Alessio Figalli receives 2024 Golden Owl

You taught Analysis I for first-year students, in a very large class of 600. What did you have to think about when you were planning lessons?

Teaching Analysis I was both challenging and rewarding. I actually reorganised the lecture script based on my own perspective on mathematics, making it easier for me to teach in a way that felt natural. This was my first time teaching such a large introductory class, so I saw a lot of fresh students who were just starting their university journey. It was amazing to witness that lightbulb moment when they understood a new concept.

What teaching methods did you use to convey the ideas from complex analysis?

For me, mathematics is all about ideas and techniques. I often start with visualisations or drawings to help students see the concepts before diving into rigorous proofs. It’s important to balance abstract thinking with clear, relatable examples. When I was studying, I also had professors who emphasised ideas over technical details, and I think that balance made a lasting impression on me.

This was the first time that Analysis I was taught in English at ETH. How did that transition go?

I was a bit cautious about it, so I frequently checked in with students to ensure they were comfortable with English. Most of them actually preferred it, especially the students from Italian and French-speaking regions in Switzerland. We also provided exercise groups in different languages, and I offered the exam in both English and German.

During the breaks and after the lecture, you made yourself available to answer students’ questions. What advice did you give them?

I often stayed more than half an hour after lectures to answer questions. And I also strongly encouraged them to come along to the exercise groups. At the start of a course, it’s easy for students to feel overwhelmed, so I encouraged them to learn by working through exercises. With practice and time, they gradually improve. My goal was for all students to build confidence and be able to tackle problems by the end of the semester.

You made an unusual decision regarding lecture recordings. Can you tell us about that?

Yes, I asked the students to attend the class in person instead of watching the recordings. I even went so far as to allow access to the recordings only at the end of the semester. ETH traditionally records classes and makes them available immediately. So, there was some resistance from students at first. But I felt strongly that attending in person created a much better learning environment. Eventually, most students understood the value of being present and interacting with their peers.

Why was it a priority for you to create a welcoming environment?

I encouraged students to ask questions and emphasised that it was important for their learning progress – and also for their classmates, because students often feel hesitant or shy in large classes. But I wanted to create an atmosphere where they felt comfortable speaking up. I also introduced videos from a Respect campaign to promote inclusivity, reminding students that respect for and awareness of others are essential qualities.