The Shape of Uncertainty

Early years: from physics to machine learning

What did you want to be as a kid?

A scientist. I have a vague memory of an art class where we had to draw ourselves in the future. Other kids drew a pop star or a football player. I drew myself in a lab coat, with glasses. For a long time I thought I'd be a chemist, because I had this picture of the lab, mixing things together, things going poof. I found that fun when I was eight or nine. As time went by I realized I was better with the abstract stuff.

Yet you started out on the experimental side of physics.

I did — until the lab courses. I had a summer internship in Heidelberg, an incredibly complicated atomic physics setup that filled rooms three times the size of this one. I spent two weeks building a tiny device to go inside it: a little coil I had to wrap by hand and glue in. Then we put it in, pulled the vacuum — that took another week — started the measurement, and discovered that my device didn't work. A short circuit, which happened while putting it in. So I spent two more weeks taking the whole thing apart again.

During those two weeks I remember telling myself: this is so stupid. I need a job where starting over doesn't have such an overhead. In theory, you can just crumple up the paper, throw it away and start again.

That led to machine learning?

Through a few detours — a master's in quantum field theory, then a year in biomedical physics, and finally, I convinced David MacKay to be my PhD advisor, because I wanted to learn about empirical inference. I didn't even think of the field I entered as “machine learning” then. It was a small niche then. The first NeurIPS I went to had 500 participants. Coming in from somewhere else was completely normal: for me, as a student of physics, it was possible to just go in there and be part of this. Geoff Hinton is a psychologist by training, right? These days it's much harder, because the competition is so insane.

Research: computation is machine learning

What is probabilistic numerics?

It's a formalism unifying information from data, and information from computations. To understand why this is needed, we have to realise that data was originally not part of scientific computation: the scientific process used to be: someone goes out into the field with a lab book. A physicist at her telescope, a biologist collecting samples — with a piece of paper, not with a computer. They come back, plot points on millimeter paper, draw a line through them, and that line becomes a law: a physicist writes down a differential equation. And now the computer comes in — you turn the equation into a simulation. The important thing is that there used to be a filter between the data and the computer: the human, who produces the equation. Of course, we have long since moved all the data right into the computer. But the algorithms for simulation are still set up for this paradigm.

And here's the twist: numerical computation is by nature an inference. Solving a differential equation, a minimization problem, a very large linear system: these are too complicated to solve exactly. You have a finite amount of computation for an infinitely complex task, so the answer is always an estimate — which is exactly the situation statistics is in with finite data. And statistics knows how to say how wrong an estimate is: a posterior, computed from a prior and the information you have. Probabilistic numerics applies that to computation itself — a solution that quantifies its own uncertainty.

Your 2022 book was subtitled Computation as Machine Learning. Your ICML tutorial this year says computation is machine learning. What changed?

Machine learning is now the dominant driver of computer science. It used to be a sub-discipline; now there is no field of computer science that is not touched by it. Which probably also means that the canonical way of thinking about what computers do should pay more attention to inference, data and learning.

And computation itself has changed. The data now comes to us on a disk, and building the model from it doesn't involve a human anymore — it's automated. Meanwhile the computations we do in ML are themselves numerical: to train a deep net you solve an optimization problem; to generate an image you solve a differential equation; for scientific inference you solve a PDE. So it makes sense to phrase the computation in the same language as the inference.

I entered this field wanting to convince the old folks, the numerical analysts, that there might be something interesting for ML to contribute to their field. Now it has reversed: the field is driven by ML, so it's more important to tell the ML people that the methods they already use can also make their computations more efficient and more reliable.

Work and life: being a professor in an uncertain age

Researcher, teacher, director — how would you describe your role?

I used to have a relatively good picture of what an academic is; that picture is now challenged by how our field is evolving. But it's still clear to me that an academic is neither an eremitic thinker nor a publicly funded entrepreneur, but a teacher first and foremost. We are the keepers of the garden of knowledge. Our central job is to help young people think straight, by handing on hard-won patterns of thought. And to find and offer new ones. Because, in contrast to school teachers, professors don't just convey a fixed canon, but also have to figure out what there even is to know. This is why research is an irreplaceable part of this job.

