Algebraic Geometry and Commutative Algebra

Algebraic Geometry merges Algebra and Geometry, expanding beyond pure Algebra through geometric constructions. Grothendieck's introduction of schemes in the late 1950s transformed the field, linking it to Algebraic Number Theory. This innovative perspective led to significant advancements, including the groundbreaking proof of Fermat's Last Theorem by Wiles and Taylor, showcasing the profound impact of these concepts on modern mathematics.