Born in Bielefeld, Germany • Birth year 1972 · Studied Mathematics and Computer Science at University of Paderborn in Germany • Highest Degree Habilitation in Mathematics • Lives in Munich, Germany • Occupation Professor for Mathematical Foundations of Artificial Intelligence
I had never planned to become a professor of mathematics, and if someone had told me when I was young, I would have said: This is impossible. Due to my excitement for mathematics in school and the fact that my mother and my grandfather were both teachers, I first wanted to become a high school teacher myself. And this is how I then started my studies, choosing computer science as a minor. Although the change from high school mathematics to university mathematics was difficult and required a lot of hard work, I enjoyed my studies very much. I however could not get excited about didactics for high school teaching, hence I switched to diploma studies in mathematics. And since at the University of Paderborn, it was quite easy to pursue a diploma in computer science at the same time, I enrolled in this as well.
(…) In retrospect, this period trained me to follow my own path and be very independent.
In my last year, a professor working in abstract harmonic analysis approached me with an offer for a Ph.D. position. I was hesitant about whether this was the right career path for me. Eventually, I accepted the offer but quickly realized that not pure mathematics was my passion but applied mathematics. Hence, in agreement with my supervisor, I chose a more applied topic and got assigned a second supervisor in Munich. This arrangement was not optimal. However, in retrospect, this period trained me to follow my own path and be very independent.
One of the reviewers of my Ph.D. thesis then offered me a position as a Visiting Assistant Professor at the Georgia Institute of Technology. Since I was hesitant about what to do next, I embraced this opportunity, taking it as a chance to see whether I am good enough for continuing as a post-doc. My time as a Visiting Assistant Professor was again hard, since I had never taught a course before, and I now even needed to teach in English. But research-wise a whole new world opened to me; having now collaborators with similar interests as myself, namely the area of applied and computational harmonic analysis. I then spent another year in the US with a research fellowship at both Washington University in St. Louis and again at the Georgia Institute of Technology. It was a very productive time for me, leading to a Habilitation in Mathematics at the University of Giessen in Germany.
I overcame my shyness and approached [some professors in the US whose work I had always admired] for an invitation (…).
Due to the uncertainty of obtaining a professor position in Germany, I applied for a Heisenberg Fellowship from the German Research Foundation to visit some professors in the US, whose work I had always admired. I overcame my shyness and approached them for an invitation and eventually got the amazing chance to visit first Princeton University, then Stanford University, and finally, Yale University, learning about new research areas such as compressed sensing.
Returning to Germany, I started as a full professor at the University of Osnabrück. This was a very fulfilling experience, and I loved building up my own research group. However, it was a very small department, and finding good students was hard, and I soon started looking for other positions.
I was again lucky and was offered an Einstein Chair at the Technical University of Berlin. Soon after, the advent of deep learning started and affected my research area significantly. I decided to embrace this paradigm shift and delve research-wise into artificial intelligence. Looking back, this was one of the best decisions in my life.
For the first time, I am now not the only female professor in my department.
This might have also led to a personal offer from Ludwig-Maximilians-Universität München for a Bavarian AI Chair for Mathematical Foundations of Artificial Intelligence, which I was surprised and delighted to receive. Due to the excellent conditions for AI research in Munich and Bavaria, I accepted the offer and moved to Munich. For the first time, I am now not the only female professor in my department. In fact, I have several wonderful female colleagues, which is an entirely new experience for me.
In general, I learned in my career that one should be open to opportunities, as they often arise unexpectedly, and also not be shy to approach colleagues for advice and help. If you ask whether being a woman has impacted me in my career, I have to say that the first time I realized that one is treated differently was when I became a professor. As committee meetings increased, I learned the hard way that men do not behave better or worse, but just differently. Looking back, a course on gender-specific behaviors in professional environments, as it is, in fact, custom for higher positions in industry, would have helped significantly. On the other hand, I also had and still have several amazing male colleagues who support me tremendously, also with advice, and I am deeply grateful to them.
Born in Germany • Birth year 1975 · Studied Maths at University of Hamburg • Highest Degree PhD in Optimal Control • Lives in Hamburg, Germany • Occupation Senior Business Consultant
I am sitting on the train. The ICE drives from Cologne to Hamburg. In this dark evening. My head is spinning after four days of learning about actuarial subjects in a seminar. I use my time to reflect. Thinking a little about the past, a little more about the future and a lot about this moment right now. I am happy. Grateful.
I like being here and in this moment. I am thankful for my talent for mathematics my mom and dad gave me. Thankful for meeting other people in my life, so I could learn and grow and become the person I am right now. Thankful for all the nice people who believe in me and support me. One of my mottos: you are what you have made of yourself. I will never be finished. This would result in stagnation.
The solution of any mathematical problem seemed so easy and elegant to me when I was young: true or false. Nothing else.
