Miloslav Druckmüller is famous in the Czech Republic and around the world for his images of the solar corona. He considers himself an educator rather than a scientist, and the reason he has not yet retired is clear: he would be missing teaching. Students of the Faculty of Mechanical Engineering love his lectures and for five years in a row he has been voted the most popular teacher in the master's program in the annual best teacher award. What is his recipe for a successful lecture?

The first question is self-evident: What do you think makes a good educator?

It is difficult to say, a good educator can be completely different from me. Everyone has to find their own way of to how to teach well. I think the most important thing is to have good students, and I am lucky to have such students. Secondly, teaching must be entertaining, and must not be understood as a necessary evil that distracts one from their scientific work. Quite on the contrary, if I had not enjoyed teaching, I would have already retired. But I still enjoy it and I would even say that when I am tired, teaching gets me back on my feet. You also need to be yourself and do it the way that suits you best. I wouldn't be able to lecture if I had papers in my hand or the text of a lecture in front of me. To this day, I lecture only with a chalk in my hand, and if I have any materials to show to my students, I share it during e-learning, never in a lecture. But it is true that I have an advantage being a mathematician. For example, my fellow physicists would probably find it difficult to draw a spectrum on a blackboard with chalk when they want to show it.

Can you define what you enjoy most about teaching?

Interaction with students. Knowing that I am explaining to them something they didn't know before and now they can understand. I remember very well the time when I was a student myself and I really enjoyed some lectures and certain others. It was all because the teacher knew how to rise attraction of his students, so that we would all be on the same wavelength, so to speak, so that we could understand each other. I actually enjoy teaching not because it is fun, but I enjoy it when I feel that students understand and are interested.

You mentioned that every educator has to find their own way. Did you have any role models?

I remember two prominent lecturers from my college studies, but I don't copy any of them. I had a teacher who taught me probability and statistics, and he taught in a terribly messy way. He created everything on the spot and had us completely immersed in the process. At that time it seemed to me that the lecture was not well prepared, but later I found it brilliant, I was leaving the lectures with the feeling that I understood it and I did not even have to study for my exams. And then we had another lecturer, who was the complete opposite. I have never seen such a perfectly prepared lecture in my life. I didn't understand it at all during the lecture, but I made notes from which I learned and I still use these notes today. Both of them influenced me. I found out that an absolutely perfect lecture is not the key aspect, and neither is the opposite extreme.

Learning to teach is a lifelong process. Do you still remember how you started? Can you recall your first lecture?

I remember it exactly, because they just threw me into the lions' den. In 1987, when I joined the faculty, I came to work on my first day, which was a Monday, and on Tuesday they sent me to teach a lecture as a substitute for a sick colleague. It was held in an auditorium in the former premises of the Faculty of Mechanical Engineering in Jiříkovského Street, a large lecture room that was also used as a theatre hall. There was a stage and about a twelve-meter board with absolutely inadequate space in front of it. I wrote something on the board and as I backed away, I fell off the stage. So, I remember that first lecture to this day. At first, I was afraid that I would not be able to remember everything, so I was keeping my notes on the desk, but I did not use them. Later, I had notes in my briefcase leaning against the wall. And after about a year, I gained the courage to go to the classroom without any notes at all. And that's how I teach to this day.

So each of your lectures is unique because it is partly created on the spot?

Having been teaching for so many years, I try to partially invent things on the spot because it maintains my attention. And the lecture can evolve in many different ways based on the students' questions. I have to say that online learning during Covid pandemics meant pure pain for me, I missed live students terribly. I would have been happy just for a single student sitting in the lecture hall. Interaction with students is absolutely crucial, in my opinion teaching needs live students and a live teacher, otherwise it is not it.

Does it happen to you that students catch you making a mistake?

This happens very often. And I love those restless students. For me, a deadly silence in the lecture hall is a synonym for horror. It is good when students have comments or when jokes on the topic are made. I usually teach quite late in the afternoon, I often have lectures until eight o'clock in the evening when the students are tired, so I like it when there is fun in the lecture hall, it helps keep the attention.

Perhaps the highest recognition of my pedagogical work is the moment when I was finishing a problem at 7:50 p.m., my thoughts ran away and as I was writing automatically, I suddenly started to hesitate. I was not sure if I was supposed use a plus or a minus. And suddenly, from behind the room, I heard: "Minus". I turned around and there was a student sitting, to whom I immediately complimented; despite all her fatigue, she was attentive enough to know the correct solution. I probably don't have a stronger moment in my teaching life than this, I found it amazing.

What is your favourite teaching topic?

I like analysis in a complex field very much, it is one of the most beautiful mathematical disciplines. Everything in it fits together beautifully. And it is definitely the subject where my students get the best grades. I also like teaching a topic that belongs to what I "play" with most often, which is image analysis. I have a course "Numerical Methods of Image Analysis", where mathematics and hardware are intertwined: I teach how CCD cameras, CMOS cameras work... This subject is also very entertaining for my students. But I enjoy all the subjects I teach.

What do you think is beautiful about mathematics?

That is a question of definition. For example, in the 15th century, high mountains like the Alps were considered ugly, downright hideous. The reason is simple: people were afraid of them, living in them was extremely difficult, if not impossible, and for people it was synonymous with something terrible. Today, we consider the Alps beautiful and fantastic. So, you can see that it is changing and it is not possible to say objectively what is beautiful.

For me, one significant feature of mathematics is that once you get into it, discovering it becomes an amazing adventure. You do not have to go hunting lions and tigers and you will find adventure here, too. On the other hand, mathematics has one tricky property, which is that it makes a person feel insignificant. When, after five years of trying, you finally figure out how something works, you do not feel like setting off fireworks or champagne, but you rather think: "Why am I so stupid that I didn't figure it out right away, it is completely clear!". In mathematics, things are not divided into simple and complex ones. The things you understand are simple, and the things you do not understand seem hellishly complicated. So, mathematics is both beautiful and tricky.

But how to explain that a large part of the population feels about mathematics like about the aforementioned Alps in the 15th century: terrible and incomprehensible? Can we get today's children excited about mathematics?

Unfortunately, I think that high schools and elementary schools have relatively little freedom in what and how to teach. University, on the other hand, is paradise. I know what I'm talking about, my wife has been teaching at the high school all her life. We should stop managing education from above and start to believe that there are enough sane people in every school to teach children what needs to be taught. I taught my daughters, who were in their first and second grades, Gaussian elimination method. This is material taught at university, and I managed to teach it in one afternoon, and they not only understood it, but enjoyed it. Children have an excellent ability to learn, even university mathematics can be interpreted to a first-grader in such a way that it will take their breath away. But one must have a positive attitude to it and must inspire the children.