I miss the friendly atmosphere of the Research Training Group, which made my PhD time both fun and educational. I also miss the freedom to organize my schedule and plan my research work.

What I miss about my work in the Research Training Group is that I was able to organize my work very freely at any time and pursue my own interests. It was fun to be able to dive so deeply into a topic. It is also exciting to work in an international environment with such great colleagues. I do not miss the rainy weather in Aachen.

I had a great time and the chance to meet new people with whom I can talk about math and share my everyday problems. I also miss a lovely coordinator with an always open ear for the everyday problems of the doctoral students. I do not miss the pressure to publish and accomplish as much as possible in order to maybe obtain a permanent position some day. I also absolutely do not miss having exams, the personal perception of my work getting graded and a hierarchy with supervisors on whom I am dependent.

What I miss specifically about the research training group in Aachen is the kind atmosphere among all (post-)doctoral students involved. In particular, one could always find someone to discuss or bounce off mathematical ideas and it always felt like people try to help each other and try to lift each other up. Beyond mathematical questions we usually also discussed unrelated topics during our early morning coffee breaks.

The thing I have always missed is the friendly environment in the institute. All our offices are close to each other, and we often gather in the kitchen talking about academic or non-academic stuff. This is what I have never had since leaving RWTH.

I mostly miss the absence of any bureaucratic duty. This permits to completely focus on your research project with no time limitation. What I do not miss is having a non-permanent job.

I miss the city of Aachen, my friends, my colleagues, and the open atmosphere at the institute where I did my Ph.D. I do not miss the rainy weather in Aachen.

Do miss: the freedom to work on research questions that are of personal interest, working together with other Ph.D. students/colleagues at the institute (the special university working atmosphere), working with LaTeX, international collaborations. Not Miss: the (implicit) pressure to publish, correcting exams.

I really appreciated my postdoc at RWTH. It was very rich from the scientific point of view (discussions and work with professors, seminars, workshops and conferences) and the university offers really good working conditions. I do not miss the weather.

I miss being able to decide relatively freely and without any financial pressure what I spend my time on. I also miss larger periods of time in which I can work concentrated and without major disturbances. I do not miss grading the exams and the self-imposed stress to work outside of office hours. I definitely do not miss the uncertainty and lack of security that come with a non-tenured position.

I really miss the regular lectures that were organized by the institution. It helps to be updated about new trends within your research area. At the same time, it helps to make new contacts. I miss the time where I had more freedom and independence in research activities.

The opportunity to focus deeply on a single research project. Currently, I have to do quite a bit of context switching in my work, so I miss having a primary topic to focus on for extended periods of time.

Surprisingly, I miss rather minor things. The freedom academia offers in everyday life; the involvement with complex and kind of important scientific topics; the possibility to meet and communicate with interesting, original people. I definitely miss teaching. I do not miss the isolation during my graduate years. I do not miss the knowledge that everything I was doing during my doctoral studies was making a huge impact on my future career in academia, for which, in turn, there is only one option — to get a tenure in 10-15 years. I do not miss the constant feeling that nobody except for me was interested in what I was doing and that the work I was doing may not be good enough.

I miss the camaraderie and family feel environment with the group. I remember that we went tree-climbing my first semester in the group. It was fun and we got to know each other. Even though I don’t speak German, I always felt comfortable and was helped along the way.

A lot of my graduate education is important for my current position in academia. I have continued working on my graduate research topic, and all that I learnt then comes in handy. Besides this the opportunities to be a teaching assistant, presenting at conferences, etc. have improved my presentation skills and are helpful in my current teaching duties.

I now work in industry. In doing so, I use many skills that I learned during my graduate education. I can quickly familiarize myself with papers/documentation, can hold technical discussions at a high level of abstraction and understand complex systems in a structured manner.

The most important ability for my current job is not of scientific nature but rather to develop the right mindset for solving problems, staying focussed and not getting frustrated when things don’t work out right away.

Since I am still working in academia many aspects of my doctoral studies are relevant for my current work. My current work is closely tied to the topic of my doctoral thesis so that all the concepts I learned in books and research papers during my doctoral studies are highly relevant now. Some other concepts which I learned by visiting lectures during my doctoral studies as well as learning from colleagues during our basic notions seminars (a seminar organised by us (post-)doctoral students among ourselves) now became relevant as well. Other topics which I learned about but did not have to use yet might very well become relevant when applying for future positions in academia.

Having an academic job, I think each single part of my graduate education has been and is fundamental to my work. During the first year I attended as many graduate courses as I could to broaden as much as possible my mathematical culture. In the following years I then learned how proper research work should be done. For different reasons both periods had a big impact on my career.

It is important for me that I had a close connection to my Ph.D. advisor and could talk to him at any time. The support from other colleagues was beneficial for my work and personal development. I could learn a lot on other topics not related to my own research during the various seminar talks and from international visitors. It was also good to be integrated in the teaching duties to get in touch with students, work with other professors, and have more variety throughout my Ph.D.

