November 02, 2022
Mathematics is a journey, first and foremost, to yourself. So, let me use this space to share helpful advice I gathered along the way.
1. There is no magic.
Great ideas are always intuitive and they are simple, ridiculously simple even. Why? We can only understand things that are obvious. It's a human law. The paradox: we first need to build the right mental representations that allow for clarity to arise naturally. This is the hard part. Hence:
2. Mathematics is about constructing strong and clear mental pictures.
3. Passer pour un idiot (original title of a chapter in "Mathematica", a book I really love).
"After having patiently listened to the speaker (the occasion: a research talk in Cambridge), Serre came to me and told me word for word "You will have to explain it to me again because I didn't understand anything." "
Extensions of the above are always welcome, as are your thoughts and comments. I wish you the best of luck and most importantly fun along the way.
Loujean is a PhD student at the University of Tübingen.