This paper explores the philosophical significance of algebraic geometry by addressing Federigo Enriques' question on the relation between logic and intuition. Through a historical and conceptual analysis, it traces the transition from the Italian school of algebraic geometry to the abstract frameworks developed by Grothendieck and Lawvere. The article highlights how key categorical notions — such as schemes, sheaves, and toposes — transform the interplay between geometry and logic, allowing logical principles to be internalized within geometric structures. It argues that the philosophy of mathematics cannot be reduced to meta-mathematical reflection alone, since algebraic geometry itself generates conceptual innovations with direct philosophical import. Ultimately, the paper shows that algebraic geometry reshapes the foundations of mathematics by dissolving the separation between formal rigor and spatial intuition and providing support to the reasonable effectiveness of "conceptual mathematics". This approach not only provides an answer to Enriques' question but also defines a new sense for the foundations of mathematics, where logical principles are intrinsically linked to the geometric structure of a mathematical universe.