Teaching: during my doctoral studies I was teaching assistant for more than 6 courses in 3 years. During the courses, I needed to lead practice sessions, prepare homework assignments, and help prepare exams. The experience was really helpful for my current position where I need to teach 5 courses every academic year. Regular presentations: during my doctoral studies I was very lucky that my advisors let me make regular presentations to them. Group meetings: we had at least 2 group meetings per week. During these meetings we discussed many current and technical problems in our research work. Many times it helped to get new insights about the problems.

Since my work is rather interdisciplinary, repeated practice in placing research in other subjects in a mathematical context has been particularly invaluable. Additionally, my research is relatively far removed from my dissertation topic, so having a broad background in several mathematical subjects that weren’t directly related to that topic has served me well.

As a Humboldt postdoctoral researcher, I did not have any teaching obligation, so I could devote all my time to my research work, including a considerable portion of time in writing computer codes. On the one hand, my codes written in Aachen were very helpful for my later research work so far; and on the other hand, my programming ability was well-trained, which may benefit me my whole career.

Of great importance are the ability and habit to work independently and judge any situation independently, to be curious and skeptical at the same time, to think clearly. The immunity to frustration and the ability to work on a problem that does not seem to give in for a long time is also important. The next most important thing is the willingness to learn new things and techniques, to explore new tools. I know no better way to acquire such skills than doing a Ph.D. — in mathematics or a similar theoretical area. When you are in the graduate school, you believe that everybody can do all the things I listed above — but no, those skills are rather hard to come by in the larger world.

In my current position I can make use of most of my research experience since I still work in the same field of application. In general, important parts of my graduate education in my job are verification and validation of codes and methods, presenting skills (oral and written) regarding complex (research) issues. Important mathematical skills are numerical optimization and statistics.

I’ve learned at RWTH new mathematical concepts that I’m still using in my current reseach.

No parts of my graduate work are important for my current work. Important are personality traits that most mathematicians share: being able to quickly master a subject, being persistent, problem solving skills, …

During my graduate studies I have interacted with professors in other subfields of PDE in my department. These interactions have broadened my perspective and have continued to enrich my work later on. In addition, the opportunities to teach I have had in graduate school have contributed to improving my teaching and communication skills.

The thing I like about my current position in academia is it allows me to work on research topics that I find interesting. I dislike that I do not get enough time for research due to teaching and related activities, administrative duties, etc.

What I like about my current position in industry is that I can continue to deal with complex issues. I also like that I can support people in their work with my skills. However, I can shape my work less freely than before.

Having found a tenured position as a professor, my current job offers most of the positive aspects of being a doctoral researcher (teaching, free allocation of time), without most of the negative aspects (uncertainty, lack of security, pressure). But the job also comes with a few new advantages (being a German civil servant, being independent and my own boss) and disadvantages (focus on teaching hence limited time for research, bureaucracy).

I like the opportunity to solve real world problems not only a handful of people in the world care about. I like the cooperation with my colleagues within the company and to share and solve problems together. I dislike having to get up early.

What I like about my current position is the warm welcoming I received and the fact that I feel that I actively contribute to new research results and am able to come up with relevant new ideas on my own. We regularly discuss the current state of affairs with my postdoc supervisor and through that we find new ways to attack problems and propel our research. What I do not like is the current ongoing Corona situation, which makes contact with other postdoctoral employees more difficult.

I’m currently working at the National University of Singapore as an assistant professor. I like it since I can still work on what I like to do. I’m still working on numerical methods for kinetic equations as I did at RWTH. Working for a university, I’m still experiencing a relatively friendly relationship among colleagues. However, as a faculty member, due to the teaching load and other obligations, I’m not able to focus only on my research work.

I basically like everything.

After my undergraduate and graduate studies, I had to leave Aachen because I needed to change my environment and get some new impulses. The changes made me aware of how convenient life in Aachen was and how different life can be. I am currently working abroad, where I get to know a different research culture. I often think back to my time in Aachen but it feels both far away and long ago.

Like: reliable working hours, close contact to research (universities and reasearch facilities). Dislike: project work, formal duties such as project management including work and time scheduling, enforcement and controlling of such plans, financial constraints “requiring” certain (positive) research results.

My current position ensures great freedom in research. Through my scientific collaborations, I can also travel regularly.

I like that I have have to deal with interesting and demanding problems, that I’m actively engaged in designing a product, and I enjoy working together with colleagues and customers. I also like that I have a secure and well-paid job where I stop working when I close the office door on my way home. I do not like the financial and time pressure that I’m put under at times and as a consequence that there are important issues that cannot be dealt with because of these restrictions.

