Chance and (lack of) plans
Since 1996, Emo Welzl has been a professor at the Institute of Theoretical Computer Science. He has dedicated his career to developing and analysing combinatorial algorithms and discrete mathematics. Among other things, he has worked on algorithmic geometry and the analysis of geometric structures. As he will be retiring at the end of January, we look back on his career in this interview and learn how he found his way into theoretical computer science and what fascinates him about it.
After nearly 30 years, your time at D-INFK is slowly ending. What have you been working on as a researcher over the past decades?
When people ask me this question, I often struggle to explain what I do and what fascinates me about theoretical computer science. In conversations with laypeople, the question of the practical applications of my research inevitably arises. While an example may help them understand, for me, it's about something other than specific applications. It's about the pure joy of the abstract. The topics I explore are inherently abstract and offer countless potential applications. From my perspective, science advances through abstraction as it enables efficient comprehension and description of extensive knowledge. However, this doesn't mean that applied research is less important. But as a mathematician, certain neurons in me simply fire differently. When an application arises, I am happy about it, but it wasn't my original motivation to engage with the topic. Of course, other theorists, especially mathematicians, work at an even higher level of abstraction than I do. You can see this in the fact that I like to immerse myself in the field of geometry, where I still have something concrete and can draw or sketch something, at least in small dimensions.
Perhaps you can relate to the pleasure of solving a Sudoku puzzle. People enjoy engaging with things that are detached from practical applications. When you decipher a Sudoku, it doesn't serve an immediate purpose either. Yet, it brings joy. For a theoretician like me, it can be a fascinating challenge, for example, to explore whether the Sudoku can also be solved automatically by an algorithm. That sounds as if you can research just anything. In fact, you have to find problems and solutions that others also find important, even after many years, otherwise you won't be successful.
Can you give me an example of a change that has occurred in theoretical computer science throughout your career?
An essential development in theoretical computer science and computer science overall was the inclusion of randomisation. Randomised algorithms emerged in the early seventies, and I began my studies in 1977. A classical algorithm follows individual, clearly predefined steps to achieve a desired goal. Recipes can be considered algorithms as they provide a step-by-step sequence to cook a delicious dish. However, that is a relatively dull algorithm. More interesting algorithms have branches where a decision must be made. It's like real life when you're at a fork in the road and must decide whether to go left or right to reach your destination. A classical algorithm would stop until it has determined the correct path and only then continue its journey.
On the other hand, a randomised algorithm involves random decision-making. Instead of spending too much time thinking, it flips a coin. Through this random choice, it reaches the destination on average faster than the classical algorithm. This is also an ongoing discussion with my wife. I want to continue only when I know and have control over what comes next - so to speak, a classical algorithm. On the other hand, my wife often just continues and decides spontaneously. While I am still contemplating what to do, she has already reached the goal.
Regarding randomised algorithms, there are two categories: Some are always correct but slightly slower, while others are, on average, faster but may occasionally produce a wrong result. By accepting a certain error rate, problems can be solved more efficiently. This approach is more akin to the human approach to problems since we all make mistakes.
When did your interest and enthusiasm for mathematics begin?
This question is easier to answer. I liked mathematics even in primary school, but around the age of fifteen, I realised in retrospect that it was my true passion. Unlike other children, I spent my holidays delving into mathematical problems and found immense satisfaction in it. I am the black sheep of a family of lawyers. My parents had no particular interest in mathematics, but they never had a problem with me wanting to dedicate myself to it and recognised my talent. Looking back, I consider it fortunate to have attended a humanities-oriented high school that didn't focus exclusively on mathematics. I wasn't particularly interested in history, literature or languages at that time, but I appreciate having received a broad education.
“At some point, I realised that I had always followed my passion and never really had to make a decision.”Prof. Emo Welzl
After secondary school, you decided to pursue your passion and study technical mathematics at the Graz University of Technology. How did you come to enter the field of computer science?
Back then, computer science studies were scarce. Fortunately, during my studies, I had a professor named Hermann Maurer, who later became my doctoral advisor. He delivered captivating lectures on algorithms and formal languages. I was utterly fascinated by these recently discovered concepts. In contrast, mathematics often deals with centuries-old theories. While mathematics seemed less dynamic, computer science was characterised by constant innovation. Professor Maurer enthusiastically shared the latest breakthroughs, making me feel like I could be a part of it. It should be clarified that mathematics also undergoes changes, but I was less aware of these constant developments at the beginning of my studies.
The fact that I ended up in theoretical computer science is thanks to individuals like Hermann Maurer. He quickly noticed that a fellow student and I were interested, so we were both admitted to his research group. At some point, I realised that I had always followed my passion and never really had to make a decision. I also gave a presentation on topology during my studies, which I also enjoyed and where I was able to improve something in the work I dealt with. If this professor had recognised my interest, I might have ended up in that field.
You then obtained your doctorate under Hermann Maurer and pursued an academic path. Was it always clear that you wanted to stay in the academic world?
No, it just happened that way. I never consciously intended to obtain a doctorate, become a professor, and stay at the university. Instead, it presented itself as an opportunity to pursue what I truly enjoy.