Like a central theme, my interest and my ability in mathematics affect my whole life. I love mathematics! The solution of any mathematical problem seemed so easy and elegant to me when I was young: true or false. Nothing else. I wanted to immerse myself in this subject. It was not easy to continue with this wish in a male-dominated world: unmotivated teachers, incompetent advisors at the job center, traditionally-thinking professors at the technical college. Thus, my central theme evolved in a different direction. One constant in my life stayed: me reflecting on my current situation – Who am I? What have I made of myself?
I grew up in a family where natural sciences and logic discussions were welcome. My parents met at the university, later becoming a math high school teacher and a physicist. In highschool, I have always been interested in math and natural sciences. I once asked my math teacher about the mathematical olympiad but I felt completely left alone by him when he didn’t show much interest and asked me to contact the organizers instead of telling me about it. It was frustrating that the lessons in math neither prepared me for the kind of exercises solved at mathematical olympiads nor showed me the possible career paths in science. The job center employee I talked to did not recommend studying math either. Thus, I chose a different path at first. While preparing for my engineering studies, I worked at a locksmithery. In this men’s world, the break room was decorated with a calendar with “aesthetic” images of women. Some old-established professors at the technical college weren’t pleased about women studying engineering.
Remember: if you love something, you will get great at it. I am grateful for being able to realize what I love. I love mathematics.
Finally – I just couldn’t get enough of math – I switched to studying mathematics at the university and went my way to diploma, PhD, being a mother, a teacher, a developer of final exams in math, to leadership in the climate and sustainability working group. I left the “typical” career path of mathematicians again. And came back to my profession: Now I have developed my skills in actuarial subjects working in insurances. And I will continue looking for new challenges.
Right now, I am sitting on the train. Driving from Cologne to Hamburg. And I am happy living in this moment. Happy with my talent for mathematics. It helps me developing, being curious and following interesting new paths. My path leads me further to being an actuarial consultant. I am sure I will encounter interesting tasks, opportunities and people in my future. And I want to show my beloved children: it is worthwhile to look deep within yourself. Be true to yourself. Find a subject that interests you and follow your ambition. Yes, there will always be drawbacks. Fortunately, the world is not as men-dominated anymore as it has been. Remember: if you love something, you will get great at it. I am grateful for being able to realize what I love. I love mathematics.
Born in Wittlich, Germany • Birth Year 1986 • Studied (Applied) Mathematics at Trier University, Germany • Highest degree PhD in Mathematics • Lives in Madrid, Spain • Occupation Postdoctoral Research Associate
Honestly, I do not really know when my passion for science, and in particular math first manifested itself. But from my experience, I can definitely say that being surrounded by the right people and mentors plays a big role in continuing in this direction and not steering towards following one of your other passions.
[..] in all of the career options that I tried, I was missing the logical and structured thinking and the challenges that math brings along.
My favorite subjects in high school had always been math and languages. It was after high school that I was thinking about combining the two subjects but I did not see myself becoming an elementary, middle, or high school teacher which probably would have been a natural choice. I tried several other options realizing internships and applying for study programs but in the end in all of the career options that I tried, I was missing the logical and structured thinking and the challenges that math brings along. It was after a gap year in Australia that I remembered one of my math middle school teachers telling me that I would be the right person to study math. Despite not agreeing with him at that point in time, in the end, I decided to give it a try. I went from a Bachelor’s to a Master’s to a Ph.D. degree in (applied) mathematics.
[..] I am very grateful for my choice as it allows me to not just learn more within my discipline but also about many others.
On the way, I kept learning languages and following my other interests especially learning more about other cultures and getting to know more of the world. After my Ph.D., I decided to go to the US for a postdoc where I stayed for about two years. Then I moved to Bilbao, Spain for another postdoctoral position. After almost two years there, I decided to stay in Spain and move to Madrid. This is what brought me to my current position. Currently, I am a postdoctoral research associate at IMDEA Materials. Here, I mainly develop models and algorithms for the acceleration of materials discovery for finding materials alternatives that are for example more sustainable. This means for instance that they are more inspired from nature, less toxic and do not deplete important limited resources. Having a background in applied mathematics, over the last 10 years I have had the opportunity to apply my mathematical knowledge in many areas reaching from cardiovascular stent design to optimization of fermentation processes to modeling cell metabolism to control of disease transmission dynamics to materials discovery. Looking back at my career decision, I think I would have been happy with studying computer science or engineering as well but it definitely had to be a science subject and I am very grateful for my choice as it allows me to not just learn more within my discipline but also about many others.
An academic research career can bring along a lot of frustration, uncertainty, and not always supportive environments but enjoying the process of learning from every experience, having the opportunity to make the world a better place, and following your passion make it worthwhile.
There have been tough phases and I definitely cannot say that I have never thought about switching careers. But I think that I have always enjoyed the challenges that my career path has brought along, maybe not always at the moment but overall, I believe that from facing challenges you learn the most. An academic research career can bring along a lot of frustration, uncertainty, and not always supportive environments but enjoying the process of learning from every experience, having the opportunity to make the world a better place, and following your passion make it worthwhile. Mentorship programs can give a lot of support on the way to keep you focused on your path and dealing with many of the given challenges. I am definitely very grateful for those mentors along the way that supported me and encouraged me to follow my passions.