Teaching: I teach 5 mathematics courses per academic year to massive numbers of students (more than 1000 students) who study computer science and engineering. I really like to work with students and enjoy teaching them mathematics from engineering perspective. Independence in terms of curriculum and the syllabus: I can change the curriculum and the syllabus of the mathematical subject taught. We can concentrate more on applications and concepts rather than theoretical proofs.

I have the freedom as a professor now to pursue research topics that I personally find engaging and interesting. However, this comes at the cost of additional commitments which reduce the time I get to spend on research and teaching.

I like everyday communication, I like working with other people on a joint problem. I like experiencing success a bit more often than in academia. I do not like the hierarchy and I am not very happy with the fact that I am using very little mathematics and am working on slightly outdated topics. However, I solve these problems by changing the company. :-)

My current position provides me with good resources and opportunities for research and I am also happy to contribute to the training of younger mathematicians. Sometimes, I wish there were more people in my field of research to interact with at a local level.

Firstly, enjoy your time as a doctoral student. Build connections with other researchers you meet at conferences, guests visiting for seminars. Work on your soft skills such as presentation, scientific writing, etc.

Enjoy your time at Eddy! It will probably never happen again that you can follow your own interests so freely.

Focus on doing your research, follow your ideas and don’t get distracted too much by obstacles you encounter during research and by other problems. Tackle each problem in small steps and be patient with yourself, and the results will pop up automatically. It is better to communicate too much than too little. Don’t be reserved when it comes to talking about the problems you encounter, you can save a lot of time when asking your supervisors and colleagues. They may have a helpful comment and even if they don’t, the act of discussing may already be enough to help you to solve the problem. Try to learn some programming languages and have at least one private programming project. Not only will the ability to program help you find jobs after your PhD, but the act of solving problems during programming is similar to solving mathematical problems as you split large problems into smaller and smaller subproblems until they get trivial.

Do not be too harsh on yourself in the beginning of your doctoral studies. It is normal that things take time to unfold and at times all it takes is to accidentally stumble upon a relevant research article or to have a sudden idea while going for a walk to find a solution to a problem. These things can often neither be planned nor forced. In particular during the first year of your doctoral studies you will conduct a lot of literature research and probably won’t produce many research results of your own (if any at all). This is nothing to worry about and I advise you to talk to other colleagues. Once you see that everyone has/had a hard time and shares similar feelings (during the initial phase in particular) it will make things easier for you to bear.

Value your university life. Once it’s gone, it’s gone forever!

Be curious and try, when possible, to follow your own intuition. In the long run following your ideas, even with mistakes, will make you more independent.

My advice is to make the most of the freedom during the Ph.D. time. For me this included research visits and conference travels during which I could connect to other researchers in the field and present my research. In addition, these contacts led to my current position, so it is important to think about the follow-up position early on. It helps dramatically to have a next position secure, when finishing the Ph.D. and struggling with dissertation and defense organization.

Start searching for a job at least one year before graduation/expiration date of contract. Try to establish helpful contacts during your research related work. Take career related seminars at CDS.

Stay curious and open-minded from the mathematical point of view, discuss with other students as much as possible, and of course try to enjoy the great scientific environment (seminars, doctoral courses, conferences, etc.) offered at RWTH.

Take some time to work on/understand related problems (sometimes working on another problem is just what you need to make progress with your initial task). Find someone to talk to (your advisor, a colleague, your cat, …): Some problems go away when spoken out loud. If this is not the case, your counterpart may be able to help you. For prospective doctoral students: Do not choose your subject based on financial reasons or the reputation of your advisor; choose a subject that you find exciting instead.

I would advise current doctoral students to determine sometime before they graduate if a career in academia fits their personality and overall goal in life. It is always good to have a candid conversation with Postdocs and Professors to have a good feel of what life would look like at different stages of the process.

I know that it is really difficult to find time for teaching during the doctoral studies since sometimes it is difficult to feel the importance of teaching. I would suggest them to take more teaching duties since it helps to improve many soft skills: presentation skills, team work, leadership. At the same time, it improves the technical skills as well: scientific writing, learning and explaining many theoretical topcis from practical point of view. If you would like to continue your work in academia, it is incredibly important to improve the presentation skills. I was very lucky that my advisors encouraged me to do regular presentations. The regular presentations really help to improve your abilities to explain your ideas. Sometimes it gives you some fresh ideas about your work.

Establishing connections with other researchers and coming into contact with research from a wide field of mathematics is particularly useful if one is to sustain technical expertise and research beyond the doctoral program.

Since I am not familiar with the current situation at EDDy, it’s hard to give any specific advice. If I had to give some advice to my younger self going through graduate studies, I would urge myself to talk more and not being afraid of talking more about mathematics with the fellow doctoral students (actually, not only them — with anybody interested), no matter what kind of mathematics, no matter how far away from the topic of the Ph.D. project.