PureMathematics

27
Apr
2022
Rachel Thomas

Rachel Thomas

Born in Perth, Australia • Birth year 1974 • Studied Mathematics at the University of Western Australia in Perth, Australia • Highest Degree MSc (Research) in Pure Mathematics • Lives in London, UK • Occupation Editor of Plus magazine (http://plus.maths.org)

When I started university, I planned to be a physicist or astronomer – I can’t deny I was heavily influenced by a love of scifi! I had a great time working in a gravity wave lab one summer, but the experience also made me realise I didn’t have the patience or practical ingenuity to be an experimental scientist. I found the theory fascinating. But at the lab flanges wouldn’t seal properly and huge niobium bars couldn’t be cooled low enough – I wasn’t as fascinated by the practical experimental problem solving.

I then remembered my other film-influenced career plan of becoming an archaeologist and took courses in Australian archaeology and Greek art and architecture. I had a brilliant time but again, I realised I didn’t have the patience required for the field work and analysis. I spent weeks trying (and not really succeeding) to make sense of tray after tray of very small grubby objects that I had dug up. I loved the ideas behind both of these glamorous careers, but the actual nitty gritty doing of the work just didn’t excite me.

Academia wasn’t appealing to most of the women I had studied with.

In the meantime, I’d been doing maths all along and I loved it. Originally, I took maths because I needed it to study physics. Then I kept studying maths because it turned out to be really fun. I really liked the actual doing of the maths – playing with linear algebra, proving something in group theory – each new area we were taught was so exciting with new concepts and new language or giving familiar ideas an entirely new perspective.

I loved doing research in semigroup theory for my Master’s degree and often couldn’t wait to get back to the desk to move my work forward. Unfortunately though, I didn’t really feel part of the community of my maths department. With hindsight, I’m sure this was partly due to being one of just a few female students when I was at honours and then postgraduate level. Academia wasn’t appealing to most of the women I had studied with. When things didn’t work out with my supervisor I nearly dropped out and left academia to work as a consultant mathematician on projects in government and industry. But fortunately, my generous boss, a brilliant female professor from the department, and my good friends supported me to finish my Master’s dissertation.

(…) it was in this job, and during the writing of my Master’s dissertation, that I discovered how much I loved communicating mathematics.

My work as a consultant was varied, and despite rarely crossing paths with the maths I’d learnt at university my degree had prepared me to learn quickly and to discern the structure of a problem and how I could use available data to answer meaningful questions. My maths training also helped me to communicate with the clients and it was in this job, and during the writing of my Master’s dissertation, that I discovered how much I loved communicating mathematics.

When I moved to the UK, I knew I wanted to write about maths. I was lucky enough to get a job with the Millennium Mathematics Project (MMP), a maths and education outreach initiative based at the University of Cambridge, before I left Australia. I quickly moved into working on Plus magazine, the part of the MMP that enables anyone who is curious about maths and the world to see the maths behind current events and keeping up to date with current maths research.

To see maths so visibly making a difference in the world, and to witness the passion, creativity and dedication of the mathematicians involved has been amazing.

Twenty years later I still love working at Plus, every day learning about new maths and new applications and talking to the mathematicians who make it all happen. My brilliant co-editor of Plus, Marianne Freiberger, and I get to go on all sorts of amazing mathematical adventures. Our work has taken us around the world, we’ve spoken to brilliant mathematicians from academia and industry, we’ve written several popular science books, appeared on TV and radio and worked on documentary series for the Discovery Channel working with our colleagues at the Centre for Theoretical Cosmology. And over the last two years we’ve been lucky enough to work with epidemiologists working on the mathematical front line of the COVID-19 pandemic, helping to explain and communicate their work. To see maths so visibly making a difference in the world, and to witness the passion, creativity and dedication of the mathematicians involved has been amazing.

Things have changed a lot since I found myself as one of only a few female students at the end of my time at university.

Things have changed a lot since I found myself as one of only a few female students at the end of my time at university. Despite no longer being an academic mathematician, I feel firmly part of the maths community today.  And I’m very happy that nearly half the mathematicians and researchers Plus has collaborated with over the last year are women. A new community spirit seems to be rising in many mathematics departments, heavily influenced by the experience and hard work of the female researchers already there. I hope that these networks, and projects including Her Maths Story, are helping women in mathematics find the support and the supporters they need to follow their own maths stories.

