Are higher mathematics exercises mostly about proofs?

Question

Im not a math student and thus I've never studied mathematics at a high level (i just know some calculus, linear algebra and abstract algebra), most of the exercises I've done were all about computations (I'm an engineering student) and never really about proving things. Recently I've started to self study math and I've noticed that most of the exercises in textbooks are about proving things (when I studied math in college I didn't use a textbook, so this was new to me), and even googling "unsolved math problems with prizes" I noticed that many problems are about proofs. So my question is, are higher level mathematics exercises all about proofs and not really about computations (or exercises like, for what $k$ is the function differentiable? Find the solution of the equation ...)? Can you guys tell me "what is like" to study higher level mathematics? What kind of problems students have to solve?