Is that harder in AI than in other fields?

It's an old adage that computer science is a new discipline every ten years. At the moment, though, it is changing its very nature, its mechanisms. What even is a scientific contribution in an age when the scientific process itself is increasingly automated? The machine learning I joined in my PhD was an academic discipline, like physics. Now it is increasingly an engineering discipline, a technology that can be used to empower domain scientists, as well as generate tools of economic value. But most importantly, it's rapidly also becoming the technology that “does” computer science now.

The increasing autonomy of agents obviously raises fundamental questions about what skills students of this discipline should actually know and learn. I don't think I fully know the answer yet — which is both concerning and exciting, because, as I just said, it's my job to figure this out! This will be the key question of the coming years, for academia.

What does a normal week look like now?

I rarely have a “normal week” these days. A typical day is a rapid sequence of context switches. I was lecturing this morning, then had meetings with some of my PhD students, then with the AI Center's executive office. This afternoon, I will present a proposal to the University Senate. Yesterday, I was in a phone conference with officers in the federal and state ministries, to coordinate Germany's AI strategy.

Is there something you'd want to spend more time on?

Constantly. All of the things I just mentioned are very exciting. I love teaching. I feel great responsibility for my PhD students. I want the AI Center to be successful, and of course I want to help our politicians make good decisions. Unfortunately, I can't do all things, all the time. The hardest part of my job is that I very frequently have to tell people no, or to apologize for not being able to fully meet their concerns, or that I even sometimes just forget about that one email, or that one appointment.

How do you hold it together?

I have a very structured schedule. I get up at a fixed, very early time every day, get the kids ready for school, go to work, leave at a particular time to pick up my younger daughter from school, some sports, dinner with my family, and then some more work when they sleep. I stopped having lunch completely. And I have gotten more confident to take decisions directly, rather than pondering them until I feel fully confident about the right path.

I want to be clear, though, that I'm not recommending this way to live to PhD students. This setup works for me where I am in life. In your mid-forties, the things you built earlier in life are set up, and life becomes more about maintenance. A PhD student should experiment. Try out things. Get lost in ideas, for days on end.

What do you use the time for?

At this point in my career my primary responsibility — whether as an academic teacher, as an advisor to PhD students, or as a director of the AI Center — is to make this place the perfect starting point for young people who come here with a passion for AI. I have the privilege of tenure, so I don't have to worry about myself anymore, and can think about the institution, and the students.

So what do you think the Center should deliver to undergraduates and PhD students?

While I have found my path in life, the students are here to find theirs. The better we help them in this crucial phase, the better for them, but also the better for our society and all the challenges it faces (not least from AI).

For undergraduates the main value we must deliver is raw technical knowledge — and incredibly, this is also what they clearly seek. The passion of young students for arcane knowledge is incredibly motivating to me. Every time I walk into the lecture hall, I have a short moment of disbelief that this is my job: a room much like a theatre. The door opens, and — depending on the course — between 30 and 250 people walk in, sit down, and go quiet, naturally, and wait expectantly to hear about some of the most mind-bendingly abstract stuff humanity has ever produced.

But as the students advance, especially when they become PhD students, the AI Center's task becomes to empower them as individuals taking their own path. We do this quite concretely, by providing technical infrastructure, access to compute, space to work and to grow in, even to found a company or some other venture. But we also want to be a spiritually empowering place, a community in which students feel comfortable to try out bold things. I'm very glad that my colleague Matthias Bethge shares this vision for the center.

Shouldn't professors also found startups?

Professors can play a crucial role in getting a startup off the ground initially. But a successful startup path is a wild ride over easily a decade. Most of it — building an organization, funding, hiring the right people — has little to do with the initial technology idea. And it's not something you do twenty percent on the side while teaching lectures. It's a formidable job for an amazing young person with a passion. I believe it is important for the institution to celebrate and credit these young people who dare. This doesn't mean professors shouldn't think about business opportunities or economic value creation at all, quite the contrary. But, personally, I feel that I am more effective by bringing young people to found, than by trying to do it all myself.

