Masaki Kashiwara: Advice to Young Mathematicians (2025)

Thank you very much. Yeah, I think I'm supposed to speak about how I started my mathematics, but unfortunately I'm now 78 years old and when I was, so that is already 60 years ago when I was so I can't remember very well. I forgot almost all the things, but I can perhaps say something. So, as you know, there is an axiom of Euclid's axiom of plane, so there is a parallel if two lines are parallel then they don't intersect and so on. And so Euclid explained axioms, by axioms he gave some axioms and explained and developed that there is such an axiom then what holds and so that was Euclid's very old idea and unfortunately it has a gap and later, much later, I think it was Hilbert who added axioms. So what were the axioms? So there is a line then they say there are three points on the same line then there is in fact an order between among three points and so Hilbert added an axiom with respect to those orders. I can't remember the details, but so that was. So I saw it in some encyclopedia, I found, I think I was very young, so something like 10 years or 12 years old, and I thought it's very interesting and so starting from the Euclid axioms and Hilbert axioms what is possible to prove and I made the proof of many theorems derived by those axioms. So I wanted to say that so that is a very not very big things, just very small things, but to create, but there is something, so something that I mean so that although those axioms come from Euclid or Hilbert but you can create something based on those ones. So the creation is very important for mathematics, first not only in mathematics but in mathematics also, and I think that so and for young people I think it's more important than adults to create by yourself. I think that is what I want to address you, the young talented students. Okay, thank you very much.