Interdisciplinarity

01
Mar
2023
Anna Konstorum

Anna Konstorum

Studied Biology/Bioinformatics at McGill University, Canada, and University of California, Los Angeles, USA, and Mathematics at University of California, Irvine, USA • Highest Degree PhD in Mathematics • Lives in United States • Occupation Research Staff Member at Center for Computing Sciences, Institute for Defense Analyses

I came to applied mathematics slowly, and circuitously – but sometimes that makes for the best stories. When I was young, I fell in love with the complexity of biological processes, and thus I chose to study biology for my BSc. My grandmother was a math teacher and I have fond memories of us playing all sorts of educational math games growing up, which instilled in me a joyful, non-competitive view of math. But I never saw myself as a mathematician, it was just something I enjoyed ‘on the side’.

I sat there in complete astonishment of the beauty and power of math to describe a world that I had realized I had always wanted to see in a mathematical light.

It was only when doing my Master’s, when I took a course focused on using dynamical systems to study the life sciences, that I came to see that mathematics needed to be more than a hobby for me. I sat there in complete astonishment of the beauty and power of math to describe a world that I had realized I had always wanted to see in a mathematical light. And, I felt then, everything clicked. That my love for math and complex systems such as biology were not separate, but actually completely intertwined. It was this realization that led me to do my PhD in mathematics. I performed research modeling interactions of growing tumors with their microenvironment and took classes in a wide range of mathematical subdisciplines. It was very difficult as I knew I had less experience with mathematics than many of my peers, but I also had complementary skills in working on real-world scientific problems, which gave me a unique vantage point to think about the methods I was studying. When I kept my focus on the subject matter, I knew I was where I needed to be. It was one of the hardest, but most rewarding experiences in my life.

I work at the interface of data science and applied mathematics to help address challenging problem sets in national security, and more generally in the computational and data science realms.

Something you come to understand by taking a strong pivot, is that both you and the world have the capacity to honor a new stage in your life and career, especially if you approach the challenge thoughtfully and creatively. I had come to understand that for me, the next stage that I wanted to reach was to expand my applied mathematics capabilities to new domains in addition to the life sciences. And, really, I was ready! Studying the life sciences from a mathematical perspective prepares you to handle a variety of complex data problems. The field is full of extremely noisy data – but data that has, if you chip at it long enough, fascinating patterns and meaning underneath the noise. I now get to do just that as a Research Staff Member at the Center for Computing Sciences, Institute for Defense Analyses (CCS/IDA). I work at the interface of data science and applied mathematics to help address challenging problem sets in national security, and more generally in the computational and data science realms. I’ve used approaches ranging from applied dynamical systems (PDEs and ODEs) to, more recently, unsupervised learning methods employing matrix- and tensor-decomposition frameworks. I also hold an adjunct faculty role in the Laboratory for Systems Medicine at the University of Florida, which allows me to continue to collaborate on projects in mathematical and systems biology.

I wish I had known to take advantage of all [professional societies] have to offer earlier in my career.

What I’ve come to realize is that your unique interests and capabilities, even when they may not fit easily into a clear label, do have a place in this world where they will be valued. My background in mathematical biology has given me a unique perspective on the challenges I face in my current role, both from a mathematical and applied sense. And it makes for some fun intersectional research.

Finally, I’d like to make a quick shout-out to the power of professional societies. I wish I had known to take advantage of all they have to offer earlier in my career. Societies like the American Mathematical Society (AMS), Society for Industrial and Applied Mathematics (SIAM), Association for Women in Mathematics (AWM), and Society for Mathematical Biology (SMB) all provide opportunities to network via conferences and meetings, and to learn more about opportunities in and outside of academia utilizing the skills you learn. You don’t need a minimum degree to join – just an interest to connect with like-minded researchers.

Posted by HMS in Stories
01
Sep
2021
Christina Graf

Christina Graf

Born in Vienna, Austria • Birth year 1994 • Studied Mathematics at Graz University of Technology in Graz, Austria • Highest Degree Master’s in Mathematics • Lives in Graz, Austria • Occupation University Assistant at the Institute of Medical Engineering, Graz University of Technology, Graz, Austria

As far as I can remember I have been in love with math. In school, I always did my math homework first, and I actually procrastinated a bit to spend more time doing math without having to move on to further homework. I was interested in many things as a kid and I was always enthusiastic – this enthusiasm never left! But honestly, I did not realize that being a mathematician could be my job description one day. My mom is a teacher -yes math- so I thought about math only from a teaching perspective for a long time. My dad was a radiologist and I considered becoming a doctor myself. I knew what his daily work and workload was like and I was fascinated by this clear boundary setting between „good“ and „bad“ (he specialized in breast cancer detection and divided tumors he found in “the good, the bad, and the ugly”). Funnily, clear decisions also occur in math! So, for a long time my plan was to apply for medical school after graduating from highschool and my parents generously supported me, not only in terms of financing, but – more importantly – emotionally. 