If I had the opportunity to talk to my 20-year-old self, I would have told her: “Never regret anything, be grateful for the good things that every decision brought along, follow your passions, hold on to your core values, do not let your fears rule you and most importantly enjoy the process and live in the moment without holding on to the past or having fears about the future. You do not choose your destiny but you choose your company. You will find your way. Do not get lost in too much work, there are also other important things in life and remember success is one thing but you do not want to die one-day having regrets, such as not having shown enough care for your beloved ones and not having followed your other dreams and passions.”
To be honest, most maths students who are just about to finish their studies have no specific plan of what kind of job they want to pursue after graduating. Up to that point, they might have realised what they did not know in their first semester, namely that there are plenty of opportunities in different areas of industry and academia for a mathematician besides the “obvious” choices, like the financial sector and insurance companies. Artificial intelligence, automation technology, big data, deep learning, computer vision – just a few fields of great interest for modern industry, and all of them are very closely related to maths. Most of them seem to promise a much more exciting job opportunity than an insurance company – with so many possibilities, why did I finally decide for a job as a software developer in an insurance company? The short answer: Because it offers a huge lot of fun, exciting tasks, complex mathematical and computational problems, and besides, great colleagues and an outstanding working atmosphere.
Let’s have a look at the long answer. For me, during my last years at the university it became clear that I wanted to be a software developer. Solving specific tasks using logical skills and computational tricks and contributing to something “useful” were the important parts for me, in addition to a strong desire for a preferably stress-free and enjoyable working atmosphere, while I did not really care about the specific application behind my work. The job advertisement at a big and well-known German insurance company sounded exactly like what I was looking for, next to the very good reputation of the employer regarding the labour conditions. So I took the chance, honestly without a specific imagination of how a “typical day” as a software developer would look like.
Now, 1.5 years later, I am still not able to say what a typical day looks like, simply because every day can be very different. Every day can pose different tasks and new challenges, with almost no repetitions, with lots of new things to learn, with lots of new insights – and the more I understand how things work, the more I can participate actively in new areas of responsibility. A developer is not only the aimless “executor”, but also needs to keep an overview of the whole software architecture, stay in touch with the “client” (in my case, the company itself, especially those who are going to work with the new software after its release) and other departments and work together with the rest of the team in order to develop a viable product. Thus, the best way to describe what I am really doing is to divide my tasks into three “areas”: The learning part, the conceptional part and the implementational part.
Carolin Dirks
My first year in my new job was dominated by the learning part. A mathematician is typically not educated in many practical skills, a mathematician is educated in independence, learning receptivity and frustration tolerance – in being able to understand complex problems and find smart solutions by her- or himself. Basically (and hopefully not sounding overbearing) a mathematician is able to understand almost every problem, and this is in my opinion one of the main reasons a mathematician is hired. Consequently, I needed to learn a lot, about programming languages and especially about state-of-the-art tools and technologies in software development. This was a whole new world for me – before, I had literally only implemented “plain code” without a suitable development environment, without fancy testing tools and without connecting to databases. And for me, there are very few places which are more suitable for getting a wide insight into so many different fields connected to development. Learning is not only considered to be necessary, but also promoted – and everyone in my department is encouraged to spend time on learning. Additionally, we have the philosophy that, roughly speaking, every developer in my team should be basically able to do every task – of course everyone has some kind of focus, based on his or her knowledge, but everyone is also encouraged to undertake tasks where he or she is a complete beginner.
Today, learning new things is still a daily business in my job. Another part which becomes more and more important is the conception and discussion of particular features of the new software. The “clients” (in our case, the “specialist department”, those who, in contrast to me and my team, know how an insurance as a product needs to work) decide about new features they want. This can be a very small and simple request like “I want this button to be green instead of blue” or a big new feature like the possibility for the customer to report a damage case. The developers (like me) discuss the technical requirements and details, check if everything is technically possible, roughly figure out which parts of the software are affected and what has to be done and wrap everything up in one or more specific tasks. In addition, the developers can contribute their own ideas or write “IT-only-tasks” (tasks which do not bring a visible new feature, but are necessary for some other reasons).
Consequently, the last part is the implementation part – namely solving the tasks. This (mostly) means implementing new pieces of code, integrating them into the complete software (after a quite strict reviewing process by other developers) and writing automated tests for the new features. One task can take from a few minutes (like the green button) up to several weeks, often accompanied by further discussion rounds with the “insurance experts” or with other developers. Besides, a task can be done completely alone or even in a team of several people – in every case, the whole team discusses everyone’s tasks in a daily meeting together, where problems can be put on the table or opinions can be exchanged. All in all, everything is based on teamwork: If you don’t know the answer to a question, lots of phone calls and sometimes a whole bunch of people staring at the problem later always lead to a solution.
