studied Mathematics at The University of Iowa in Iowa City, IA, USA • Highest Degree PhD in Mathematics • Lives in Northampton, MA, USA • Occupation Assistant Professor of Mathematics at Smith College

I first fell in love with mathematics in the 3rd grade. It was by pure coincidence though. You see in the 3rd grade I learned how to multiply. Now we did not learn through the tangible way of repeated addition, but with music and memorization. Both of these pedagogical choices stimulated my interest in two ways: my love of music and my competitiveness. Let me elaborate a bit about this.

My whole family is very musical. My maternal grandfather was in a DooWop group named “The Mellows”. He taught my mother to sing, which translated to me singing in the church choir with my siblings. My father constantly played music in our home, especially on his record player. My sister and brother made music a part of their careers and I listen to music any chance I get. Needless to say music played a huge positive role in my life, and still does. So when my teacher played the SchoolHouse Rock multiplication videos for us in class, I was instantly sold! I still sing the song “3 is a magic number” sometimes. I got to see that music could play a large role in learning mathematics. It made mathematics fun and enjoyable. It also helped me memorize the multiplication table because I had memorized the lyrics. This helped with my competitive nature.

Looking at those celebrated in mathematics, I didn’t see someone that looked like me.

I think it is no secret that when learning multiplication, students are often subjected to timed “times table” tests. This was a test or quiz or even just an assignment where you had to fill out a sheet of multiplication problems in maybe around 5 minutes. Oddly, I thrived on this type of competition. It wasn’t a competition with my classmates, but a competition with myself. How many “times-tables” could I remember? How fast could I write them all down? Would I improve my previous score? I think this competitive nature pushed me to love the act of learning, keeping me excited about understanding things at a deeper level. I will also say that this competitive nature has also led to my trivia team, Juneteenth Wreath LLC, being 4 time trivia champs across 2 different platforms #humblebrag.

While this was the first experience I had that created a love of mathematics, I didn’t stay in love. I have walked away from mathematics when I felt that it was not the place for me. Looking at those celebrated in mathematics, I didn’t see someone that looked like me. I assumed that meant that no matter how much I loved math, it did not love me back. (I was a bit of a dramatic teenager.) While I came back to mathematics and made it my career, it wasn’t until recently that I felt like I had a place in mathematics. I would often tell folks “I am a mathematics professor, but I don’t see myself as a mathematician”. The distinction was that while I enjoyed teaching and talking about mathematics, did I think about it on the level that most “mathematicians” do? No. I didn’t enjoy research too much, although I loved working with my collaborators. I didn’t enjoy watching research talks, unless I knew the speaker. I would also be so nervous giving talks, always a bit unsure if I was painting the correct picture. But recently this has all changed.

If today Candice could talk to 3rd grade Candice about this great path through mathematics she is going to venture on, I would tell her about the ups and downs.

I have met so many amazing people who are also mathematicians. Many, but not all, are from minoritized groups in the mathematics community, all forging ahead creating their own definition of what it means to be a mathematician. This community helped me finish my PhD in Mathematics at the University of Iowa, supported me through my postdoctoral work at the United States Military Academy at West Point, and been a great guide through multiple career decisions/milestones I have made/passed, including starting a tenure track position at Smith College and receiving tenure and promotion. If today Candice could talk to 3rd grade Candice about this great path through mathematics she is going to venture on, I would tell her about the ups and downs. Let her know that she is stronger and more clever than she knows. And that she is a mathematician, that she became one that day. I would also give her a small reminder that it is ok to not always be super excited about something– except for music, that is a love that never dies.

Mar

2021

Hanne Kekkonen

Born in Helsinki, Finland • Birth year 1987 • Studied Mathematics at University of Helsinki in Finland • Highest Degree PhD in Mathematics • Lives in Delft, Netherlands • Occupation Assistant Professor

I was definitely not one of those scientists who showed exceptional talent from a very young age. As a child I was filled with endless curiosity about everything, but sitting still in front of a desk was not one of my strongest skills. In fact, I was rather bad at school, often arriving late because I had found a frog or wandered off after a hedgehog. I did my very best to study for exams but this did not seem to translate to good grades. I kept trying and by the time I started secondary school I finally got the hang of it. I was warned that when you move from secondary school to high school, and later from high school to university, classes become more difficult but I never really experienced this because I had always had to study for the exams. I had also learned that if I couldn’t solve a problem it just meant that I had to try harder, not that the problem was too hard. I only realised later how lucky I was to have learned proper studying techniques already as a kid.

I like knowing that mathematics has many applications but I have always been mostly interested in the theoretical parts and loved the pureness of mathematics.

