Knot Invariants

Knot invariants are properties or measurements used by mathematicians to distinguish and classify different knots, which are tangled loops of string. These invariants stay unchanged even if the knot is stretched or deformed without cutting or tearing. Think of them as unique fingerprints for knots—they help identify whether two knots are truly different or just look different because of how they’re twisted. Common examples include the knot’s crossing number or more complex solutions like polynomial invariants, which provide algebraic signatures to understand the knot’s structure.