All three parts together make this a perfect job for me. As an applied mathematician, I am still able to make use of the skills I acquired during my studies and still solve complex problems. The job does not only require programming skills, but also the ability to “delve into” specific issues and to analyse all sides and effects of a problem, while always raising new challenges and opportunities to learn new things – but without the pressure of exams and the question of “what should become of me” in the future.
Born in Steinfurt, Germany • Studied Maths at the University of Münster, Germany • Highest Degree Doctorate in Maths • Lives in Steinfurt, Germany • Occupation Software Developer at LVM Versicherung (insurance company)
When I started studying maths, I was frequently asked what I was planning to do after graduating. “Who wants to hire a mathematician? Do you want to end up in a boring job working in the financial sector or in an insurance?” Of course, like most of my fellow students, I did not have a satisfying answer to these questions. Today, after several years of studying and struggling with lots of formulas, proofs and theorems, I have learned two very important lessons: First, that there are thousands of opportunities in very different branches of industry and academia a mathematician can take, and second, that having an inspiring and exciting job and working for an insurance is not a contradiction.
And what came next finally took me to the decision to stay with maths for the rest of my life: I realised that I was not the worst student (though not the best either), and I was fascinated by the clarity and pure logic of mathematical problems, forming a huge contrast to the, in my opinion, very unclear analysis of poems and classic literature (sorry to those who would disagree with this point).
In my experience, studying maths is a decision made out of the interest for logical structures, for clarity and puzzles, but not for a particular future job. Unlike many others, the presence of this interest was not clear to me until I reached the last years of high school. Thus I cannot claim that I had always been fascinated by mathematics, though I was never a bad student, my interests lay elsewhere – largely in learning languages, which I still try to spend some time with beside my current job. This changed due to a sudden and, at least in retrospect, very fortunate coincidence: When I had to choose my advanced courses for my last two years at school (every German academic high school student has to decide for two), due to organisational reasons I ended up in the advanced maths class. For a few weeks, I was quite depressed, being sure that I would be the most stupid student next to all those maths geniuses. And what came next finally took me to the decision to stay with maths for the rest of my life: I realised that I was not the worst student (though not the best either), and I was fascinated by the clarity and pure logic of mathematical problems, forming a huge contrast to the, in my opinion, very unclear analysis of poems and classic literature (sorry to those who would disagree with this point). Out of this fascination I finally made the decision to study maths, without having a specific career aspiration and even without having any idea about possible careers.
Although in my opinion, society made great progress in overcoming gender-specific obstacles, I also made the experience that women interested in computer stuff are still a bit unusual. This caused me to be suspicious – would I be good enough, would I be able to establish myself in this branch and would I find a job as a mathematician?
At the university, I fought my way through the first few semesters without a specific plan – but instead with lots of very close new friends with the same mind-set, since studying maths is not least a matter of team work. In my fourth semester, I first encountered the field of numerical mathematics, which, roughly speaking, can be explained as the area of intersection between maths and computer science. I realised how closely related these two fields are: Computer science can be used to solve lots of mathematical problems, while every computer program uses the “language” of mathematics and logics. I was fascinated by the variety of applications and decided to concentrate on this field in my further studies. And slowly, very hesitantly in the beginning, I started thinking that maybe I could become a software developer. Hesitantly because up to this point, I never had any points of contact with computer science in my life, not because I was not interested, but simply because it never came to my mind. Although in my opinion, society made great progress in overcoming gender-specific obstacles, I also made the experience that women interested in computer stuff are still a bit unusual. This caused me to be suspicious – would I be good enough, would I be able to establish myself in this branch and would I find a job as a mathematician? To find the answers to all these questions, I needed to try it out – so I tried, and it was worth it.
Before this rough idea could emerge to a specific plan, a few more years had to pass by. After graduating, I was still insecure about what I wanted to be. Not only, but also not at least in order to postpone a “final” decision, I decided to stay at the university and do a PhD, despite again fighting with my doubts of being good enough. This turned out to be a great idea – I was now able to contribute my own ideas and, in this way, further develop my interests and strengths, all the time attended by a great, supporting and understanding scientist. And although I was for sure not the best student (thanks to my supervisor’s patience at this point), I finally made it, having learned one of the most important lessons in life: You can do it if you really try.
At this point in my life, I knew what I wanted: To use my mathematical logical knowledge in combination with my (at this point, quite acceptable) programming skills to contribute to something “tangible”, something someone could really make use of […].
