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Interview with Jürgen Jost

29 November 2023
This is our sixth interview in the interview series of the outreach committee conducted by Raffaella Mulas.

Jürgen Jost is a Professor of Mathematics and Director of the Max Planck Institute for Mathematics in the Sciences (MPI-MiS) in Leipzig, Germany, and an External Professor at the Santa Fe Institute in New Mexico, USA. He was born in Münster, Germany, in 1956. He studied mathematics, physics, economics and philosophy at the University of Bonn from 1975 to 1980, and in 1980 he also completed his PhD in mathematics at the same university. He has held various postdoctoral and visiting positions at IAS Princeton, UC San Diego, ANU Canberra, MSRI Berkeley, Harvard, ETH Zürich and IHES Paris. From 1984 to 1996 he was Professor of Mathematics at the Ruhr University Bochum, and in 1996 he moved to Leipzig, where together with Eberhard Zeidler and Stefan Müller, he founded the MPI-MiS. To date, Jürgen Jost has written more than 600 research articles and more than 20 books, spanning many different areas of mathematics and applied sciences, as well as philosophy and history of science.

Raffaella Mulas (one of Jürgen Jost's former PhD students) interviewed him in November 2023, during his visit at VU Amsterdam.

Thank you, Jürgen, for agreeing to do this interview! I would like to start with an unusual question. Of course, you know that the Erdős number of a researcher is the distance from Paul Erdős in terms of research collaborations. And you might also know that the Bacon number of an actor is the distance from Kevin Bacon in terms of acting collaborations. One then defines the Erdős–Bacon number as the sum of a person's Erdős number and Bacon number. Do you know what your Erdős–Bacon number is?

Well, I think that my Erdős number is three. I don't know what my Bacon number is, but it's probably low because I recently acted together with Hanns Zischler, who is a well-known German actor.

This is exactly what I wanted to talk about! I have checked it, and because of your collaboration with Hanns Zischler, also your Bacon number is three. So you have Erdős–Bacon number six, which is exceptionally low.

Haha, thank you! Very interesting information that I am learning from this interview!

Can you tell me something about this theater play?

Well, it originated when Hanns Zischler at  the Academy of Science and Literature at Mainz, of which we are both members, asked me whether I would be willing to perform together with him in a play that he had seen and translated into German. The play was about how John von Neumann, after his death, had a meeting with God and asked many questions but ended up arguing because God did not provide satisfactory answers. I said yes to Hanns, but when I asked him to send me the script and  looked at it, I found that while the basic idea was very good, the details needed a lot of rewriting. So, I kept the original idea of the plot, but otherwise I completely rewrote the piece. It turned out that Hanns liked my version, and we decided to perform it! I had the role of John von Neumann, and he had the role of God, which, of course, was completely appropriate for him. We first had a practice session in Leipzig, and then last June we performed the play at the Academy of Sciences and Literature, in a public event in Mainz. And it was quite well received, somewhat to my surprise because I'm not a professional actor, whereas Hanns, of course, is one of the best German actors.

I am not at all surprised that it was well received, and I hope that you will perform again in the future! Can you tell me something about your PhD? On paper, it looks like it was two-months long, but you explained to me that you actually worked on your PhD project while you were still an undergraduate student.

Yes, exactly. Well, at some point, I was undecided between pursuing a career in mathematics or economics, and I had an offer for a PhD position from a very well-established economics professor in Bonn—Wilhelm Krelle. But then I also talked to Stefan Hildebrandt, and he gave me some problems for both a diploma thesis (which corresponds to a master's thesis today) and a subsequent PhD thesis. These problems were in the field of geometric analysis, and they involved applying methods from partial differential equations to geometric problems, which at the time I found very interesting. I first looked at the diploma problem that he gave to me, but I figured out pretty quickly that this wouldn't work, and I explained that to him. He said: "Why don't you start working on the PhD topic already? This is a very interesting problem, and if you solve it, it will be quite well received by the community!". So, I looked at it, while I was still an undergraduate student, and I found out that it was easier than what he had anticipated, so I could solve it relatively quickly and I submitted it as a PhD thesis two months after submitting my diploma thesis. In fact, it could even have been slightly earlier, but in between, he was away for a sabbatical in the United States, and at that time, communication was by ordinary mail, so it was not so quick.

