The Evolution of String Theory from a Mathematical Point of View

This review paper explores the evolution of string theory from its origins in hadronic physics to its emergence as a mathematically rich framework with potential implications for fundamental physics. Beginning with the Veneziano amplitude and the dual resonance models, the narrative follows the development of worldsheet conformal field theory, the introduction of supersymmetry, and the intricate web of string dualities. Alongside these physical ideas, the paper highlights the increasing role of mathematics in shaping the theory, focusing on structures such as Lie superalgebras, Calabi-Yau manifolds, modular forms, and topological field theories. Recent developments in category theory, derived geometry, and homological mirror symmetry are presented not as formal embellishments but as conceptual tools that deepen our understanding of the theory’s internal consistency and geometric underpinnings. While the empirical foundations of string theory remain incomplete, its mathematical trajectory continues to illuminate profound connections between physics and modern geometry.