This is why affine schemes as a thing never really took off until Grothendieck, despite Noether and Krull noting some of their interesting properties decades be

This is why affine schemes as a thing never really took off until Grothendieck, despite Noether and Krull noting some of their interesting properties decades before. If you're just using affine schemes you don't get anything you don't get just by doing commutative algebra. However, once you start gluing affine schemes together, you start getting things that represent functors you can't represent if you're working over the category of commutative rings alone.