Could anybody explain what divisors and the Riemann-Roch theorem are intuitively, motivating them, without any jargon or vagueries (i.e. using actual math), and preferably offering a nice example necessitating this stuff? I'm sure there is a nice way to explain it in an absolutely natural way, that explains why it applies to classical algebraic curves, differential forms, homology etc... without ever having to use a definition like abelian group, or vector space, i.e. only using definitions Riemann had handy. Thank you.