Now, once I was having dinner with the research group of Bernd Sturmfels, when Bernd said: "You probably all know that the Max Planck Society has three sections: the Biology and Medicine Section, the Chemistry, Physics and Technology Section, and the Human Sciences Section. But what you might not know is that, among the 25,000 people who work at the Max Planck Society, only one person is a member of all of its sections. This person is Jürgen Jost!". Another time, your collaborator Marius Gardt from the European Central Bank said to me: "Jürgen has such a deep knowledge and understanding of economics, that when I talk to him, I cannot believe that he is a mathematician!". And countless times I have heard mathematicians talking about how unbelievable it is that you have made important contributions in so many different areas of mathematics. So, my next question is: How do you do this? How can one person be so productive in so many different subjects and areas?

This is, of course, first of all, a very kind way of putting it. But over the course of my life, I have learned to systematically explore connections and relations between different fields, and that is probably my strength. I can put things that I learned in some field into perspective and translate it into a mathematical question or relate it to a question in some other field. And so, of course, this makes it relatively easy for me to work in different fields. I can analyze the conceptual structure of one field and relate it to formal structures that I may know from mathematics or from other areas.

This is very interesting! A related question is: What are you not good at?

Well, I have no talent for music, for instance! I took flute lessons when I was young, but without much success.

In mathematics, what is your creative process? How do your ideas take shape?

I don't know whether there is any general answer to that, because it depends on the particular problem. But of course, since I've explored many different fields, I know some techniques or methods from different areas that I can then bring to bear on a problem. For example, at the beginning of my career I was combining geometry and analysis, and in particular nonlinear partial differential equations and the calculus of variations. But I understood more geometry than most of the people working in analysis, and in contrast to many people who were then working in geometry, I was not afraid of applying different difficult methods from nonlinear analysis, from partial differential equations and the calculus of variations. And while other people were very good in quickly doing complicated estimates with partial differential equations, I rather tried to use some geometric imagination to understand what was behind it. So, combining different fields can make you productive because then you have access to different concepts and methods. I did this also for example when, later on, I moved to discrete mathematics. Exploring analogies between Riemannian geometry and graph theory helped me a lot to understand and address questions in discrete mathematics from a different perspective than the people who are usually working in these fields.

Is there a mathematical result you are most proud of?

I think that a very good mathematical result of mine is the existence and the control of so-called generalized harmonic maps, or equilibrium maps, between metric spaces when the target has generalized non-positive curvature. This result opened many directions, and it was also useful for looking at certain problems in algebraic geometry when it came to representations of fundamental groups in fields of non-zero characteristic. I worked on this in the 1990s with Kang Zuo, who is a very good algebraic geometer.

You will retire in 2024. What will change for you, and what will remain unchanged?

Of course, one thing that will change is that I will no longer have the possibility of having a large group of students and postdocs. Usually, I have between 30 and 40 people working with me in Leipzig, if I count students, postdocs, regular and long-term visitors. So, the group will become much smaller, but I will still have a number of PhD students and also some postdocs for some time. And I just plan to continue to work as a scientist. I have many ongoing research projects and books that I want to complete, and of course, I'm open for new scientific problems with new collaborators.

So, it sounds like, apart from the size of your group, not much will change. This is nice! What advice would you give young researchers?

It's always good to try to go into new directions that have not yet been explored so much but offer exciting questions and problems. So, my advice is: be open to new directions. Do not just  follow others and try to slightly improve the results that some great minds before you have achieved already. Try to find your own way!

This is great advice! Besides research, what makes you happy?

Clearly, my family is a great source of happiness!

Besides that, I am an outdoor person and like hiking and biking, and I also have many, many cultural interests. I read a lot of literature for instance. I have many friends who are writers or poets, and talking to them is of course very stimulating. 

Thank you so much for this very inspiring interview!