That was the first time I learned about the Fourier Transform – I was so fascinated, I could not stop reading about it!

I was in 11th grade when my mom said, more incidentally: „You know, you always start with your math homework!“. I think she had no idea what she started with that! So, I slightly started thinking: „Could math be an option?“ My social environment was not so supportive, I heard comments like „It is so damn hard, do you want to do it?“ or „Mathematicians just do programming“ (and I hated computers during that time). But I am not a person who is easily influenced and when someone doubts my ability to do something, I usually get in the „I am gonna show them“ mode. During that time I learned that I need to have the faith in myself that others might not have in me! I often sneaked into my mom’s office to read some applied math books and soon she found her missing books on my bedside table. That was the first time I learned about the Fourier Transform – I was so fascinated, I could not stop reading about it!

So my plan changed and my new aim was to go to a technical university. My parents were extremely supportive from day one, believing in me, but also always telling me that I had the option to leave to do something else if math did not turn out to be the right thing. With that in mind, I started university, as motivated as I could ever be, completely oblivious to what will follow. The first months were hard, there is nothing to gloss over here, but not a single second I thought about leaving, I just loved it.

I still enjoyed math a lot, but I got the feeling that I learnt plenty of things „for nothing“ and that I actually wanted to start doing something with it now.

The years went by, I received my Bachelor’s degree with plenty of ups and downs and enrolled in the Master’s program. During this time I was not entirely happy with what I was doing. I still enjoyed math a lot, but I got the feeling that I learnt plenty of things „for nothing“ and that I actually wanted to start doing something with it now. Ultimately, I was unsure if math was still the right subject for me. So, during a Sunday afternoon in the university library where I was unhappy with doing my homework, I scrolled through other institutes‘ webpages, interested in what they do. I spent a few minutes on the webpage of the Institute of Medical Engineering – the curiosity in medicine never left – and there was an open Master’s thesis sounding mathematical, but with an actual application of that. On the next day, I met with the PI (who is my PhD supervisor now) and soon after, I started working on my thesis. I just loved it from day one. I finally felt like being „home“, I could use all the fancy math skills I learned and I could actually utilize them for real-world problems. Eight months and some exams later, I graduated and received my Master of Science in mathematics with specialization in technomathematics. I did not need to think about what to do next for too long, as I knew exactly that I wanted to continue with math. And so I started working on my PhD at the same institute after two months of traveling the world.

I love to do research, to try out new things, to travel to conferences and to get to know like-minded people, and I really enjoy teaching.

For my PhD, I’m working in the field of optimal control for Magnetic Resonance Imaging (MRI). Here, I’m optimizing radiofrequency (RF) pulses, which form the basis of every MRI scan. Goals of the optimization include making the RF pulses shorter, reducing the scan time, and reducing the energy it produces, among others. It allows me to combine mathematical methods with a medical application, namely Magnetic Resonance which is used to obtain images of the human body. During my PhD, my enthusiasm for this subject has not decreased – I grew even more fond of it. I love to do research, to try out new things, to travel to conferences and to get to know like-minded people, and I really enjoy teaching.

At the moment, I have the strong tendency to stay in academia; frankly, I can‘t think about anything else. While writing these lines, we are at the end of the third „Covid-19 wave“ in Austria and I really feel this desire to leave the country and go abroad. Due to Covid, I was not able to travel to international conferences, but as always, this is not an excuse, but a motivation to get going again. I am excited to leave my home and ready to take every opportunity that is presented to me. For the future, I’d like to make the world a little bit better with my knowledge and what I do. Furthermore, I would like to continue sharing the joy of mathematics with my students every day.

