In mathematics, schemes connect the fields of algebraic geometry, commutative algebra and number theory. Schemes were introduced by Alexander Grothendieck in 1960 in his treatise Éléments de géométrie algébrique, with the aim of developing the formalism needed to solve deep problems of algebraic geometry, such as the Weil conjectures (the last of which was proved by Pierre Deligne). Schemes enlarge the notion of algebraic variety to include nilpotent elements (the equations x = 0 and x² = 0 define the same points, but different schemes), and "varieties" defined over any commutative ring.