Posted by HMS in Stories
19
Jan
2022
Marina Murillo

Marina Murillo

Born in Cádiz, Spain • Birth year 1987 • Studied Mathematics at Universidad de Cádiz, Spain • Highest Degree PhD in Mathematics • Lives in Valencia, Spain • Associate Professor of Mathematics at Universitat Politècnica de València

Ever since I was in high school, I realized that I wanted to pursue a degree in science. Since I was a kid I loved reading mystery novels and discovering the murderer. Soon, I realized that I enjoyed solving problems and exploring their solutions and that was the reason why I studied mathematics. My high school teachers also inspired me and had a lot to do with my decision.

After graduation, I was not totally sure what to do because I had always liked teaching but I also wanted to do research.

At the beginning of my university studies, I was a bit scared because everybody told me mathematics was very different from the way  it was studied at high school. However, I enjoyed studying for my degree a lot and surprisingly, most of my classmates were women. During my university experience I was totally focused on my degree. After graduation, I was not totally sure what to do because I had always liked teaching but I also wanted to do research. So I started my PhD with the objective of being a university professor. I opted for pure mathematics during my PhD and I selected linear dynamical systems as my field of research.

The academic path is very hard. It takes a lot of time to obtain a permanent position and you must make sure you will be willing to live in different cities and not achieve job stability for a long time. However, it has its advantages.

During my PhD, I should say I had some doubts if I was doing the right thing and if I had taken the correct decision. The academic path is very hard. It takes a lot of time to obtain a permanent position and you must make sure you will be willing to live in different cities and not achieve job stability for a long time. However, it has its advantages. You can travel all around the world and meet a lot of people. Despite my doubts, I finished my PhD in three years and I got a postdoc position in Bilbao.

Now, at 33 (years), I am happy to have the opportunity to do what I love, to teach and research, while enjoying a decent salary and the desired stability.

As I mentioned before, I always had in mind my goal of working at the university, so when I had the opportunity to get a temporary position in Castellón I didn’t think about it. I moved there and although I knew that I did not want to spend my whole life there, I followed the necessary steps to achieve my goal. After three years and a long time earlier than I dreamed of, I got a permanent position in Valencia where I studied for my doctorate. Now, at 33 (years), I am happy to have the opportunity to do what I love, to teach and research, while enjoying a decent salary and the desired stability.

During my academic career I have had wonderful experiences and I am pretty sure that I have done the right thing, although I have encountered some difficulties. I have met some high-level mathematicians who treat young students with an air of superiority. This situation can be frustrating and makes you wonder if you are in the right place. However, I have also met some great mathematicians who have helped me a lot.

If I were to give advice to someone who wants to start an academic career, I would suggest that you take some time to think about whether you are willing to sacrifice time to gain some stability and travel around the world.

Mathematics is still a man’s field. Most of the top positions are held by men but, fortunately, today women are gaining prominence. Summing up my experience as a researcher, I can say that it has been positive. If I were to give advice to someone who wants to start an academic career, I would suggest that you take some time to think about whether you are willing to sacrifice time to gain some stability and travel around the world. If the answer is yes, I would definitely recommend that you follow your dream.

Posted by HMS in Stories
22
Dec
2021
Dr Ems Lord

Dr Ems Lord

Born in El Adem, Libya • Studied Pure Mathematics at University of Lancaster, UK • Highest Degree PhD in Mathematics Education, University of Cambridge, UK • Lives in Lincolnshire, UK • Occupation Director of NRICH, University of Cambridge

My journey is a story of twists and turns. There never was a grand plan, just a love of maths to help steer the way.

I wasn’t the healthiest of children, I missed more school days than I ever managed to attend. It would have been easy to fall behind in my studies, but my headteacher had different ideas. Textbooks appeared in my home and my mum was roped in as my teacher. Perhaps rather frustratingly for her at times, my curiosity was never satisfied; I always wanted to try different ways of doing things. I loved playing games, but also inventing new maths games too! I’d even collect the numbered cardboard doors off my advent calendar to use in them in my latest creation.  Numbers had a special place in my life from a very early age.

