braid theory

Braid theory studies the mathematical properties of how strands can intertwine without cutting or breaking. Imagine multiple strands hanging vertically that can be woven over and under each other in various patterns—these are called braids. Mathematicians analyze all possible ways to braid strands, focusing on how the patterns can be combined or transformed. This field helps understand complex entanglements in areas like knot theory, physics, and computer science, providing a systematic way to classify and study intertwined structures. Essentially, braid theory explores the mathematics behind twisting, weaving, and linking objects in a structured manner.