How research works in a lab is something many can easily imagine. But what about mathematics research? What's left to explore there? And what does a typical day look like for researchers? Members of Mathematics Münster answer these and other questions - sometimes from quite different perspectives.
(Collection launched Summer 2023)
“I think the most important function of a research building is to encourage conversation between mathematical disciplines, by putting lots of people doing different things together, unexpected ideas and collaborations form.
Different mathematicians work differently. Lots of my friends never use their office, preferring to work anywhere, anytime. But for me, going to my office puts me in a thinking mood, and also draws a distinction between work and life. It makes me feel more normal.”
(2026)
“One of the most important aspects of mathematical research is the exchange with others. In a well-thought-out building you naturally meet people from different mathematical disciplines and can engage in conversation with them. Today mathematicians are very specialized in one topic, which makes this exchange with people from different backgrounds very important for progress and prevents people from getting stuck in their own research field.”
Benjamin B., postdoc (2026)
“It accelerates both the publication procedure & competition.
It helps a lot with administrative tasks.
It makes it harder to compete with universities that have cooperations with AI companies.
It makes a substantial part of my work obsolete.”
(2026)
“YES.
But only if you have no ideas whatsoever. Normally, when you can′t solve something, you must try many different directions and approaches, and it may take a long time to even come up with ideas.
But as long as you have ideas to try, it is not boring. It is only boring and scary when there are no ideas – then it helps to go work on some other problems for a while, or to learn something new. They might give you more ideas.
In the end, when you solve it, it is very satisfying and the longer it takes, the more satisfying it is.”
(2026)
“Absolutely not! It is usually the case that the problems that take a long time to solve are the hardest ones, and they can be divided into several smaller, more manageable problems. So, we are never really thinking about the exact same things, only about different approaches/solutions to some big difficult problem. It’s quite fun in fact!”
(2023)
“Eventually, but it is much more frustrating than boring most of the time.”
(2023)
“It depends on the problem. If its solution can make you famous, then it’s not boring at least for me. Of course, if one runs out of ideas, one should leave it at the back of one’s mind for a while until one gets a new input. That can take several years.”
Christopher D., professor (2023)
“Sometimes it is! But most of the time problems are so complex that they give you a lot of different aspects to think about. The same problem doesn’t look the same all the time.”
(2023)
“We live in a society where research is valued for its own sake, because it has been repeatedly demonstrated that seemingly mundane theoretical progress can become applicable to solve real-world problems.
No major first-world country can afford to stop investing in its theoretical science programs without the risk of falling behind the others. And once utility is discovered within the field (e.g. nuclear physics, cryptography) the country could face a major geopolitical disadvantage.”
M.P. (2026)
“Mathematics provides the formal language and tools for the natural sciences and engineering. Problems and ideas, for example in physics, can only be satisfactorily solved if the necessary mathematical methods exist. Research in these fields often progresses in both directions: new discoveries in physics frequently require new mathematical approaches, while properties of mathematics often lead to new insights in physics. Mathematics also delivers entirely new approaches and solutions in medicine and engineering, enabling concrete improvements in the treatment of cancer or epilepsy. Fundamental research has the potential to improve our lives!”
Pia D., doctoral researcher (2023)
“Because we strive for answers! Mathematical research enlarges our view and knowledge of math, which strengthens the base of all exact sciences.”
(2023)
“‘The unreasonable effectiveness of mathematics in the natural sciences’ is the title of an article published in 1960 by physicist E. Wigner, and it is, in essence, the motto of mathematical research. While some of us tackle and solve practical problems with immediate application to the real world, some others of us work on abstract issues whose relevance might be debated even within mathematics. In any case, we all have faith that the language of mathematical research can and will answer questions that cannot be answered (or formulated) otherwise.”
Alex T., doctoral researcher (2023)
“Computers can calculate a lot of things nowadays which has led to mathematicians having to calculate less ‘by hand’. Instead, they are focussing more on conceptual questions and proofs or program computers to do calculations. Though sometimes it can be beneficial to do some calculations by hand to get some first ideas.”
Benjamin B., postdoc (2026)
“Depends on what you mean by calculation. If you mean solving arithmetic questions or algebraic equations then yes. But a lot of different types of problems require algorithms to solve them which might be too slow to be helpful. Some computer scientists & mathematicians try to figure out what kind of problems can be solved faster so they are helpful in practical application.”
(2023)
“There are actually several theorems about the fact that computers cannot compute everything, see for example the famous ‘Halteproblem’. You can even prove that you cannot prove every true statement once your mathematical theory is ‘expressive’ enough.”
