Mathematics of string theory

String theory is a theoretical framework in physics that suggests the fundamental building blocks of the universe are not point-like particles, but tiny, vibrating strings. The vibrations of these strings determine the properties of particles, such as mass and charge. Mathematically, string theory requires extra dimensions beyond the familiar three of space and one of time—often proposing 10 or 11 dimensions. These dimensions are compactified, meaning they are curled up and not easily observable. The mathematics involved includes advanced concepts from geometry and topology, which help describe how strings interact and the shape of the universe at a fundamental level.