Having decided that maths was the subject I wanted to study at university, the transition from school to university maths was not as straightforward as I hoped; coming from an all-girls school, it was a shock to find myself on a course dominated by boys. I’d never really associated maths as a ‘boys thing’ until that point. Maths had always been something I just enjoyed doing, but perhaps not everyone enjoyed the same opportunities as I had growing up.

Wednesday afternoons at University  were spent on the sports field or at a local teaching college. Although I love sport, my curiosity meant that I eventually tagged along with the teaching group one day – and never turned back! Our tutor challenged everyone to subtract two numbers and record our method – not exactly a tough challenge for soon-to-be maths graduates but I soon discovered that I was the only person in the room to use my chosen approach, and there were two or three other methods in general use around the room. When we were asked to explain our approaches, there was a discussion about ‘milk bottles on doorsteps’ which totally confused me. What did milk bottles have to do with subtraction?  Turns out that the ‘milk bottles’ were place value jottings. No wonder so many people complain that they find maths confusing!

[…] through the college session I realised that my ongoing love for investigating different approaches could be usefully applied to teaching. If someone was struggling or could not understand an approach, I could perhaps suggest another way which might work for them and explain it too.

At the time of that college visit, I was focusing on my thesis exploring the different ways mathematicians had proved the Pythagoras Theorem, and through the college session I realised that my ongoing love for investigating different approaches could be usefully applied to teaching. If someone was struggling or could not understand an approach, I could perhaps suggest another way which might work for them and explain it too (without referring to milk bottles). And, as a female mathematician, perhaps I could be a role model too. Suddenly all the pieces fell into place and I applied for teacher training.

[…] I quickly discovered that hardly any primary schools had a maths graduate on their staff and creativity was often being stifled by a lack of confidence and subject knowledge.

As a maths graduate, I opted for a secondary teacher programme which came with a generous grant for signing-up to teach a shortage subject. Tutors required trainees to spend their first fortnight in a primary school, I quickly discovered that hardly any primary schools had a maths graduate on their staff and creativity was often being stifled by a lack of confidence and subject knowledge. Even though it meant losing my ‘welcome’ grant, I switched to a primary course and I’ve never looked back. Primary teachers are incredibly hard-working individuals who need to cover a wide range of subjects and inspire their charges all day, every day. They are amazing people. I soon found myself leading maths in my school and supporting the teaching of maths in other schools nearby by sharing useful resources. At that time, I became an advocate for the types of maths resources designed by NRICH which challenge and engage young learners.

After joining my local authority’s maths team, I helped to set up schools’ maths competitions and lead parental engagement events – opportunities for families to enjoy problem-solving and rethink commonly-held negative views about maths. By volunteering to lead maths masterclasses introducing some of my favourite undergraduate classes such as topology and networks, I hoped I could also act as a role model for younger female students. Ever curious, I began reading more widely about maths education and signed up for my Masters and later my PhD at Cambridge (where I investigated different approaches to calculation, of course!). Today, my love of maths means that I get to work in one of the world’s finest maths departments at the University of Cambridge, helping to support school teachers to inspire future mathematicians and researching ways to increase diversity in my chosen subject as the Director of NRICH – a project which had inspired my classroom teaching. It’s such a privilege working with the NRICH team, and we’ve got exciting plans for the future. Watch this space!

Posted by HMS in Stories
13
Oct
2021
Angela Tabiri

Angela Tabiri

Born in Tema, Ghana • Studied Mathematics at the University of Glasgow, UK • Highest Degree PhD in Mathematics • Lives in Accra, Ghana • Occupation Lecturer

Growing up in Accra, Ghana, I loved mathematics. I found joy in solving mathematics questions but I did not envision a career in mathematics as a thing for me. My older sisters studied business courses at the university so I decided to follow in their footsteps and applied to study Business Administration as my first choice course at the University of Ghana. Fortunately or unfortunately, I could not gain admission for my first choice program and had to settle for my second choice which was mathematics and economics. Nevertheless, I loved the challenge mathematics presented. I had to spend hours after lectures revising lecture notes and solving exercises. I found this thrilling.

My motivation for giving back to the community where I grew up was to give students from less privileged backgrounds access to quality education.