Nowadays, it is more common for young people to have clear career goals. I didn't have specific plans back then. The field of theoretical computer science, which I was involved in, made significant advancements and was in high demand. I was fortunate to be a part of it. Perhaps it is advantageous not to constantly overthink and meticulously plan every detail of life. I still feel that one becomes best at what they are passionately interested in. However, I have also met doctoral students who had the ability to plan strategically. This form of self-discipline, though, personally suits me less.
You joined the Freie Universität Berlin in 1987 at the young age of 28 and became a professor of mathematics there. Why did you decide to move to ETH Zurich and Switzerland in 1996?
The ETH Zurich is a fantastic university that is highly regarded in Europe and internationally. I am grateful for the opportunity to come here. However, my time in Berlin has also left a positive and lasting impression on me, which was a great stroke of luck. I had the privilege of working there in a fascinating city with exceptional colleagues. However, I was still relatively young when I arrived there, and after some time, I wondered if I wanted to spend the rest of my life there. It was not about Berlin but rather my desire to experience something different.
In addition, the Swiss mentality and the mountainous landscape feel closer to an Austrian from a sentimental perspective. When we moved from Berlin to Zurich, our relatives in Linz thought we were getting closer to them. Interestingly, when comparing the distances on a map, the distance from Linz to Berlin is approximately the same as from Linz to Zurich. However, on an emotional level, Zurich feels much closer to an Austrian, which undoubtedly influenced our decision.
“I have always been fascinated by the dedication and self-reflection demonstrated by a significant number of students.”Prof. Emo Welzl
Which moment from all the years at the department will you always remember fondly?
I thoroughly enjoyed my time in Zurich and have never regretted coming here. It's not just about a single moment that I value the most, but rather a period. While I was in Berlin, we had the Graduate School "Algorithmic Discrete Mathematics", of which I was the spokesperson from 1990 to 1996. The idea for a joint Graduate School between Berlin and Zurich emerged when I came to Zurich. This gave rise to the European Graduate School "Combinatorics, Geometry, and Computation". There were times when some researchers from Berlin were here in Zurich, and we worked closely together in the offices. It created a great atmosphere, and we all really enjoyed it. Looking back, it's a time I fondly remember.
Collaborating with the doctoral students and other students in the department was also a joy for me. I have always been fascinated by the dedication and self-reflection demonstrated by a significant number of students. That's also the beauty of this job: working with curious and interested individuals.
You seem to be very committed to the success of the students. You received a Golden Owl from the Association of Students at ETH Zurich (VSETH) for your excellent teaching in November 2023. How did that come about?
Oh, that is a lovely story. Personally, I prefer to teach primarily on the whiteboard, especially in subjects like mathematics or theory, where concepts need to be developed and the details are often essential. Taking the time and letting the solutions unfold while writing on the board is valuable. The writing speed determines the pace, allowing students to absorb the material without feeling rushed. Additionally, it allows students to catch their breath while the content is erased from the board.
However, I had to adapt and create slides for my lectures due to online teaching during Covid. I thought about how to design them best and invested a lot of time. I already enjoyed creating slide sets for my scientific presentations. I enjoy the creative aspect and find it necessary to consider what is essential to include on the slide to avoid overcrowding it with text. To my surprise, I was awarded a golden owl, and the recognition highlighted the quality of my slides. In hindsight, it's a bit funny that I was praised for my slides when I actually love giving lectures on the board. That aside, I was delighted to receive the award.
“Various things that I have been doing for forty years I have now done for the very last time this year - that is sometimes quite emotional and quite surreal.”Prof. Emo Welzl
Is there anything that you will miss when you retire?
I'll let myself be surprised. I can't say that it passes me by without a trace. Various things that I have been doing for forty years I have now done for the very last time this year - that is sometimes quite emotional and that is quite surreal. But what I will miss the most, I don't know yet. If I long to give lectures in the future, I will look for opportunities to continue sharing my knowledge. And in research, retirement is often referred to as a "big sabbatical" for scientists. It allows you to relinquish all additional responsibilities and focus solely on research. When I was department head from 2016 to 2018, I had less time to research, and at that time, I was no longer sure if I was still fascinated by research and if it still worked for me. It's similar to running, where things slow down with age. But with running, you can measure and see how fast you run the 100 meters. With the mind, you can always have the illusion that it still works as well as before. Then, during my sabbatical in 2019, I was positively surprised at how well it still functioned and how much I enjoyed it. It was a great year, where I worked for six months in Vienna and Berlin and then another half year in Zurich.
What do you have planned now?
My wife and I are staying in Zurich. It's a wonderful city, as everything runs smoothly here and you have nature and the lake nearby. We have made very good friends here. Moreover, our two sons also live in Zurich. As long as they are here, there is no reason for me to even consider moving somewhere else. Now that I am retiring, it is time to think about what I want to do next. I was worried about my lack of plans for a while, but then I decided that it doesn't necessarily have to be a negative thing. Instead of jumping from one demanding activity to another, I will take a step back, relax, and see what the future holds. On one hand, it might be a bit early to retire. However, the advantage is that I am doing it at a time when I am still open to new opportunities. Perhaps I will spend more time in our garden after retirement, or maybe I will continue my research. I'll see where life takes me.