Recently I've been reading Naive Lie Theory by John Stillwell. In the book our aim usually concerns finding whether Lie algebras or Lie groups are simple.
I wonder what beautiful properties does a simple Lie algebra have?
Well, I've only learned linear algebra, mathematical analysis and a bit of abstract algebra, so I might expect a more amateur answer~ I think there may be other readers of the book sharing the same question. And a good answer may help us gain more motivation to learn about Lie theory~