After undergraduate studies, I went to the African Institute for Mathematical Sciences (AIMS) Ghana for postgraduate studies. It was at AIMS that I got exposed to different fields of mathematics. From AIMS Ghana, I went to the International Centre for Theoretical Physics (ICTP) for a postgraduate diploma in mathematics. The program at ICTP was very challenging but it helped convince me that I could pursue mathematics further.

After postgraduate studies, I became conscious of the opportunities available when one studies mathematics. Prior to this, most of us thought anyone who studied mathematics at the university would end up as a teacher. This is not to say that teaching is not a good profession, I love teaching. When I realised the many opportunities available after postgraduate studies, I volunteered as a mathematics teacher in a junior secondary school in my community. This would inspire the young students that mathematics is not impossible to study as perceived and one could pursue a career in mathematics. In subsequent years, I volunteered as a mathematics teacher for at least a month and donated books to the library of this school. My motivation for giving back to the community where I grew up was to give students from less privileged backgrounds access to quality education.

My research interest is in noncommutative algebras which are abstract analogues of subtraction and division.

I was awarded a Schlumberger Foundation Faculty for the Future Fellowship in 2015 to pursue PhD in Mathematics studies at the University of Glasgow (UofG). In 2019, I graduated with a PhD in Mathematics from UofG, returned to my home country Ghana and started working as a postdoctoral fellow at AIMS Ghana. I am currently a research associate and academic manager for the Girls in Mathematical Sciences Program (GMSP) at AIMS Ghana. I decided to pursue a career in academia because I love teaching and doing research.

A summary of my research interest is as follows. Consider the operations of addition and multiplication, it does not matter the order in which you perform them. That is, 2 + 3 = 3 + 2 and 2 × 3 = 3 × 2. In mathematics, we call this the commutative property. However, the operations of subtraction and division are not commutative. That is 2 − 3 is not equal to 3 − 2 and 2 ÷ 3 is not equal to 3 ÷ 2. We say that subtraction and division are noncommutative. My research interest is in noncommutative algebras which are abstract analogues of subtraction and division. For any shape that you can draw on a flat surface whereby the shape can be described by an equation, we investigate whether we can put a noncommutative structure on the shape to make it a quantum homogeneous space. This area of research is abstract but our hope is that there will be useful applications of our results in a few years time.

Our mission is to inspire young girls about the diverse career options available when you study mathematics and our vision is to see girls being confident to pursue a career in mathematics and related fields.

I am passionate about supporting and promoting women in mathematics which ties in well with my new role as the academic manager for the GMSP. The GMSP is a hybrid 9 month program for high school girls from Ghana to nurture their talents in the mathematical sciences. We meet students monthly online for masterclasses with experts in different fields of mathematics. Then during vacations from school, the students visit the AIMS Ghana campus for residentials where minicourses in mathematics, industrial visits, interactions with mentors and extracurricular activities are undertaken.

I am also the founder of Femafricmaths, a charity that promotes female African mathematicians. We host guests by interviewing them about their journeys with mathematics and share the videos on the Femafricmaths social media pages. Our mission is to inspire young girls about the diverse career options available when you study mathematics and our vision is to see girls being confident to pursue a career in mathematics and related fields.

There are few of us and we need to ensure that barriers are removed so more women can pursue careers in mathematics.

Mentors have played a critical role in my academic and professional journeys. Ken, Ulrich, Prince and Chelsea have been phenomenal mentors who mentor me every step along the way. I have also benefited from the Women in Noncommutative Algebra and Representation Theory (WINART) research group. This is a collaboration between women in mathematics from different universities. I learnt a lot working with this research group comprising both early career and established mathematics.

It is important to be intentional about creating opportunities for women in mathematics. There are few of us and we need to ensure that barriers are removed so more women can pursue careers in mathematics. I was awarded a Schlumberger Foundation Faculty for the Future Fellowship for my PhD studies. This fellowship is for women in STEM from developing countries to enable us to study at top universities abroad and return to our home countries to support teaching and research. It would have been challenging to find other sources of funding for my PhD if I had not been awarded this fellowship by the Schlumberger Foundation.

