I recently had a conversation with one mathematician who reckons that all sorts of combinatorial results are nothing compared to the things done in the algebraic geometry. As I do not have any expertise in AG, I have the following question:
Is AG really that important?
Surfing over the book of Hartshorne, one may get a feel that this is just some bunch of definitions with the hope to be able to do some big problems. First steps of AG, as far as I have been told, indeed lead to solutions, but is AG still natural, or just a trend in Maths (for producing Fields medalists).
To get things clear, I have nothing against AG, but it really got me upset that some mathematicians do not count such things as results about the random graph as Maths.