I never had anything against mathematics (other than mental arithmetic which I’m still very bad at) but I only really got interested in it at high school. At high school maths problems are like puzzles you have to solve using given rules and tricks. In university the emphasis changed and the weight was more on understanding where those rules and tricks come from and why they are true. I like knowing that mathematics has many applications but I have always been mostly interested in the theoretical parts and loved the pureness of mathematics. It is the only field where questions have indisputably correct answers and where the trueness of a statement can properly be proved.

I have to admit that I didn’t really think too much about what I would do after I got my Master’s degree. Throughout my studies I was told that there was a shortage of skilled mathematicians at the job market but there seemed to be a big gap between what I had learned at the university and what was needed in the real world. Thankfully, my Master’s degree advisor suggested that I should apply for one of the open PhD positions in the Inverse Problems group at the University of Helsinki, where I was doing my Master’s degree.

Starting the PhD was the biggest shock in my studies. Even though the exercises at university were much longer and more complicated than the ones at high school, they always had a clear answer, even if I couldn’t find it. But when I started to do research, I had to get used to the idea that no one knew the answers to many problems I encountered or even if they could be solved. Also, instead of following well-structured courses, where I usually had at least some idea on what was going on, I was now attending several seminars about topics I had hardly even heard of. I was feeling really uncertain about my skills and progress. I was told by several more senior members of my research group that they also used to feel like that and it would get better, but this was only somewhat reassuring. I think the key point they forgot to make was that you won’t stop feeling uncertain because one day you learn to understand all those talks, but because you just get used to the idea that there are so many research topics that you can’t possibly understand them all.

I really like showing people how mathematics is so much more than just the arithmetic they learned to hate at school.

During my PhD I was part of a great research group with supporting advisors and I really enjoyed working at the university. I decided quite early on that I wanted to stay in academia and so after I finished my PhD I moved to the UK for a postdoc position, first in Warwick and then in Cambridge. As a postdoc I had to learn to work even more independently than as a PhD student and how to combat the ever-present imposter syndrome. I also started to do some outreach, giving talks to the general public and school students. I really like showing people how mathematics is so much more than just the arithmetic they learned to hate at school. Nowadays I work as an assistant professor at Delft University of Technology. My current job is a nice blend of research and teaching, and it also offers me possibilities to do outreach. I’m happy if seeing a woman mathematician, who is excited about the subject, makes some little girl consider a science career as a real possibility.

Jan

2021

Carmen-Ana Domínguez Bravo

Born in Cádiz, Spain • Birth year 1987 • Studied Mathematics at University of Seville in Spain • Highest degree PhD in Mathematics • Lives in Cádiz, Spain • Occupation lecturer at the Department of Statistics and Operation Research, University of Cádiz

My relationship with mathematics began before I was even born. My father was a high school teacher and so was my grandmother. They both were very enthusiastic about maths and wanted to support our development of mathematical thinking. Despite this, I don’t remember adoring maths when I was a child. What I do remember though is loving books. I spent most of my childhood time reading books, from comics to mystery novels. I devoured every book, and I still do nowadays. As a child I was keen on writing my own stories, I even won a literary contest! But above all, I remember that I wanted to be a teacher. Being a teacher was kind of an obsession, that was enforced by members of my family inspiring my teaching vocation. In addition to my father and my grandmother being high school teachers, my mom was a history, art and geography teacher. My own teachers have always been very inspiring for me too. I have had the opportunity to enjoy a wide variety of excellent teachers that fed that vocation. I would say that I wanted to be a teacher since I was a child but I chose the subject to teach later on.

Above all, I remember that I wanted to be a teacher. Being a teacher was kind of an obsession, that was enforced by members of my family inspiring my teaching vocation.

My sister and I were both good students before University, very good ones. We stood out in our classes even if we did not want to. I imagine that it was also due to the persistence of our parents by instilling good study habits and the passion for knowledge in us. My father was also very (very) insistent on strengthening our analytical thinking and we spent one hour every day of the week during summer vacation solving maths problems. I was not proud of myself. For instance, I wasn’t as good as my sister at doing quick calculations. Nevertheless, for some reason I chose to study mathematics. It might be because maths seemed difficult to me, or because I was influenced by my grandmother and father, or because I wasn’t good at memorising concepts and I thought that in mathematics memorising didn’t seem that important.

Once at the university, during the first year I discovered that mathematics was something totally different from the maths taught in high school. But I enjoyed that the classes were more theoretical and had less quick calculations! I started loving the theory more than the exercises. Every year, I was struggling with a different subject which I had to study during the summer to pass the exam. I felt frustrated, especially in the first year, but I also started to enjoy living in a different city and making new friends. I remember those years as a very special time in my life and I met professors who inspired me a lot.

