I have a new mathematical hero. What a fantastic interview!
Sylvia Serfaty on mathematical research:
One of the first pieces of advice I got as I was starting my Ph.D. was from Tristan Rivière (a previous student of my adviser, Fabrice Béthuel), who told me: People think that research in math is about these big ideas, but no, you really have to start from simple, stupid computations — start again like a student and redo everything yourself. I found that this is so true.
On the nature of mathematical knowledge:
It’s really beautiful to observe, as you progress in your mathematical maturity, how everything is somehow connected. There are so many things that are related, and you keep building connections in your intellectual landscape. With experience you develop a point of view that is pretty much unique to yourself — somebody else would come at it from a different angle
I’m not super-optimistic, in terms of women in the field. I don’t think it’s a problem that is going to naturally resolve itself. The numbers over the last 20 years are not a great improvement, sometimes even decreasing.
We prove theorems because there is an audience to communicate it to.
There is a lot of ego in this profession, let’s be honest.