After finishing my PhD (and now, with a particular plan, namely to become a software developer), I applied for my first job outside of academia. At this point in my life, I knew what I wanted: To use my mathematical logical knowledge in combination with my (at this point, quite acceptable) programming skills to contribute to something “tangible”, something someone could really make use of (sadly this is something missed by many maths students during their studies). The explicit sector was not important for me, since I found for myself that those really deep and specific programming problems are fascinating no matter if the application behind is just a web-enabled water boiler. So I thought, why not an insurance company? The job advertisement sounded very interesting. The company was looking for developers for a completely new contract software, which would be used by the insurance agencies all over Germany. This promised not to be the boring insurance job every first-year maths student is afraid of, so I took the chance. Retrospectively, I am very happy about the path I took, and proud of having had the courage to take it, regardless of my doubts and fears of not being good enough. Although this is something several maths students have in common, most of my former fellow students also share the ability of tenacity, they do not give up easily, but make their way and realise that it works – in the end, the struggle was worth it and I would strongly recommend to just give it a try.
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.
Born in Hanoi, Vietnam • Studied Mathematics at RWTH Aachen in Germany • Highest degree: Master of Science in Mathematics • Lives in Utrecht, The Netherlands • PhD candidate in infectious disease modelling at the Julius Center for Health Sciences and Primary Care in Utrecht (The Netherlands)
I was born in Vietnam, grew up in Germany, lived in the UK for about two years in total, and moved to the Netherlands for my PhD four years ago. Having lived in various countries, I always saw myself as a cultural hybrid – bridging the gap between different cultures and traditions. My PhD topic similarly connects two different but intersecting disciplines: I develop mathematical models to tackle the spread of infectious diseases.
When you would have asked me what my future job would be when I was 10 years old, my answer would probably have been “a detective”. I loved solving puzzles and finding solutions to a problem. What I particularly enjoyed about maths was its simplicity: In its pure form, you only need your mind and maybe a pen and a paper.
I knew I wanted to continue to do research in something math-related, but I also realised that I wanted my work to have an impact in the real world.
After graduating high school, I decided to pursue a Maths degree at university. The reason was simple: I was eager to learn more about how to solve abstract problems through logical reasoning. Despite its reputation, you do not need to study maths as a lone wolf. A lot of my university time included working together with fellow students, discussing various solutions, and looking at a problem from different angles. Studying maths at university level was not always easy for me but I had a lot of fun, and I think that’s what counts in the end. When I was about to finish my degree, I felt a bit lost as I realised that I never really had a particular job or career in mind, and I had no real plan for my life. I knew I wanted to continue to do research in something math-related, but I also realised that I wanted my work to have an impact in the real world. However, I had no idea how exactly I could combine these two interests.
By chance, I came across the 80,000 Hours non-profit organisation that tries to guide graduates towards a career that fits their personality but also “effectively tackles the world’s most pressing problems”. This gave me an impetus to contemplate more thoroughly my career choice and I started to do research on the applications of maths to address real-world problems. I quickly learned about the serious risks that infectious diseases pose to our world and how mathematical modelling can provide valuable insights into the field. Luckily, I was able to find a PhD position in infectious disease epidemiology in Utrecht. In hindsight, accepting this position was one of the best decisions in my life as I can genuinely say that I am very happy with my work, my research group, and in particular with my supervisors. They gave me just the right balance between guidance and freedom, and a positive environment to thrive.
Since the start of the COVID-19 pandemic, however, I am using my background to model the spread of SARS-CoV-2 in various settings, for example in hospitals or secondary schools.
When I started my PhD my main topic was to study the transmission dynamics of antibiotic-resistant bacteria in hospitals. Since the start of the COVID-19 pandemic, however, I am using my background to model the spread of SARS-CoV-2 in various settings, for example in hospitals or secondary schools. It has been a very challenging time as my workload has doubled but at the same time, I feel very grateful to have the opportunity to use my skills to ‘do good’ while truly enjoying my work.
The current COVID-19 pandemic demonstrates perfectly that mathematics does not necessarily have to be far from reality, and that it can be a powerful tool for solving real-world problems.
Infectious disease modelling is rather versatile: It requires translating biological problems into the language of mathematics, analytically investigating the research question using the developed model, and finally translating the results back to the real world to obtain implications for infection control policy. The current COVID-19 pandemic demonstrates perfectly that mathematics does not necessarily have to be far from reality, and that it can be a powerful tool for solving real-world problems. Maths used to be underrated and maybe even underappreciated but by showing people how mathematics can be used to stop the spread of infectious diseases, I hope we can spread a little bit more love for mathematics.
The daily routine of a mathematician in the field of Data Management & Analytics can be diverse: Data collection, preparation and analysis, the design of artificial intelligence (AI) models, and much more. The opportunities to get involved in a data project are usually not limited to one’s own field. We, Mara (Senior Big Data Scientist) and Marisa (Senior Machine Learning Engineer), are two mathematicians who juggle data in a variety of ways every day. In this blog post, we describe what a day as a data juggler is like and how we use mathematics in our everyday lives.
If you study maths, you are faced with a wide range of possible career paths. But you should definitely take a look at the field of data management & analytics – not just because the Harvard Business Review called the data scientist’s profession the sexiest job of the 21st century [1]. In recent years, many specialised job titles have emerged, for example “Data Engineer”, “(Big) Data Scientist” and “Machine Learning (ML) Engineer”. However, they all have the same aim: to process data in such a way that useful information can be extracted (learned) from it and computers can act intelligently based on this knowledge. In particular, working with and implementing AI algorithms requires more than just AI experts – it’s a team sport. Regardless of their job title, it takes many different specialists working together as a team and complementing each other. Other areas of computer science such as database management or software engineering are also becoming increasingly important.