I had a very special female professor. Her way of teaching had a great impact on me. Her classes consisted not only of theory, but of open problems, computer practices and teamwork.

During my junior year (our fourth year), some friends and I decided to apply for an Erasmus and we finished our degree in Paris. At that time, I loved numerical calculus and I chose as many subjects in that field as I could. As a maths student, I remember that year as one of the best years ever. I had a very special female professor. Her way of teaching had a great impact on me. Her classes consisted not only of theory, but of open problems, computer practices and teamwork. At the end of that year I decided to continue studying maths and I started to look for PhD grants.

After several applications, I found a PhD position related to maths and solar energy. The research in this context was very applied, more related with cracking the code, developing and implementing algorithms and analysing results. Thanks to this opportunity I was able to study a wide range of algorithms, methods and programming languages, and I also met a lot of fantastic researchers.

From that point on I knew that teaching, mathematics and coding were a perfect match for me. This is how my journey as a maths teacher and researcher started. This journey has obviously lights and shadows, but my decision remains the same. Nowadays, I am working as a lecturer at the University of Cádiz, where my family lives. My passion for knowledge, teaching and maths is the same as once my father and my grandmother passed on to me, even though they passed away.

Jan

2021

Kristina Thurmann

Born in Lippstadt, Germany • Birth year 1988 • Studied Mathematics in Münster, Germany • Highest degree M.Sc. in Applied Mathematics • Lives in Friedrichshafen, Germany • Occupation software developer (automotive sector)

I have always been fascinated by mathematics, to be precise by calculations and computations. My parents first noticed my interest in maths at the age of 5. We often played a game called Kniffel/Yahtzee where at the end all points had to be accumulated and that was my favourite part of the game. I just loved adding up all these numbers.

My interest got even stronger during high school: in the year book one of my descriptions by class mates was „i = √(-1)“. This expression summarised pretty well my time in high school. I adored mathematics and I never had any problems in studying and understanding the subject and its concepts. But then I decided to study mathematics in university and the problems began…

We motivated each other and I slowly started to love mathematics again especially the beauty of mathematical proofs.

In the beginning, I struggled a lot in how to study. I know that sounds weird but in school I never had to study to get good grades. In school we never proved any theorem, we just used all these formulas resulting from them. However, in university I learned why these formulas are correct. In the first years of studying mathematics, I learned the basics of analysis, linear algebra, stochastic, logics and numerical analysis. I failed a lot of these exams and at some point, somewhere around the fourth semester, I even thought about quitting and doing something else. Fortunately, at this point I realised that most maths students struggled with the same or similar problems. This common issue and uniting quest created a strong sense of community among the students and that was one of the best parts of studying mathematics for me. Everybody, even the professors, were very helpful and supportive and I never felt alone. We motivated each other and I slowly started to love mathematics again especially the beauty of mathematical proofs. At the beginning of the master studies, I attended courses in applied mathematics with practical applications in the field of biomedicine, e.g. image processing in MRI, PET and CT; in numerical analysis classes I learned to write code and implement algorithms. That was my first experience in coding but to be honest I was not expecting to be a software developer one day.

I also conducted job interviews and I have learned that it is not important what you did, it is important what you love and where you want to be in the future.

After finishing my master thesis, I did not have any clue about where to go or what to do, it was hard to find job advertisements where mathematicians are mentioned. So, I signed up in several job portals and got job offers as a software developer. First I started in a consulting and engineering company and gained work experiences as a developer and a project manager. I also conducted job interviews and I have learned that it is not important what you did, it is important what you love and where you want to be in the future.

At the moment, I am working for a company which is a worldwide supplier of driveline and chassis technology for cars. Specifically, I am responsible for shifting strategies. That means I am getting a so called “change request”. Within this change request I get a specification about the functional change of the software. For example, the customer (automotive manufacturer) wants the car to behave in a certain way, like shifting to second gear only when engine speed is above a defined threshold. My task then is to understand the request, to change the software/code, to test the new software and to document everything I did. Of course this is an easy example and the reality is much more complex but the complexity and the diversity of my job is what I like.

Looking back, I am so happy that I studied mathematics because it got me where I am right now. If I could tell my 20-year-old self a piece of advice: “Just do it, you will learn so much about yourself, about logical thinking. It is a long way, be patient with yourself, surround yourself with like-minded people, they will help you to stay on track and enjoy your time at university. Do whatever you like and makes you happy.”

Or a Plea for Change

by Joana Sarah Grah

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