I'd just like to point out that Grothendieck's notion of a scheme is simpler and more natural than other notions that were floating around at the same time and

I'd just like to point out that Grothendieck's notion of a scheme is simpler and more natural than other notions that were floating around at the same time and attempting to capture similar ideas. Why did mathematicians seek a general formulation of geometry (in fact, schemes assign a "natural" geometric interpretation to every commutative ring)? Well, the theory of schemes, has allowed number theoretic questions to be interpreted geometrically. An important result along these lines, that was proven only after the theory of schemes was made available, is an analogue of the Riemann hypothesis for finite fields. This result was famously proven by one of Grothendieck's students (Pierre Deligne).