How I teach
My first student was my brother. He was three, I was ten, and I had decided that he needed to understand how maths works. It went better than you would expect. He later skipped a year and sailed through school, so either the method worked or I made him stupidly smart, and I am not sure which. I learned something too: explaining a thing to someone who does not yet know it is the most fun you can have with an idea. I have not changed my mind since.
In the years after that I taught maths tutorials, first for physicists and later for biochemists, gave guest lectures in machine learning and in Theoretical Neuroscience, ran the computational neuroscience seminar with its sessions on how to read a paper, how to write one, and how to design a figure, and supervised Bachelor’s and Master’s theses. The interactive pages on this site come from the same impulse.1 This page is about what I have come to believe along the way. Believe is a strong word. I use it because it best captures the state of my knowledge: firmly held, and incomplete.
Learning happens with your hands
I am convinced that you learn something when you do it, not when you hear about it. For science that means, to me, doing the mathematics, even though I never formally studied it. You have to force yourself to play with a question, and playing means approaching it in every form it comes in: as an equation, as a picture, as a simulation, as a limiting case, as something you try to explain to someone else. Only then do you get to trust the answer, and even then only for now. The things I trust are the things I have taken apart myself, and I keep a list of the ones I have not.
In practice this shapes how I write exercises. I compose them, in the way a musician composes a piece, with a theme, a build-up, and a place where the student has to carry the melody alone. The task is rarely “derive the result” by itself. It is “derive the result, then implement it, then find the parameter range where it stops being true.” A simulation that produces the expected figure on the first try is a reason for concern, not celebration. Finding out why the integration step was too large, or why the noise term had the wrong scaling, is where the learning happens, and I try to leave room for that instead of handing out code that already works. A slider you can move while a model runs does the same job on a smaller scale, which is why these pages exist.
Mathematics as a language, not a hurdle
Students arrive in theoretical neuroscience from biology, physics, psychology, computer science and medicine, and their comfort with mathematics varies enormously. I do not think the answer is to water the mathematics down. The answer is to always say what a symbol means in words, to connect every equation to a picture, and to be explicit about which steps are routine and which are the actual idea. An eigenvector is a direction the matrix does not rotate. A Fourier transform asks how much of each frequency is in a signal. Once that is in place, the algebra is bookkeeping, and most people can do bookkeeping once they are told that is all it is. I say this with some authority. My father is a bookkeeper in the literal sense, a Steuerberater, and there was a time when I thought I would become one too.
In the same spirit, I try never to use an idea from a previous course without saying so. Being told “you have seen this before” when you have not is one of the fastest ways to lose someone.
Confusion is where the good things come from
Behaviour is always multidimensional. The people I teach will confuse me, and I will confuse them, and I have stopped treating that as a failure of either side. Some friction is exactly what you want: it is the sign that two ways of thinking have actually met. The trick is to keep it at a useful level, enough that something new can come out of it, not so much that someone gives up. A good deal of teaching, as I now understand it, is tuning that level.
Diversity needs support, not just approval
I believe that diverse groups do better science, and the previous section is part of why. People who think differently ask different questions, notice different things in the same data, and catch each other’s blind spots. But wanting diversity is not the same as having it. A group that is open to everyone on paper and then runs on one unspoken set of habits, one way of speaking up in meetings, one idea of what a productive day looks like, will quietly lose the people it says it wants. Support has to be concrete: expectations written down, several ways to contribute and not just the loudest one, and the willingness to change how the group works when it is not working for someone.
I say this partly from the inside. I consider myself very neurodiverse. What I lack in diversity of outer appearance I make up for in inner chaos, and I have spent a good part of my career working out which structures let me do my best work and which ones get in the way. That makes me quicker to notice when a student is struggling with the format rather than the content, and more willing to change the format.
Helping each other is the point
Science is not a solo sport, whatever the authorship conventions suggest. The groups I have enjoyed most, and that produced the best work, were the ones where asking for help was normal and giving it was expected. I try to make that the default in anything I run: in exercises, where I would rather students solve a sheet together and understand it than alone and not; in the seminar, where feedback on a draft or a practice talk is something everyone gives and everyone receives; and in supervision, where I want to be asked early rather than late.
My time with you
When I supervise someone, our meetings work like office hours. The time I have reserved is yours, and you can spend it on whatever is most useful to you right now: the derivation you are stuck on, the figure that will not come out right, the question of whether a PhD is the right next step, or something that has nothing to do with the project but is getting in the way of it. I will tell you at the start how much time I have that day, so that you can decide what to spend it on. And I will say so when I do not know the answer.
One small print: I am not a licensed doctor or psychotherapist, so I can only give oral referrals. They are drawn from vast experience, some of it my own, and they come with a warm recommendation to also ask someone with an actual licence.
Outreach is teaching too
Since 2019 I have helped organise the German Neuroscience Olympiad final in Frankfurt and run its computational tutorial, and for several years I was part of the team behind the Night of Science on the Riedberg campus. Teaching a sixteen-year-old why a neuron is a leaky bucket uses exactly the same muscles as teaching a master’s student about pattern formation, just with less notation. If anything, the younger audience is less forgiving of hand-waving, and I have brought more than one explanation back from the Olympiad into my university teaching because it worked better there.
Footnotes
An impulse is, physically speaking, what it takes to overcome inertia. Inertia is also what my family name means, more or less, so I have had to deal with the pun for a while.↩︎