Marisa, what is your role as an ML engineer in the team and when do you still use maths?
Due to the above-mentioned diversity and the numerous connections to other team members, it is difficult to describe a typical day of an ML engineer because every day is characterized by new challenges – fortunately. However, even with the most complex challenges, our mathematical-analytical approach does not make us despair.
The mathematical modelling of data in a learning algorithm, be it through a slightly more applied, specialised linear regression, or through a fancy artificial neural network, usually takes up no more than the last 5-10% of a whole data project. For a prediction to work really well, the end-to-end idea is crucial. Where does the data actually come from? And what data do I need to arrive at a valid result? Do I have the right data? Can I get to more profitable data, or do I have to change the prediction goal? It’s crucial to understand the big picture. After all, you need exactly the data that fits the problem you want to solve.
All of AI […] has a proof-of-concept-to-production gap. […] The full cycle of a machine learning project is not just modeling. It is finding the right data, deploying it, monitoring it, feeding data back, showing safety — doing all the things that need to be done to be deployed.
Andrew Ng [2]
In general, an ML engineer is a person who helps deploy machine learning or artificial intelligence algorithms in a productive environment so that they can be used in the day-to-day business without difficulty. That sounds like a lot of infrastructure operations and software engineering, and yes, that can be a big part of an ML engineer’s job. You have to understand the existing IT landscapes and systems at the customer level to decide how to build a pipeline in those existing systems between the data and the output of a prediction, and how to deploy everything at the end. But as mentioned before, AI is a team sport. Of course, as an ML engineer, I’m not the specialist in everything, but it’s important to stay on top of everything.
Marisa Mohr
Now, how much mathematics is needed in this interdisciplinary field as an ML engineer primarily depends on the level and interest of the individual in the mathematical-statistical techniques that are being used. There is this type of ML engineer who spends all day building infrastructures or programming software to make an intelligent algorithm run productively in the client system. This kind of ML engineer is certainly more influenced by computer science than I am as a mathematician. I admire that, but I could never get lost in coding, and the good thing about being an ML engineer is that you don’t have to. The profession is so multi-faceted and multi-dimensional that everyone can follow their own passion and take their personal role in the team – with the bonus of dabbling in other roles every now and then.
As a mathematician, I have taken on various roles over the years. During a project phase, I often take on the role of a general strategist or project manager, ensuring that the team follows the same vision to bring together input and intelligent output in the productive environment. Then, when data modelling specialists are required in the project, I have the opportunity to follow my mathematical passion in the form of smaller data explorations and visualizations, through the evaluation of mathematical relationships in the data, to the selection and training of learning algorithms. The latter also includes consideration of accuracy, training time, model complexity, number of parameters, and number of features. In addition, parameter settings and validation strategies have to be selected, underfitting and overfitting have to be identified by understanding the bias-variance trade-off, and confidence intervals have to be estimated. A deep dive into maths for ML can be found on Medium [3]. As a mathematical minded ML engineer, my role can therefore be similar to that of a data scientist from time to time.
This role change and diversity is what I love about working as an ML engineer, or working in a data project team in general. Another ML engineer could certainly take many more technical roles, especially when it comes to gathering the appropriate data without which no ML or AI model works. And that’s where Mara comes in.
Mara, what do you do all day as a data engineer and when do you still use mathematics?
After my studies in mathematics, I started working as a data scientist for an IT company. When I applied for the job, I was asked in the interview what title I would prefer: data engineer or data scientist. At the time, I was convinced that the latter was the only reasonable choice for a mathematician like me. Even during my studies, I was a working student in the fields of data science and in addition to that, I also attended lectures on data mining, neural networks and other related topics.
The connections between mathematics and data science are numerous – in fact, data science is mainly the application of mathematical models to various use cases. And I wish this fact would be taught more often and more emphatically at university.
Have you ever wondered what all that mathematical theory is good for? If you are a mathematics student – have you ever been frustrated about all the types of matrix factorizations one has to learn in numerical mathematics? Or perhaps you are a high-school graduate contemplating the high art of analysis and algebra but you fear it will end in nothing?
I can soothe you: The use cases for mathematics and its theories are boundless.
Mara Hermann
One of my favourite examples that I encountered during my job as a working student are recommender systems. A great introductory article on this topic can be found on Medium in which recommender systems are defined as “algorithms aimed at suggesting relevant items to users” [4]. Those items could be for instance products in an online shop or movies on a streaming platform. The interaction between items and users can be represented by a sparse matrix where each entry describes e.g. how a user rated a specific movie or if a user bought a given product. One approach to retrieve information and learn recommendations from this matrix is to decompose it into two smaller and denser matrices, the so-called matrix factorization. One matrix then describes the user representation and the other one the item representation – a great illustration of how a mathematical framework can be used in practise, just to name one example. Also other mathematical methods find use in the theory of recommender systems.