Link:
Femafricmaths – Female African Mathematicians

Posted by HMS in Stories
15
Sep
2021
Maylin Wartenberg

Maylin Wartenberg

Born in Braunschweig, Germany • Studied Math (diploma) at the Technical University in Braunschweig, Germany • Highest Degree Doctorate in Math (Dr. rer. nat.) • Lives in Meine, Germany • Occupation Professor at the Hochschule Hannover – University of Applied Sciences and Arts, Department of Business Information Systems, Field of Data Science

Analytical thinking has always been easy for me. Therefore, I enjoyed the rules and patterns that occur in math from early on. Luckily, I recovered quickly after the German high school greeted me with the minimum pass mark “adequate” in the first two math exams in 7th grade. In 9th and 10th grade, we had a very strict “old school” teacher who left a lasting impression. We always had to stand up to greet him, and if you used a swear word in class, you had to wash the glasses in the chemistry room during the next break. He was strict, but he liked me and I learned a lot. In 11th grade I spent a high school year in the US and after this year I wanted to take math as one of my advanced courses. That was a tough decision because all I did at the American high school was statistics whereas in Germany everyone had started with curve sketching. After my return to Germany, the first exam in 12th grade was about this topic. I didn’t know anything about it and I had 6 weeks of summer break to study. A former very kind teacher helped me with the material and I studied by myself and achieved a good mark. That was a major milestone to my decision to study math, since I was able to teach myself the topics of almost a whole school year. But I still wasn’t sure. Math or psychology?

After all the ups and downs you typically encounter during this phase – 3 years for me – I finished my doctoral thesis in math (graph theory) two weeks before my first daughter was born.

Both sounded very attractive to my 19-year-old self. The plans to move to Braunschweig with two of my friends were already settled and I finally chose math because it was giving me a wider range of options on what future opportunities to follow – because I had no clue what to do after my studies at that point. In the beginning we were quite a few students, but in the end only 4 of us were left in pure math – 25% women 😉. I chose most of my courses in abstract math – algebra, combinatorics – and did as little applied math as possible. I really enjoyed the study of group and ring structures and the book Algebra by Serge Lang was always by my side. I already dreamed of becoming a professor myself.

Yet, in the end, the question what to do with all the knowledge I gained crept more and more into my consciousness. That is why I didn’t pursue a strictly academic career, nevertheless I still wanted to secure the option, and chose a PHD position in business at Bosch (formerly Blaupunkt) in Hildesheim. No more group and ring theory, suddenly I had to write code in C++ for algorithms in navigation systems. I had avoided any computer science so far, thus, I was thrown in at the deep end. But I never regretted this step because I discovered that coding is not all at all as difficult as I thought – after all it’s logical – and I learned a lot about working in a bigger company. After all the ups and downs you typically encounter during this phase – 3 years for me – I finished my doctoral thesis in math (graph theory) two weeks before my first daughter was born.

I found the fitting position where I can combine my passion for analytical thinking, my academic background, and my work experience (…).

I stayed home with her and somehow managed the defence of my doctoral thesies with a 5-month-old baby and still deprived of decent sleep. After 8 or 9 months at home, my brain started asking to be challenged again, and I began to apply for jobs in industry. As a young mother I wanted to start part time, but as a woman holding a doctorate in mathematics that was not as easy to get as I hoped. After a long search, including several offers with 40 hours and more, I was finally rewarded by starting a job at VW Financial Services. My one-year-old daughter was able to stay at the company’s own childcare facility and I started with 27 hours a week as a systems analyst in the business intelligence department in IT. In almost 10 years I made my way from analyst, to project lead, to team lead all the way to head of two sub-departments and got enrolled in the management trainee program – most of this in part time including a maternity leave when I had my second daughter in between. Then, suddenly, another option which had gotten a little out of sight but was still a silent dream popped back in.

And that is my way to my current position as a professor in business computing, especially data science. I found the fitting position where I can combine my passion for analytical thinking, my academic background, and my work experience – all of that with the advantage of being my own boss, still doing interesting projects with different companies, giving talks about AI for lay audiences (schools, senior clubs, …), and guiding young people on part of their own story.

Posted by HMS in Stories
02
Jun
2021
Marianne Freiberger

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. 

Posted by HMS in Stories