(2023)
“They can, and that’s great! But, so far, all they can do is calculate, that is, making some computations on some data and arriving at some numbers. However, they still cannot think, they can’t discern the meaningful from the meaningless, and they can’t even propose themselves new interesting problems (they lack initiative). All in all, computers are great at calculating, but mathematicians are still better at thinking.”
Diego M., postdoc (2023)
“No, they cannot; and most importantly they do not speak the language of mathematical research – which, in turn, is not the language of our everyday life. A computer may only compute what is within its limited capabilities and what we are able to translate into its (limited) language. Moreover, before asking a computer to compute something for us, we have to understand what to ask, which is often the hardest task of them all.”
Alex T., doctoral researcher (2023)
“If I gave you a game with n rules chosen from some set containing N≥n rules, there would be (N over n) distinct games to play! As the gap between N and n (and 1) increases, the number of possible games skyrockets.
In math, these games are theories or frameworks, and N is probably infinite or very large. Other times, we study the structure of the rules themselves, which might decrease n by finding an underlying subrule, or expand N.
We are also interested in understanding what N rules are ‘valid’ (and in what sense) to assume, given the context.”
M.P. (2026)
“Mathematics is its own cosmos, of which we know only a few galaxies. At school, one encounters such specific examples that it creates the impression that mathematics is something complete. However, there are plenty of problems that we are still unable to answer or solve precisely with our current knowledge and methods! As long as there are problems—whether in medicine, engineering, the natural sciences, or mathematics itself—there will always be a need for research into new approaches, methods, and concepts.”
Pia D., doctoral researcher (2023)
“Define ‘everything’!”
(2023)
“Directly: doctoral researchers & postdocs themselves, maybe following their advisor’s recommendation/guidance.
Indirectly: Editors & senior professors who referee papers & grants and thereby decide which topics are fashionable.”
Julian K., postdoc (2026)
“Depends on the level of seniority. At each level there is a degree of freedom but usually the ‘big problem’ that spawns the smaller issues we work on day to day, is chosen by the professor.
On which smaller issue to work on is freedom of the researcher.”
(2026)
“The community does (as in, we decide ourselves). We want to solve some big open problem, or maybe we want to use some technique to generalize some previous result, and then we start thinking. At some point, however, we might get onto a point we can’t solve (or don’t know how to), and then we are really interested in that. And then the community as a whole starts thinking about it, and it becomes interesting.”
(2023)
“Famous mathematicians.”
(2023)
“Read papers, write papers, chat with colleagues. Sometimes prepare talks.”
(2026)
“It depends on the stage my projects are in. Especially in the beginning I sit in front of a sheet of paper and only think about it while making a few handwritten notes. Later I sit in front of a computer to write an article. In between I attend (Zoom-) Meetings with co-authors, teach classes, go to seminars, and sometimes visit conferences. I have also started to chat with LLMs a lot, e.g. for researching literature.”
Benjamin B., postdoc (2026)
“There is a lot of sitting around and staring into the void, a lot of talking to colleagues, some reading of papers and way too much coffee.”
Simone R., doctoral researcher (2023)
“I wake up at whatever time allows me to get enough sleep, otherwise I cannot be productive. I slowly get ready and typically go to the office. I try to work for two hours in the morning and three after lunch; if it’s a good day, even more, but if the math is working against me, I’d rather stop before it makes me too sad.
A good day is any day where I did not let the difficulty of the job make me demotivated and sad; it does not matter how long I work as long as I do it every day. At some point, a good day will come and I’ll solve all my problems in thirty minutes.”
Alex T., doctoral researcher (2023)
“Putting math on blackboards is like projecting your inner thoughts and intuitions to your collaborators, in a way that they could disagree and make further changes! This is cool!”
(2026)
“Blackboards make it easy to change or correct things by just wiping it away. You can also expand diagrams and formulas in every direction if needed. Above all you can work and write on a blackboard together. All of this can′t easily be achieved with pen and paper.”
Linus K., professor (2026)
“Mathematics thrives on the exchange of ideas – formalising concepts together, drawing diagrams, and continuously refining them. Ideally, this happens dynamically. The blackboard is perfect for that!”
Pia D., doctoral researcher (2023)
“Because it is easier to visualize what you want to think about, when you write it down somewhere. At a blackboard you can easily erase mistakes you made, and you can discuss your work with colleagues more easily.”
(2023)
“Because you need to get your hands dirty sometimes.”
(2023)
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