Now I fancied about how various and “sexy” [1] the applications of pure (and sometimes dry) mathematics in data science can be. But if you read this article carefully, you may have noticed that I wasn’t asked about my work as a data scientist but as a data engineer. Why?
As already mentioned, working on AI or – generally speaking – a data project is a team sport and in this course you also get in touch with other roles and switch positions from time to time. With my mathematical background I always had great respect for the role of a data engineer which I thought would be reserved for “real” programmers with an IT background. In the beginning of my studies I wouldn’t have thought that I would ever be interested in coding and, like Marisa, I will probably never be as much into programming as someone who studied computer science. But data engineering is so much more than sitting in front of the laptop, producing green letters on a black screen while typing at the speed of light.
The “unsexy” sibling of data science sure inherits more aspects from computer science than from mathematics [5]. As a data engineer, one designs, implements and monitors data pipelines which may feed a Data Scientist’s ML models. Additionally, data storage and quality are a huge part of the cake. Programming skills and willingness to permanently learn new technologies are indispensable in this job.
With this role description in mind, it’s true that you don’t necessarily need maths for being a data engineer. But that doesn’t mean that mathematicians can’t be good or even excellent data engineers at all. Their education entails a lot more than knowledge in algebra, analysis and many other subjects. It is often said that mathematics and philosophy are closely interrelated, some universities like Oxford even offer lectures combining both disciplines [6]. Even without attending such a course, a mathematics student acquires a lot of soft skills which are basic tools in the everyday life of a data engineer: One has to handle complex systems consisting of different data sources connected through various pipelines. With logical and analytical thinking one can better understand and design ETL (extract, transform and load) processes. Thoroughness and checking for accuracy are key to monitoring data pipelines and ensuring high data quality. Resilience, deduction and reasoning are of great help during performance tuning or debugging data pipelines. With some of these capabilities in your tool kit you have a great foundation for the role of a data engineer, practical experience comes with time.
Thus, the opportunities for a mathematician in the data sector are broad. Different types of people and skills are required and there are numerous further training possibilities. Also, data projects can be very diverse, since data is everywhere: e-commerce, food and fashion retail, logistics, mobility, smart buildings,… One can always find a use case which fits one’s taste. I can definitely recommend taking the chance and gaining an insight into this branch.
Regardless of which field of study or career path you choose, I can only encourage you to look beyond the horizon and also get a taste of other roles and fields than the ones you are already familiar with. Be it positive or negative, it will be a learning experience for you. And you will be an enrichment for every team if you can think out of the box.
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.
Born in Trier, the oldest city of Germany • Birth year 1966 •Studied Business Mathematics at the University of Trier • Highest degree Diploma in Business Mathematics •Lives in Mainz, Germany •Leading teams in Software Development and acting as Chief Agility Master in the Airline IT Industry
In primary school, I struggled with math. My mother put a lot of effort into making me understand the difference between “plus” and “minus”. We were the first kids in Germany familiarized with set theory, working with books but also with these small boxes with plastic shapes of squares, circles, and triangles in different colors. My fascination for math started with geometry, with divisibility rules that our primary school teacher encouraged us to identify by ourselves and with the first mathematical proofs. When I was at grammar school, our teacher in mathematics told my mother: “She will never study mathematics, she is too lazy.” He was right about the laziness. My nickname is sloth, as I love lying in my hammock reading books. But I was fascinated by the ability of mathematicians to transform one problem into an equivalent one we can (easily) solve. The University in my hometown organized an open day and I attended some lectures. That’s when I decided to study math. It was a lecture about infinity and one on how to describe oscillations. This convinced me finally. When I was at university, our professors told us: “Later in your job most of you will never deal with mathematical problems like at University.”
Contrary to my professors’ prediction, I was one of the rare species among my fellow students who applied what we learnt at University.
My professor in numerical mathematics gave me the opportunity to work in a research project on optimization in robotics. Moreover, I received the opportunity to present the project at the industry exhibition in Hanover. He gave me trust, which created self-confidence I never had before. He changed my life. At this exhibition, I met my later husband. As he was living in the Rhine-Main-Region, I skipped my plan to obtain a PhD at my University. Instead, I searched for a job. This is how I started working in a very fascinating industry, the airline IT, as a software engineer in the area of flight optimization. Dijkstra for many years was and still is the algorithm of choice for solving shortest paths problems. At least it is a good basis. It is no longer sufficient due to many influencing factors such as regulations of air traffic flow. Cost optimality means reduction of fuel consumption, but also of overflight costs that are very hard to model. Contrary to my professors’ prediction, I was one of the rare species among my fellow students who applied what we learnt at University. Of course, not all problems in our industry are of this complex nature. However, developing algorithms and implementing software was complicated enough to keep me enthralled. So finally, both were wrong, my math teacher who said I would never study mathematics and the professors. Or did I want to prove them wrong?
