Mathematical knots are a fascinating area of study in topology, a branch of mathematics that explores the properties of space. A knot is defined as a closed loop in three-dimensional space that cannot be untangled without cutting it. Mathematicians classify knots based on their complexity and structure, using diagrams and specific notations to represent them. The study of knots has practical applications in various fields, including biology, where it helps understand the structure of DNA, and in physics, where it can model certain phenomena. Researchers also explore concepts like knot invariants, which are properties that remain unchanged under knot transformations, aiding in the classification of different knots.