Posted by HMS in Stories
20
Jan
2021
Joana Sarah Grah

Joana Sarah Grah

Born in Germany • Birth year 1987 • Studied Mathematics in Münster, Germany • Highest Degree PhD in Applied Mathematics from the University of Cambridge, UK • Lives in Düsseldorf, Germany • Occupation Scientific Associate

My decision to study mathematics was anything but straightforward. I always enjoyed maths classes throughout my primary and secondary school years. I also have to add that I personally believe this experience was significantly influenced by the fact that I had great maths teachers. Luckily, against a sadly very common (mis)perception of society I never felt that maths was not for girls. Maybe this was unconsciously strengthened by the female maths teachers I had in early school years. Shortly before my last two years of secondary school began, I decided against choosing mathematics as a major (which always seemed to be clear beforehand) because I did not enjoy the maths classes I attended in the preceding year. Nevertheless, I very much enjoyed the following two years of maths classes, which is among other things certainly due to the amazing teacher (and possibly first maths mentor) I had. From the beginning, he made quite clear that he did not really understand why I only chose maths as a minor, but he would motivate, encourage and challenge me even more throughout the two years. He also was one of the few persons I could consult when I was thinking about applying to study maths at university.

In the end, (…) I decided to study maths but was pretty much clueless about how a typical workday of a student even looked.

I was the first family member to attend university, let alone having received a university-entrance diploma, and so my family could not really provide me with a lot of advice or experience in this regard. However, they were incredibly supportive in multiple other ways throughout my studies and without their support I certainly wouldn’t be where I am now.
In the end, after considering other options such as linguistics and language studies, I decided to study maths but was pretty much clueless about how a typical workday of a student even looked. At first, I thought it was sufficient to attend the lectures (like the classes in school) and go home after. This also fit snugly with the hours I had to work in my side-job. The ‘homework’ was surely very similar to the one at school and I would just solve the mathematical problems we were given by myself like I did in school. Preparing for the exams would certainly be similar to schooldays and I would not have to study too hard. It did not take too long until I realised that I was completely wrong. The first unsuccessful exams hit me quite hard and ultimately, I found myself in a situation that I had not known up to this point in my life. It was already pretty late to turn things around completely and after many thoughts and conversations, I decided to start all over again one year later.

It is essential to have role models to look up to from the beginning and ideally to be mentored and supported by experienced and committed persons. I am extremely lucky and thankful to have those people in my life.

The further I got and also the more I was able to specialise in my studies, the more I enjoyed student life. I was lucky enough to have a strong and supportive network of fellow students and friends. What is more, especially in the final year of my Bachelor’s, I had two extremely dedicated, passionate and encouraging advisers, one of which was going to become one of my main mentors throughout my academic career. And this is the main message I would like to convey here. It is essential to have role models to look up to from the beginning and ideally to be mentored and supported by experienced and committed persons. I am extremely lucky and thankful to have those people in my life. In addition to my Bachelor’s and Master’s supervisor, I had two incredibly supportive, heartening and inspiring women as a PhD supervisor and co-supervisor. I believe that my passion for women encouragement was significantly influenced by my main PhD supervisor who herself has given numerous talks on her own experiences as a woman in maths, her career path and her very personal journey to become an excelling mathematician and leader.

We realised that we were not alone with our struggles and doubts and this was extremely liberating and empowering.

Already during my Master’s, I participated in a mentoring programme that was coined by a very committed (male!) diversity officer at our maths department. We had regular meetings in small groups of three mentees and one mentor who was a female PhD student. We were able to informally chat about positive and negative experiences, the decision whether to continue as a PhD student or search for a job in industry and how being a woman in a still male-dominated field poses some challenges. We realised that we were not alone with our struggles and doubts and this was extremely liberating and empowering.

Without all of this amazing support and encouragement I am 100% sure that I would not have continued doing a Master’s respectively PhD respectively post-doc, as I have fairly often thought about quitting at various points in my career. In the end, persevering, listening to my mentors and believing in myself was worthwhile. Nowadays, I try to identify situations in which I observe sexism, female students and colleagues struggling with imposter syndrome, or simply the exhausting and competitive environment that academia sometimes is. Then I try to speak out or even manage to become a mentor myself.

My PhD research was in applied mathematics. More specifically, in one of my main projects I developed mathematical image analysis tools for an application in cancer research. In an interdisciplinary collaboration I worked with biologists that studied the efficacy of anti-mitotic drugs trying to slow down or prevent mitosis, the process of cell division, in cancer cells. I developed a graphical user interface that facilitated the automatic analysis of sequences of microscopy images showing the treated cells over time.

I loved the communication part of post-grad academic life; not only discussions and exchanges, but also communicating my work to others at conferences, workshops and during outreach projects. 

I always liked collaborations in my academic career and I believe that against all stereotypes, at least applied maths is a very team-oriented discipline and it is essential to discuss lectures, papers and ideas with fellow students and colleagues. I loved the communication part of post-grad academic life; not only discussions and exchanges, but also communicating my work to others at conferences, workshops and during outreach projects. Recently, I even quit research and started working as a scientific associate at university focusing on science communication as well as education.

Posted by HMS in Stories