It is a welcome change in a captivating profession of forming high performing teams, of dealing with trust-building and the soft facts of human interaction.
After 7 years, I decided to do something completely different. With my knowledge about software production, I joined a small team, the staff in the strategy department of our company. I gained insight into many different departments, sales, production, evaluation of acquisitions and business plans. Finally, I realized software production fascinates me most. So I returned, working in the role of a project manager for a completely new product development. Growing more and more into the leadership role, I was responsible for forming teams to build and operate many of our software products, applications managing the schedule preparation and operation of our airline customers worldwide. After 20 years, I returned to my roots, flight optimization. Developing algorithms for trajectory optimization is not my occupation any longer. Today, I am acting as a sponsor for our projects with the Zuse Institute in Berlin. It is a welcome change in a captivating profession of forming high performing teams, of dealing with trust-building and the soft facts of human interaction. I feel privileged, working in an international environment with diverse teams. Enhancing my knowledge by newest research in neuroscience and systems thinking is combining my private interest and profession.
The combination of rationality and empathy is not only possible; it is the theme of my story.
My favorite shape is the circle. Or is it more an upward spiral? Trust creates self-confidence. This is what I learnt in the research project at University and from my professor and my husband, who encouraged me very much in my professional development. Feedback and reflection create learning and improvement. The most amazing teams I know learnt from their mistakes and never stopped deriving actions to improve. Fearlessness creates the willingness to take responsibility. This describes very well the environment in which I could and still will grow from one role to the next. I had and still have colleagues and superiors I can talk to very openly, speaking my mind. I am not “punished” but supported in case things go wrong. As a mathematician, I have shown my ability to solve complex problems, as a leader I need to support teams to grow in a changing world. I love the following quote from Virginia Satir very much: “We get together on the basis of our similarities; we grow on the basis of our differences”. The combination of rationality and empathy is not only possible; it is the theme of my story.
Born in Münster, Germany • Birth year 1988 • Studied Mathematics in Münster, Germany • Highest Degree PhD in Mathematics • Lives in Hamburg, Germany • Occupation Research Scientist in Medical Imaging
The decision of what to study was not clear to me for a long time. I always liked math, but I could not really imagine what a job as a mathematician could look like. Only after discussing with family and friends at the end of my high school time, but especially with my godfather who very convincingly told of his positive experiences of working with mathematicians and of the usefulness of their skills, I discovered the diversity of applications. Being a person who had always been struggling a bit with making decisions, I immediately liked the idea of not limiting my future job perspectives in industry by the choice of the subject. I probably made my final decision during one of the annual university events where high school students can attend different university lectures for one day. Since I was quite undecided, I prepared a schedule and planned to attend lectures in different departments, amongst others in the medical and pharmaceutical department. I had seen some math lectures before and I liked them a lot, so I wanted to explore other options and focus on subjects other than mathematics to try and see if I would like those even more. So, I decided to attend a pharmaceutical lecture, but I knew immediately that this was not going to be my profession. I left 10 minutes after the lecture started and just went over to the math department again to yet attend another lecture. As soon as it started, I realized that the only reason I went there was to treat myself at the end of the day, because I knew I would enjoy it. That insight finally led me to the conclusion that I did not need to continue searching for anything else. I had already fallen in love with mathematics, especially the logic and the fact that everything makes sense if one just follows every single step in calculations or proofs accurately.
In the end, it did [work out], and I am more than happy that I took the risk to fail.
In the beginning of my math studies, I was surprised about the speed of the actual lectures and how different they were from the classes taught in school. I never regretted my decision, but the first two or three semesters were not easy for me to master. However, things became easier once I was able to specialize further in my studies. Even though I always thought I wanted to stay away from numerical mathematics, I eventually ended up putting the entire focus on applied mathematics and I also specialized in this field during my Master’s. Despite my previous hesitation, I quickly realized how much I liked the lectures and that they suited me more than the purely theoretical ones. The question about whether to do a PhD or not was a tough one again. I was doubting myself, but I already knew deep down that I had to give it a try. Otherwise, I would have always regretted not trying and wondered whether it would have worked out. In the end, it did, and I am more than happy that I took the risk to fail.
(…) I am happy that I still need many of the concepts and techniques that I learned at university.
After finishing my PhD, I left academia and I am now working in industry. I feel lucky that I still work in the same field I researched when I was at the university with similar applications in medicine. Therefore, the transition from academia to industry was quite smooth. Even though mathematicians are often in high demand on the job market for their way of thinking, but not necessarily for the direct knowledge obtained in math lectures, I am happy that I still need many of the concepts and techniques that I learned at university. I work in medical image computing and contribute to different aspects of enhancing CT and MRI acquisitions. Hence, I still apply some learned algorithms and I can also still be creative in the way of optimizing and adapting them to be suitable for specific applications.
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.”
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