Community: changing generations of AI researchers

Have the students changed over the years?

The personalities have. When I joined, the field was small and niche, and the PhD students of my generation were nerds who wanted to tinker and do cool maths. Then there was a phase, around the mid 2010s, when AI was the social part of computer science: the role of data and users, the connections to psychology and neuroscience. A lot of the students I worked with then cared about social questions, and that made for a more diverse group. Then it became unquestionably clear that a lot of money could be made, and many of the very smartest, driven students in the world decided to do AI. This also made for a very competitive environment.

So what is the field like now?

We are momentarily in a paradoxical situation: every field has become perfused by AI. Materials science is now AI. Biology is now AI. Medicine is now AI. Mechanical engineering is now AI. And yet, there's a perception that there are no more good jobs for AI PhDs. Of course, these two things cannot both be true at the same time! I believe the answer is that the job profile of AI PhDs is now, very suddenly, quite different from what it used to be until very recently.

Mathematical insights are still crucial, but “coding” now means a different thing. Literature research, writing papers, implementing baselines is becoming drastically simpler, and thus a smaller part of the job. Scaling up ideas to big data and big models is much more feasible. All of this means it is now possible, and valuable, to transfer AI knowledge into other domains. This requires social and new intellectual skills, to communicate and cooperate with people from other disciplines. Eventually, this will all make the field more enjoyable. But right now it feels painful, because many of these changes are taking place on a time-scale shorter than a single PhD thesis.

My younger brother is choosing a major right now. Five years ago AI was the obvious answer; now it feels much trickier — you might be automating yourself, or automating others and being blamed for it. You've written that choosing it today takes a kind of leadership.

Yes, it seems to me that deciding to work in AI now is much less natural than it was five or six years ago, when much of the world agreed that this was the hot field to study. There's a lot to dislike about AI, the technology and its effects on society and the world economy, at the moment. I hope this means that the people who come to us now arrive with visions for change. That they want to build a technology that benefits humanity, and shares its proceeds fairly.

Ten years from now, what would make you say the Center really worked?

I hope that by then many people will have gone through this community, this building, this campus. And that they look back to their time in Tübingen fondly, feeling that this place was where they set their seeds for success, because they were surrounded by inspiring, smart, passionate, and kind people.

Afterwards: on not knowing what comes next

If you could send one line back to yourself as a PhD student, what would it be?

I would like to tell my own alter ego from more than a decade ago something that many PhD students must be told: “It's going to be fine.”

The PhD is a pivotal point in the student's life. Some PhD students need to be reminded of this, so they can make use of this unique moment. But for most, especially those used to success, the intensity of the thought can be overwhelming. I was like that as well. For those among your readers who sometimes feel like it is all a bit too much, I wish that our community, your peers and my colleagues, can help you find joy in this wild ride.

This interview was conducted in Tübingen in July 2026. It has been edited and condensed for clarity.

In June, a record-breaking heatwave hit Tübingen at the same time that a lot of us were traveling to oversea conferences. As our offices started to heat up, we started to think about personal attitudes and systemic issues around flying in academia and the climate crisis. And we wondered how our community thinks about these topics.

So we sent out a survey about flying behavior in the machine learning community in Tübingen that many of you answered! While it falls short of ready-to-be-published levels of scientific rigor (we consulted a social scientist for this, but survey methodology is of course a complex discipline…) and is not representative (both in the number and selection of people filling out this survey…), we of course wanted to share the results with you.

Thank you to Ben Schwarz and Nils Weinhardt for helping with survey design and evaluation, and of course thank all of you for completing the survey!

Overall, there does not seem to be a connection between how people feel about the climate crisis and their flying behavior. This could of course be due to the small sample size — or there is actually not much of a connection. Looking at the individual questions, the overwhelming majority of people believe that the climate crisis is an urgent problem. Moreover, many people think that they have a choice in what conferences to attend, and that individual behavior can at least have somewhat of an impact. However, flying to conferences is considered to be an important part of academia.