Mathematical Knot Theory

Mathematical Knot Theory is a branch of mathematics that studies knots as closed loops in three-dimensional space, like tangled strings with the ends joined. It examines how these knots can be deformed without cutting or passing strands through each other, identifying when different knots are essentially the same or different. The goal is to classify and understand the properties of knots, which has applications in fields like biology (DNA tangles), chemistry (molecular structures), and physics. It’s a way to analyze complex entanglements through rigorous mathematical tools, revealing patterns and invariants that distinguish one knot from another.